Araceli Lopez-Martens

Jurgen Gerl

Sandrine Christian Fink

Marie-Hélène Sigward

Kseniia Rezynkina

François Didierjean

Michael Ginsz

Vlad Marian

Andy Boston

Joa Ljungvall

Fraser Holloway

Marco Siciliano

Benoît Gall

Louise Stuttgé

Dominique Curien

Olivier Dor- Vaux

Christelle Schmitt

Mohamad Moukaddam

Kamila Sieja

Frederic Nowacki

Rodrigo Sviat

Marketa Reem

Feifei

Alex Guillaume

Robin, Clément Jean Dylan

Federica

Annabella Fabiana

Daniela Giovanni

Michele Nicla

Federico

Valentina Debora

Salvo, Ciccio, Nando Davide Simone

Teresa Chiara

Roberta Michela

Ciro

A great thank you goes to

Introduction

Despite the knowledge collected in more than one century of research, the descriptive and predictive power of nuclear physics models is wide but still limited. The nuclear structure can't be yet described by a single universal model but it is instead described by a variety of models that t the data more or less well depending in which part of the chart of the nuclides the nucleus of interest is located. In addition, the predictions of the dierent models diverge more signicantly when approaching the proton and neutron drip lines. Obviously, new data are required in order to improve the actual models and modern nuclear physics looks with particular interest to the study of nuclei under extreme conditions such as large atomic number, very large angular momentum, very neutron rich or decient isotopes and high temperatures. Such nuclei are produced in a variety of reactions such as fusion-evaporation, fusion-ssion, multi-nucleon transfer, nucleon transfer, knock-out, Coulomb excitation, etc... where the nucleus is produced in an excited state that decays nally by gamma-ray emission. The latter gives information on the structure of the residual nucleus as its level scheme can be build through gamma-ray spectroscopy. Generally, the production rates of these nuclei is several orders of magnitude smaller with respect to reactions in which stable nuclei are produced. Moreover, they are produced in large background conditions and generally at much larger recoil velocities. This calls for development, construction and exploitation of state of the art gamma-ray detectors in order to maximize the quality of the information obtainable in an experimental run.

The development of techniques for the production of GeLi detectors [START_REF] Pell | Ion Drift in an n-p Junction[END_REF][START_REF] Freck | Gamma-Ray Spectrum obtained with a Lithiumdrifted p-i-n Junction in Germanium[END_REF] in the 1960s allowed for the building of progressively thicker planar detectors (with relative eciencies of few percents). These GeLi detectors marked the birth of high-resolution gamma-ray spectroscopy but had the disadvantage of having long production times and the fact that they needed to be constantly maintained at low temperatures. The rst high purity germanium (HPGe) detectors, developed in Berkley [START_REF] Hall | High Purity Germanium for Detector Fabrication[END_REF]4] and put on the market in the late 1970s, solved both the issues. The size of these detectors grew during the following decades reaching, for a cylindrical geometry (diameter × lenght), 50 mm×50 mm during the 1980s, 70 mm × 70 mm at the beginning of the 1990s up to 80 mm × 90 mm in the current days. The size increase meant a better photopeak detection eciency of the germanium crystals. In parallel, during the mid 1970s, the rst Compton shields, composed by NaI(Tl) scintillators [START_REF] Beetz | An in-beam Ge(Li)-NaI(Tl) Compton suppression spectrometer[END_REF][START_REF] Aarts | A Compton-suppression spectrometer for gamma-gamma coincidence measurements: Large solid angle and excellent suppression[END_REF], were developed, pushing further the progress in gamma-ray spectroscopy. These shields, surrounding the HPGe detector, reduced the Compton background but because of their large size (25 cm × 20 cm ) an array could be 1 INTRODUCTION composed of only few shielded germanium crystals. It was at the beginning of the 1980s that the rst BGO scintillator detectors were used as Compton shields, implemented in HERA (high energy resolution array) at the Berkley National Laboratory [START_REF] Diamond | Proposal for a high resolution ball[END_REF][START_REF] Diamond | Proc. Conf. on Instr. for Heavy Ion Nucl. Res[END_REF]. BGO detectors are about three times more ecient per interaction length than NaI(Tl) detectors. Thus the shield size could be reduced and this allowed for the allocation of more germanium detectors into the array. Moreover HERA used the newly developed n-type coaxial detectors with ∼ 25% relative eciency 1 . These new technologies prompted during the 1980s the building of several national arrays in Canada, Denmark, France, Germany, Italy, UK, and USA. As the price of the new larger detectors rose quickly, the late 1980s and the beginning of the 1990s saw the rst international eorts to build large 4π arrays of shielded germanium detectors resulting in ESSA30, EUROGAM I and GASP in Europe and GAMMASPHERE in USA [START_REF] Sharpey-Schafer | Escape suppressed spectrometer arrays: A revolution in gamma-ray spectroscopy[END_REF][START_REF] Beausang | Measurements on prototype Ge and BGO detectors for the EUROGAM array[END_REF][START_REF] Bazzacco | Proc. Workshop on Large gamma-ray Detector Arrays[END_REF][START_REF]Gammasphere Proposal[END_REF]. These arrays were composed of large germanium crystals with relative eciencies of ∼ 70%. The next major improvement at the beginning of the 1990s consists in the assembly of four germanium detectors compacted in a single cryostat [START_REF] Duchêne | The Clover: a new generation of composite Ge detectors[END_REF], each one with a relative eciency of ∼ 21% at 1332.5 keV ( 2 ). The use of this new technology brought EUROGAM II in which 2 rings composed of 12 such detectors were added around 90 • with respect to the beam axis. This conguration granted substantial improvement for Doppler correction and allowed the measurement of linear polarization of gamma rays. In the mid 1990s, a new detector encapsulation technology was developed by IKP Cologne in collaboration with Eurisys Mesures (today MIRION Technologies). The detectors could be encased under ultra-vacuum in thin sealed aluminum canisters [START_REF] Eberth | Encapsulated Ge detectors: Development and rst tests[END_REF]. This compact design was used to build EUROBALL [START_REF] Beck | EUROBALL: Large gamma ray spectrometers through european collaborations[END_REF][START_REF]Upgrading to Euroball III[END_REF][START_REF] Simpson | The EUROBALL spectrometer[END_REF], a new European array in operation from 1996 to 2003. The backward 1π of the array was paved by 15 cluster detectors each composed by 7 large volume crystals (with a relative eciency of ∼ 60%) each in a single cryostat, surrounded by BGO shields. The rst electric segmentation of coaxial crystals was developed at the end of the 1990s. The technique was rst used on some of the GAM-MASPHERE detectors (placed around 90 • with respect to the beam axis) which were segmented in two longitudinal sectors. This allowed reduced detector angular aperture and increased the granularity of the array. The segmentation technology continued to progress and at the beginning of the 2000s, IKP and MIRION developed new 6-fold longitudinally segmented detectors which composed the MINIBALL array [START_REF] Eberth | MINIBALL A Ge detector array for radioactive ion beam facilities[END_REF][START_REF] Habs | Physics with Ge-Miniball-arrays[END_REF]. These detectors were later further segmented in a 2-fold transversal fashion (reaching 12 segments per detector). MINIBALL was one of the rst segmented detector array to be used in a radioactive ion facility (REX-ISOLDE at CERN) together with EXOGAM (SPIRAL in GANIL) and SeGa (at NSCL) [START_REF] Simpson | The EXOGAM array: A radioactive beam gamma-ray spectrometer[END_REF][START_REF] Mueller | Thirty-two-fold segmented germanium detectors to identify gamma-rays from intermediate-energy exotic beams[END_REF].

The concept of an array without Compton shield arose in the mid 1990s on both sides of Atlantic ocean and developments of prototypes for a proof of concept were performed up to 2001. The success of this R&D lead to the launch of the AGATA (Advanced 1 For a given detector, the relative eciency is dened as the ratio of its absolute eciency at 1332.5 keV when irradiated by a 60 Co source placed at 25 cm from the center of the detector front face, to the eciency of a 3" × 3" NaI irradiated in the same conditions (this reference value is 1.244 • 10 -3 ). 2 In case of multiple crystals red simultaneously, the energies released in such crystals are added up (add-back mode) and a total relative eciency of up to 130% can be reached for one clover detector. INTRODUCTION tives. In particular, the collimator diameter can now be chosen among three dierent options (1 mm, 0.5 mm and 0.2 mm) and a 152 Eu source has been acquired. The latter allows to create databases of pulses with dierent energy ranges in a single scan procedure. This new feature is unique and was never tested within the scanning tables of the AGATA collaboration. The second part of this thesis presents the results obtained by several scans of an AGATA detector unit performed with 241 Am, 137 Cs and 152 Eu sources. In particular the main aim of the measurements is to prove that, by comparing the various databases with dierent energies obtained with the PSCS technique, the pulse shapes generated by a gamma ray interaction is independent from the interaction energy. This principle, which comes from theoretical assumptions, is at the base of the above mentioned PSA algorithms.

The present PhD document is structured as follows. In the rst two chapters general knowledge on the interaction of gamma rays with the matter and on the functioning of germanium detectors are given. In the third chapter the AGATA array is presented along with the description of it's HPGe detector units. In the forth chapter the PSCS technique and the Strasbourg scanning table are described, together with some preliminary results of simulations and measurements of the gamma-ray beam irradiating from the collimated sources. In the fth chapter details on the simulation methods and on the general analysis are provided. Chapter six describes the results of the simulation on the PSCS technique implemented for the IPHC scanning table. Simulations of both a planar and an AGATA detector unit are presented and several conclusions are drawn. Finally, chapter seven contains the results of real scans performed on an AGATA detector unit. Both two-dimensional and three-dimensional scans with the 241 Am, 137 Cs and 152 Eu sources are shown, analyzed and compared, and several conclusions are drawn and perspectives are suggested.

Chapter 1

Interaction of gamma rays with matter

Gamma rays interact with matter through several mechanisms, although only three major ones play an important role for detection purposes: photoelectric absorption (or photoelectric eect), Compton scattering and pair production. Photoelectric absorption dominates at low energy for gamma rays with up to few hundred keV, while pair production predominates at high energies (above 5 10 MeV ). In the range between this two Photon absorption cross section for germanium with the various contributions to the total cross section. Data from [START_REF]NIST XCOM photon cross sections database[END_REF].

CHAPTER 1. INTERACTION OF GAMMA RAYS WITH MATTER

energy limits Compton eect is the most probable mechanism (see gure 1.1). Atomic number Z of the interaction medium also has a strong inuence on the relative probabilities of these three interactions; for example, photoelectric absorption probability varies approximately as Z 4.5 . All of these processes, as it will be shown, lead to the partial or complete transfer of the photon energy to one electron, which lead to two features: gamma rays are many times more penetrating in matter than charged particles with the same energy and beams of photons are not degraded in energy as they pass through the matter, but only attenuated in intensity. The rst feature is due to the much smaller cross section of the interaction processes relative to the inelastic electron collision cross section that characterizes charged particles. The second feature, however, is due to the fact that the described processes remove the photon from the beam entirely, either by absorption or scattering, while the photons which pass straight through are those which have not suered any interaction at all. Detection of gamma rays is therefore critically dependent on the mechanism causing transfer of all or part of the photon energy to an electron in the absorbing material. In the present chapter the interaction mechanism listed previously will be briey reviewed along with the respective expected response of a generic gamma-ray detector.

Photoelectric absorption

Photoelectric absorption is an interaction in which an incident gamma ray interacts with an absorber atom disappearing completely. In its place, an energetic photoelectron is produced from one of the electron shells of the absorber atom with a kinetic energy given by the incident photon energy hν minus the binding energy of the electron in its original shell (E b ) as shown in the gure 1.2. The interaction is with the atom as a whole and cannot take place with free electrons; as result of conservation laws, the atom recoils in this process, but its recoil energy is very small and usually neglected. For typical gamma-ray energies, the photoelectron is most likely to emerge from the K shell, for which typical binding energies range from a few keV for low-Z materials to tens of keV for materials with higher atomic number. The interacting atom is left in an excited state. It inherits a surplus of energy equal to the binding energy of the expelled electron. It will then return this energy by emitting characteristic X-rays due to the rearrangement of its structure, were higher shells electrons ll the vacancies in the lower shells. These X-rays will be generally reabsorbed through new photoelectric interactions. If the electron and the X-ray are detected, then the sum of their energy is equal to the original energy of the incident gamma ray.

COMPTON SCATTERING

The photoelectric process is predominant for gamma rays of relatively low energy, typically below 130 keV for Ge (gure 1.1). The process is also enhanced for absorber materials of high atomic number Z. No analytic expression is valid for the probability of photoelectric absorption per atom (τ ) over all ranges of E γ and Z, but a rough approximation is

τ ∼ = const. × Z n E 3.5 γ
where the exponent n varies between 4 and 5 over the gamma-ray energy region of interest.

Compton scattering

The interaction process of Compton scattering takes place when a gamma ray strikes a weakly bound electron in the absorbing material. The result of the interaction is the creation of a recoil electron and a scattered gamma ray, with the division of energy between the two dependent on the scattering angle (gure 1.3). The energy hν of the scattered gamma ray in terms of its scattering angle θ is given by hν = hν 1 + (hν/m 0 c 2 )(1 -cos θ) (1.1) where m 0 c 2 is the mass energy at rest of the electron (0.511 M eV ). The kinetic energy of the recoil electron is therefore E e -= hν -hν = hν (hν/m 0 c 2 )(1 -cos θ) 1 + (hν/m 0 c 2 )(1 -cos θ) (1.2) Two extreme cases can be identied when θ ≈ 0 and θ ≈ π. In the rst case equations 1.1 and 1.2 predict that hν ≈ hν and E e -≈ 0, meaning the Compton electron has very little energy and the scattered gamma ray has nearly the same energy as before the interaction. In the second case the gamma ray is subjected at a head on collision in which it is back scattered toward its direction of origin, whereas the electron recoils along the direction of incidence and maximum energy is transferred. The Compton edge corresponds to θ = π. Ec is the energy dierence between the actual incident gamma-ray energy and the Compton edge. From [START_REF] Knoll | Radiation detection and measurement[END_REF].

The cross section for Compton scattering was one of the rst to be calculated using quantum electrodynamics and is known as the Klein-Nishina formula. For an unpolarized gamma ray it can be written as 2 1 + cos 2 θ + γ 2 (1 -cos θ) 2 1 + γ(1 -cos θ) (1.4) where r e is the classical electron radius and γ = hν/m 0 c 2 . The distribution is shown graphically in g. 1.5 and illustrates the strong tendency for forward scattering for large values of the gamma-ray energies (E γ ≥ 511 keV ).

dσ dΩ = Z r 2 e 2 1 [1 + γ(1 -cos θ)]

Coherent scattering

Related to Compton scattering is the classical process of Rayleigh scattering where the photons are scattered by atoms as a whole. In this process, all the electrons in the atom participate in a coherent manner, thus the name coherent scattering. The scattering is characterized by the fact that no energy is transfered to the medium. The atoms are neither excited nor ionized and only the direction of the photon is changed. The probability of coherent scattering is signicant only for low photon energies (typically below a few hundred keV for common materials).

Pair production

The process of pair production involves the transformation of a photon into a electronproton pair. In order to conserve momentum, this can only occur in the presence of Figure 1.5: A polar plot of the number of gamma rays (incident from the left) Compton scattered into a unit solid angle at the scattering angle θ (in degrees).

the intense electric eld of a target nucleus. To create an electron-positron pair, an energy of 2m 0 c 2 is required, thus the incident gamma ray must have at least an energy of 1.02 M eV in order that the process is energetically possible. If the incident gamma ray exceeds this value, the excess energy appears in the form of kinetic energy E e -and E e + shared by the pair of particles. One has E e -+ E e + = hν -2m 0 c 2

The electron and the positron travel in the medium before loosing all their energy (a few millimeters for germanium). The shape of the distribution in energy from a monochromatic beam of gamma rays is then, again, a delta function whose peak is 2m 0 c 2 below the actual incident gamma-ray energy (as shown in gure 1.6). However, Figure 1.6: Schematic spectrum of pair-production event. The peak of the distribution (a delta function) is shifted by 2m0c 2 from the actual energy of the interacting gamma ray due to the energy required to create the electron-positron pair. From [START_REF] Knoll | Radiation detection and measurement[END_REF].

the pair-production process is complicated by the fact that the positron is not a stable 10 CHAPTER 1. INTERACTION OF GAMMA RAYS WITH MATTER particle. Once it's kinetic energy becomes very low (thermal energy), the positron will annihilate or combine with an electron in the absorbing medium. The particles are then replaced by two annihilation photons of energy m 0 c 2 (0.511 M eV ) each. The time required for the positron to slow down and annihilate is so that the annihilation radiation appears in virtual coincidence with the original pair-production interaction.

The magnitude of probability of pair production per nucleus varies approximately as the square of the absorber atomic number and it raises sharply with energy as indicated in gure 1.1. Finally gure 1.7 shows the relative importance of each of the three processes described above for dierent absorber materials and gamma-ray energies.

Figure 1.7: Relative importance of the three major types of gamma-ray interaction. The lines show the values of Z and hν for which the occurrence probability of two neighboring eects are just equal. From [START_REF] Knoll | Radiation detection and measurement[END_REF].

Predicted response to gamma rays

If all the considerations done previously are taken into account, one can predict the response function for a typical, medium-sized, gamma-ray detector hit by a monochromatic beam. The possible outcomes of a gamma ray entering the detector are shown in gure 1.8. If the energy of a gamma ray of the incident beam is in the low or medium range (where pair production is not signicant) the predicted spectrum will show a Compton continuum and a photopeak. The Compton continuum is populated by all those gamma rays that undergo single or multiple Compton scattering before escaping the detector. These gamma rays populate also the region between the photopeak and the Compton edge (see gure 1.4). The photopeak has contributions both from gamma rays that are absorbed by photoelectric absorption and from gamma rays that undergo multiple Compton scattering, losing energy at each interaction, before getting absorbed.

The ratio between the two areas depends on the energy of the incident beam and the size of the detector. The lower the incident gamma-ray energy, the lower will be the average energy of a Compton scattered photon and the corresponding average distance of migration. Thus the probability for a gamma ray to get absorbed and the relative area under the photopeak increase with decreasing incident photon energy. At very low energies (E < 100 keV ) the Compton continuum may eectively disappear. If the gamma-ray energy is high enough to make pair production signicant, a more complicated situation prevails. The annihilation photons may either escape or undergo further interactions within the detector. These additional interactions may lead to either partial or full-energy absorption of either one or both of the annihilation photons.

If both annihilation photons escape without interaction, only the electron and positron kinetic energies are deposited. The net eect is to add a double escape peak to the spectrum located at an energy 2m 0 c 2 (1.02 M eV ) below the photopeak. Another relatively frequent occurrence is the escaping of one annihilation photon while the other is totally absorbed. These events contribute to a single escape peak, which now appears in the spectrum at an energy m 0 c 2 (0.511 M eV ) below the photopeak. A continuous range of other possibilities exists in which one or both of the annihilation photons are partially converted to electron energy through Compton scattering and subsequent escape of the scattered photon. Such events accumulate in a broad continuum in the pulse height spectrum lying between the double escape peak and the photopeak.

As nal remark one should note that the response function to be expected for a real CHAPTER 1. INTERACTION OF GAMMA RAYS WITH MATTER gamma-ray detector will depend on the size, shape and composition of the detector, and also the geometric details of the irradiation conditions. In general, the response function is too complicated to predict in detail other than through the use of Monte Carlo calculations, which simulate the histories actually taking place in a detector of the same size and composition.

Gamma-ray attenuation

As it was written in the introduction to this chapter, gamma rays are not degraded in energy as they pass through the matter, they get attenuated only in intensity. The sum of the probabilities of occurrence per unit path length that a gamma ray is removed from the beam hitting an absorber is called linear attenuation coecient µ = τ photoelectric + σ Compton + κ pair (1.5) It corresponds to the inverse of the mean free path of the photon λ = 1 µ . The number of transmitted photons I with respect to the initial number of photons I 0 is then

I I 0 = e -µx (1.6)
where x is the length of matter passed through.

x Figure 1.9: Transmission ratio of gamma rays in germanium as a function of the length of matter passed through for various energies. Data from [START_REF]NIST XCOM photon cross sections database[END_REF].

As it will be shown later, the majority of the measurements done during the study presented here were performed using gamma-ray beams emitted by sources of 241 Am, 137 Cs and 152 Eu. For these sources the transmission ratios in germanium is shown in gure 1.9. The 241 Am gamma rays and the lowest energy gamma rays of the 152 Eu are absorbed by the rst layers of germanium. This two sources can be used to study eects on the surface of the germanium detector. 137 Cs gamma ray and high energy 1.5. GAMMA-RAY ATTENUATION 13 gamma rays of the 152 Eu, instead, can travel several cm into the germanium without interacting.

Chapter 2

Semiconductors and HPGe detectors

Semiconductor detectors, or solid-state detectors, are based on crystalline semiconductor materials, most notably silicon and germanium. Their operating principle consists in the fact that an ionizing radiation creates electron-hole pairs that are then moved under the eect of an electric eld, generating a signal on the electrodes of the detector. Among the advantages of semiconductor detectors one can count the small energy required to create an electron-hole pair (2.96 eV in Germanium at the operational temperature of 77 K), a good energy resolution (∼ 2 keV FWHM at 1 M eV ), the rather fast time response (∼ 7 ns response for 60 Co and rise times of ∼ 150 to 400 ns) and their compact size. For these reasons semiconductor detectors are often chosen for high precision gamma-ray spectroscopy, especially germanium that is preferred to silicon for his higher Z which guaranties a larger interaction cross-section for gamma rays. The above mentioned advantages are counterbalanced by the fact that, being crystalline materials, they have a greater sensitivity to radiation damage which limits their long term use. Also, and this is true for germanium detectors, they operate at very low temperature (generally liquid nitrogen temperature, 77 K) which implies the usage and maintenance of an additional cryogenic system.

In the following chapter a brief review of semiconductor properties and operations will be presented. Germanium crystals will be used as main reference since they play a main role in the present work.

Band structure in semiconductors

The electrons of a perfect crystalline solid occupy the energy states in well established intervals called allowed energy bands. The energy bands are regions populated by many discrete levels so closely spaced that they can be considered as a continuum. The band structure arises from the overlapping of the electron wavefunctions caused by the close and periodic arrangement of the atoms of the crystal; since the Pauli principle forbids more than one electron in the same state, the degeneracy in the outer atomic shell energy 16 CHAPTER 2. SEMICONDUCTORS AND HPGE DETECTORS levels breaks to form many discrete levels slightly separated from each other. In between two allowed energy bands lay the forbidden energy gap which is a region in which levels are not available. The size of the energy gap determines whether the material is classied as an insulator, a conductor (metal ) or a semiconductor (see gure 2.1). In an insulator at normal temperatures, all the electrons are in the valence band and the thermal energy is insucient to excite electrons across the gap. When an external eld is applied to the medium there is no movement of electrons and thus no current. For a conductor, on the contrary, there is no gap between the two bands. The thermally excited electrons can jump easily in the conduction band where they are free to move in the crystal. When an electric eld is applied a current ows through the medium. Finally, in a semiconductor, the gap size is intermediate between the two above mentioned cases. At room temperature, electrons are excited into the conduction band by thermal energy and when an electric eld is applied, a current can be observed 1 . If the semiconductor is cooled down, the electrons will fall into the valence band and the conductivity of the semiconductor will decrease. 1 In some semiconductors devices a current can ow even without an external voltage. For example, it is the case of thin CMOS detectors, where the charges drift for a very short distance (few tens of microns).

CHARGE CARRIERS 17 2.2 Charge carriers

Germanium has four valence electrons, all participating in four covalent bonds. At a temperature of 0 K all bonds are in the lowest energy state of the semiconductor (see gure 2.2a). At room temperature, however, a valence electron can pass to the conduction band by the action of the thermal energy. This event will leave a hole in the original position of the electron. At this point a neighboring valence electron can easily jump from its site to ll the hole, leaving another hole in its original position. If this process is repeated with another neighboring electron and so on, one can state that the hole is moving through the crystal. Since the hole is positive relative to the sea of negative electrons in the valence band, one can consider the hole as a positive charge carrier. In a semiconductor, thus, the electric current arises from two sources that are the movement of free electrons in the conduction band and the movement of holes in the valence band.

n i = AT 3/2 exp -E g 2kT (2.1)
where A is a constant independent of the temperature. A typical value of n i for germanium at T = 300 K is of the order of 2.5 × 10 13 cm -3 which, related to the density of the crystal of 10 22 atoms/cm 3 , means that only 1 in 10 9 germanium atoms is ionized, leading to a very low concentration of charge carriers.

Charge mobility

If a low-to-moderate electric eld is externally applied to the semiconductor, and the dierence in temperature between electrons or holes and the lattice is not excessive, the drift velocity of the electrons and holes can be written as

v e = µ e E v h = µ h E (2.2)
where E is the intensity of the electrical eld and µ e and µ h are the mobilities of the electron and holes, respectively. For a given material, the velocities are function of E and the temperature T (see When the temperature of the charge carriers rises above the temperature of the lattice, the electron drift velocity will not be parallel to the applied electrical eld but will be inuenced and determined by the crystal lattice orientation. Germanium has a Face Centered Cubic (FCC) lattice structure and Cartesian coordinates can be used to dene the lattice axes (or planes). In the gure 2.2b the three crystallographic axes 1, 0, 0 , 1, 1, 0 and 1, 1, 1 are shown. Along the three crystallographic directions

Si Ge

Dielectric Constant (relative) From [START_REF] Knoll | Radiation detection and measurement[END_REF]. (b)Drift velocity in germanium along the three main crystallographic axes as a function of the electrical eld. From [START_REF] Milhailescu | Principles and Methods for gamma ray tracking with large volume Germanium Detectors[END_REF] and references therein.

Impurities and doping of the crystal

In section 2.2 it was mentioned that electrons and holes can recombine. In a perfect crystal this process is very rare and electron-hole pairs show lifetimes of the order of seconds. However, experimentally it is shown that charge carrier have a lifetime ranging from nanoseconds to hundreds of microseconds. This means that impurities that work as recombination centers (or trapping centers) are present even in the purest of the crystals.

These elements perturb the energy band structure by adding additional levels in the forbidden energy gap. These states can capture an electron (hole) from the conduction (valence) band and than one of the following things may happen: after a certain time the electron (hole) is released back in the conduction (valence) band or during holding CHAPTER 2. SEMICONDUCTORS AND HPGE DETECTORS time the impurity captures a hole (electron) which annihilates with the trapped electron (hole). The presence of impurities reduces the mean time in which charge carriers remain free and thus some of the charges will be lost during charge collection. This worsen the energy resolution of the semiconductor which is a major problem for radiation detection. If the dopant is pentavalent (donor dopant), the electrons ll up the valence band and the extra electron, since there is no place to t in the band, will reside in a discrete energy level located in the energy gap which is very close to the conduction band. Unlike a trapping state, this level will enhance the conductivity of the semiconductor because at normal temperatures an electron will be more easily excited into the conduction band.

In these semiconductors, electrons are the primary charge carriers and they are called n-type semiconductors.

Vice versa, if the dopant is trivalent (acceptor dopant) there will be not enough electrons to ll the valence band and there will be an excess of holes in the crystal. Now the additional level will be placed close to the valence band and electrons will be easily excited into this level leaving extra holes behind. In these semiconductors, holes are the 2.5. THE PN SEMICONDUCTOR JUNCTION 21 primary charge carriers and they are called p-type semiconductors.

The pn semiconductor junction

If a semiconductor possesses one p-type region in contact with a n-type region a so called pn junction is formed. This special zone is created at the interface between the two materials (see gure 2.5) where the dierence in concentration of electrons and holes between them generates a drift of electrons towards the p-region and a drift of holes towards the n-region. As a consequence the diusing electrons ll up holes in the p-region while the diusing holes capture electrons on the n-side. This recombination of charges causes a charge build-up to occur on either side of the junction; the p-region becomes negative while the n-region becomes positive. This creates an electric-eld gradient across the junction which will eventually stops the diusion process leaving a region of xed space charge. The potential dierence across the junction is called contact potential (which is generally of the order of 1 V ). The region of changing potential is known as depletion zone (space charge region). It is devoid of all the mobile charge carriers. This region is of particular interest for radiation detection because any electron or hole generated in this zone, say by an interacting gamma ray, will be dragged out by the electric eld. If electrical contacts are placed on the end of the junctions, it is possible to collect the resulting current which intensity is proportional to the ionization (thus to the energy of the incident gamma ray).

However, the pn junction as described above does not work at its best. In fact, the intrinsic electric eld is too weak to provide ecient charge collection and the depletion zone is too thin (of the order of few microns) to stop high energy particles. A third negative eect also arises from the fact that the small thickness present a large capacitance that interacts with the detector electronics generating noise on the output signals. A way to improve the junction is to apply a reverse-bias voltage to the junction, i.e. a negative voltage to the p-side, as shown in gure 2.6. This voltage will attract holes in the p-region and electrons in the n-region towards the contacts and far away from the junction. Consequently, the depletion zone will expand enlarging the sensitive volume for radiation detection.

The thickness of the depletion zone is given by the equation

d = 2 V eN 1/2 (2.3)
where V is the reverse bias voltage and N is the net impurity concentration in the bulk semiconductor material, is the dielectric constant and e is the electronic charge 2 .

The maximum voltage that can be applied to the junction, however, is limited by the resistance of the semiconductor; once a threshold is crossed, the junction will breakdown and the semiconductor will behave as a conductor. 2 In reality the depletion zone has soft edges. If this is taken into account, the exponent in equation 2.3 can be replaced with an empirical factor α that varies between 1/2 and 1/3.

CHAPTER 2. SEMICONDUCTORS AND HPGE DETECTORS

HPGe detectors

The two most common semiconductors used for radiation detection are silicon and germanium. Between the two, germanium is generally preferred for gamma-ray spectroscopy. Two advantages lead to this. The rst reason is that the higher atomic number of germanium (Z Ge = 32 compared to Z Si = 14) leads to a much higher cross section for gamma-ray interactions (see section 1.1). The second reason is linked to the electro-chemical properties of the material itself. In fact, at normal semiconductor purity, germanium (and silicon) can't reach depletion depths bigger than 2 or 3 mm despite having bias voltages near the breakdown level. Equation 2.3 shows that greater depletion depths can be achieved by reducing the impurity concentration N . Modern rening techniques, developed for germanium but not for silicon, reduce the impurity concentration to approximately 10 10 atoms/cm 3 that allows depletion depths of 10 mm with a 1000 V bias voltage for germanium. Detectors that are manufactured from this pure germanium are called high purity germanium (HPGe ) detectors. Depending on what is the predominant remaining low-level impurity type, the germanium can be classied as a p-type germanium (surplus of acceptors) or n-type (surplus of donors).

Two geometrical congurations of germanium detectors can be commonly found o-the-shelf: planar and coaxial (gure 2.7). In a planar conguration, the electric contacts are provided on the two at surfaces of a germanium disk. The diameter of the cylindrical crystal from which the wafer is cut may be as large as 10 cm and its thickness (i.e. depletion depth) is limited to about 2 cm. Thus, active volumes up to 160 cm 2 may be achieved. Bigger volumes, which are favorable for gamma-ray spectroscopy, can be achieved if the detector is constructed in cylindrical or quasi-coaxial conguration. In this case, one electrode is fabricated at the outer cylindrical surface of a long germanium cylindrical crystal. A second cylindrical contact is provided by removing the core of the crystal and placing a contact over the inner cylindrical surface. In this way the crystal can be made long in the axial direction still keeping a moderate distance (few centimeters) between the electrodes. This geometry allows reaching much larger active volumes. This conguration allows also to achieve lower capacitance with respect to the At normal temperature the germanium present a small band gap (0.7 eV ) which does not allow optimal operational conditions due to the large thermally-induced leakage current. In order to not spoil the energy resolution, the detector has to be operated at temperatures of around 77 K through the use of an insulated Dewar in which liquid nitrogen is kept in thermal contact with the detector. The detector must be kept in a vacuum-tight cryostat to inhibit thermal conductivity between the crystal and the surrounding air. It is worth to mention that in some applications it may be convenient to allow the detector temperature to rise above liquid nitrogen temperature (this will not have major impact on the detector as long as the temperature does not reach 130 K), in these cases a mechanical or electrical cooling system may be paired with the detector at the place of the nitrogen lled Dewar. Finally, the detector is usually coupled with a preamplier which purpose is to amplify and shape the incoming raw signals (see section 3.3.1). The input or rst stage of the preamplier is generally kept in the cold part of

ELECTRIC-FIELD CALCULATION FOR PLANAR AND COAXIAL DETECTORS25

the cryostat in order to reduce electronics noise.

As mentioned before, HPGe detectors are excellent in gamma-ray spectroscopy due to their high energy resolution which allows to resolve many closely spaced gamma-ray energies. The overall energy resolution depends on the combination of three factors: the inherent statistical spread in the number of charge carriers, the variation in the charge collection eciency and the contribution of electronics noise. The full width half maximum W T of a typical peak in the spectrum can thus be written as

W 2 T = W 2 D + W 2 X + W 2 E (2.4)
The rst factor W 2 D represents the inherent statistical uctuation of the number of charge carriers created and is given by

W 2 D = (2.35) 2 F E (2.5)
where F is the Fano factor, is the energy necessary to create one electron-hole pair and E is the gamma-ray energy. Taking = 2.96 eV for germanium, and F = 0.08

as Fano factor for large germanium volumes, the above equation predicts a full width half maximum (FWHM) of 1.32 keV at 1.33 M eV . The contribution of the second term W 2

X is due to the incomplete charge collection due to charge trapping (see section 2.9 later in this chapter). This is most signicant in detectors with large volume and low average electric eld. Finally the third factor W Finally, it is wort to mention that further peak broadening can come from the Doppler eect when HPGe detectors are used in in-beam experiments. Doppler broadening depends exclusively from experimental conditions and its eects can be corrected if the velocity vector of the interacting gamma ray is known (i.e. the position of its rst interaction).

Electric-eld calculation for planar and coaxial detectors

As previously said (2.3) the drift velocity of the charge carriers in germanium detectors depends on the electric eld in the detector volume. For a given geometry, the electric potential ϕ can be calculated by solving the Poisson's equation

∇ 2 ϕ = - ρ (2.6)
where ρ is the charge density and is the dielectric constant. The charge density, in the case of a p-type germanium detector, is equal to ρ = -eN A , where e is the electron charge and N A is the density of the acceptor impurities. In the same way, for a n-type CHAPTER 2. SEMICONDUCTORS AND HPGE DETECTORS detector ρ = eN D where N D is the density of donor impurities. The spacial variation of the eld strength across the active volume is dierent in a planar and a coaxial detector geometry. In the following the two geometries will be treated separately.

x In (a) the impurity density VD is set at 10 10 cm -3 and the variation is shown for dierent values of the applied bias V . In (b) the applied bias V is xed at 4000 V and the variation is shown for dierent impurity densities VD.

The thickness of the depletion zone of a pn-junction for a given voltage is given by equation 2.3. If a detector with planar geometry of thickness T is considered, the full depletion will require an applied voltage of

V d = ρT 2 2 (2.7)
For a mono-dimensional geometry, equation 2.6 can be written as

d 2 ϕ dx 2 = - ρ (2.8)
and since the electric eld is

E = -dϕ/dx (2.9)
ϕ(d) -ϕ(0) = V , one obtains -E(x) = V d + ρ d 2 -x (2.10)
Figure 2.8 shows the electric-eld variation in the crystal depth for dierent applied voltage values and dierent impurities concentrations as predicted by equation 2.10.

For a coaxial geometry, the Poisson's equation can be written in cylindrical coordinates

d 2 ϕ dr 2 + 1 r dϕ dr = - ρ (2.11)
If the considered detector has inner and outer radii of r 1 and r 2 and the boundary condition ϕ(r 2 ) -ϕ(r 1 ) = V is imposed, by solving equation 2.11 for E(r) = -dϕ/dr one obtains Figure 2.9: Variation of the electric-eld strength, along the radius of a coaxial detector. In these examples, the crystal radii are r1 = 1.0 cm and r2 = 4.0 cm. In (a) the impurity density VD is set at 10 10 cm -3 and the variation is shown for dierent values of the applied bias V . In (b) the applied bias V is xed at 5000 V and the variation is shown for dierent impurity densities VD.

-E(r) = - ρ 2 r + V + (ρ/4 )(r 2 2 -r 2 1 ) r ln(r 2 /r 1 ) (2.
V d = ρ 2 r 2 1 ln r 2 r 1 - 1 2 (r 2 2 -r 2 1 )
(2.13)

Signal formation

As introduced in the previous sections the mechanism of gamma-ray detection for germanium (or semiconductor detectors in general) consists in the following steps: a gamma ray interacts with the semiconductor creating a number of charge carriers proportional to the energy deposited; the carriers move in the electric eld applied to the detector inducing electric charges at each electrode 3 ; the charge is converted into a voltage signal, the amplitude of which is proportional to the energy of the interacting gamma ray.

The induced charge Q on the electrodes can be calculated by determining the instantaneous electric eld E when the moving charge q is at each point of its trajectory and then integrate the normal component of E over the surface S surrounding the electrode

Q =  S εE • dS (2.14)
where ε is the dielectric constant of the material. Nevertheless, a simpler method to calculate the induced charge was independently derived from equation 2.14 by Shockley and Ramo [START_REF] Shockley | Currents to conductors induced by a moving point charge[END_REF][START_REF] Ramo | Currents induced by electron motion[END_REF][START_REF] He | Review of the Shockley-Ramo theorem and its application in semiconductor gamma-ray detectors[END_REF]. The Shockley-Ramo theorem states that the charge Q and the current i on an electrode induced by a moving point charge q are given by

Q = -qφ 0 (x) (2.15) i = qv • E 0 (x) (2.16)
where v is the instantaneous velocity of charge q. The quantities φ 0 (x) and E 0 (x) are called the weighting potential and weighting eld, respectively. They correspond to the electric potential and eld that would exist at the charge q instantaneous position x if the selected electrode is considered at 1 V , all the other electrodes being at 0 V and all the charges being removed. As supplementary assumptions, it is considered that the magnetic eects are negligible and that the electric eld propagates instantaneously (quasi-static approximation). Summing up, the elements required for the calculation are: the electrical eld in the detector, the trajectory of the charge carriers under its action and the weighting potentials.

The electrical eld can be calculated analytically or numerically (depending on the complexity of the geometry of the detector) by solving the Poisson equation φ = -ρ

(2.17) 3 Counter-intuitively, the detector signal is not formed only when the charge carriers reach the electrodes. That would imply a time delay between the interaction and start of the signal formation. No such delay exists and the signal formation begins as soon as the carriers start to drift towards the electrodes as result of their movement within the eld. The weighting potentials can be obtained by solving the Laplace equation

∇ 2 φ i (x) = 0 (2.18)
where, if S j is the surface of the electrode j,

φ i |S j = δ i,j (2.19)
as said before. From equations 2.15 and 2.16 one can see that if a charge q, located at position x, is traveling towards the electrode S i , this electrode will collect a charge proportional to the weighting potential φ i (x). At the same time the other electrodes S j =i will collect a charge proportional to value of their respective weighting potential φ j (x). However, for the equation 2.18, when q will reach the electrode S i the net charge induced on it will be Q = -q, while the net charge collected on the other electrodes will be Q = 0. The charge collected on the electrodes S j =i is called transient charge Since the weighting potentials strongly depend on the spatial coordinates, the signals generated on the electrodes (especially for the transient signals) can be used to deduce the position of the gamma-ray interaction that generated the charge, making segmented HPGe detectors position sensitive, as it will be later shown.

In the next two sections examples of analytical calculation of pulse shapes for planar and coaxial geometries will be presented.

Pulse-shapes for planar detectors

Let consider a planar detector where V 0 is the voltage applied and d the distance between its electrodes. If a positive charge q 0 moves from x 0 to x through the medium, the energy absorbed is

∆E = q 0 V 0 d (x -x 0 ) (2.20)
and the signal voltage will be

∆V R = ∆E CV 0 = q 0 C (x -x 0 ) d (2.21)
where C is the intrinsic capacitance of the detector. This corresponds to an induced charge on the electrodes of

∆Q = C∆V R = q 0 (x -x 0 ) d (2.22)
The induced charge can be expressed in terms of growth of time-dependent induced charge Q(t). The considerations made in the previous section can be proposed again for a detector with coaxial geometry with an external (internal) radius r 2 (r 1 ). For a cylindrical geometry, if a positive charge q 0 moves from r 0 to r through the medium, the energy variation will be ∆E = q 0 α(r 2 -r 2 0 ) + q 0 β ln r r 0

(2.28)

where

α = eN A 4 β = V 0 α(r 2 2 -r 2 1 ) ln(r 2 /r 1 ) (2.29)
e is the charge of the electron, N A is the acceptors concentration and ε is the dielectric constant in the medium. The time-dependent charge induced by the motion of electrons and holes can be written in terms of the radial positions r e (t) and r h (t)

Q -(t) = ∆E - V 0 = q 0 α V 0 [r 2 e (t) -r 2 0 ] + q 0 β V 0 ln r e (t) r 0 (2.30) Q + (t) = q 0 α V 0 [r 2 0 -r 2 h (t)] + q 0 β V 0 ln r 0 r h (t) (2.31)
The shape of Q(t) = Q -(t) + Q + (t) will dier from the one for the planar detector because the electric eld in a coaxial geometry varies radially and since the asymmetric nature of the germanium mobility (see section 2.3) the drift velocities of the charge carriers may vary during collection time. One can assume an empirical form for the drift velocity of the charge carriers [START_REF] Knoll | Radiation detection and measurement[END_REF] which is

v i = µ 0i E(r) [1 + (E(r)/E 0i ) γ i ] 1/γ i (2.32) CHAPTER 2.

SEMICONDUCTORS AND HPGE DETECTORS

with i ≡ e, h where E(r) is the electrical eld value at radius r, µ 0i is the mobility at low eld values, γ i and E 0i are adjustable parameters tted to experimental drift velocity data. As the radial position can be determined numerically, it is possible to calculate the signal pulse shape for a coaxial detector (gure 2.11).

2.9 Impact of trapping on the signals It was already mentioned in section 2.4 that once the charge carriers are generated, they can nd on their drifting path some trapping centers in which they can be captured.

These trapping centers are basically impurities of the crystal which add levels in the forbidden band. These levels can be more or less close to the conducting or valence band depending on their nature. Dopants, which enhance the semiconductor conduction, create levels very close to the conducting or valence band and, for this reason, they are called shallow impurities. Other impurities, due to crystal imperfections such as discontinuities, radiation damages 4 and extraneous atoms 5 occupying lattice positions, create levels further away from the conduction and valence bands, toward the middle of the forbidden band and, for this reason, they are called deep impurities.

When a charge carrier is trapped, it can be de-trapped after a certain amount of time. The mean lifetime θ e,h of a trapped electron or hole before de-trapping occurs can be calculated with the following equation [START_REF] Gutknecht | Phénoménes de capture des porteurs de charge dans les détecteurs au germanium compensé au lithium[END_REF] θ e,h = 1 σ e,h v th n e,h (2.33) where σ e,h is the eective capture cross section for electrons or holes, v th is the thermal velocity (∼ 10 7 cm/s) and n e,h is the density of the charge carriers in the conducting band which can be written as

n e = N C • e -E C -E t kT (2.34) n h = N V • e -E t -E V kT (2.35)
where N C (N V ) is the density of levels in the conduction (valence) band, E C -E t (E t -E V ) is the energy dierence among the trapping level and the conduction (valence) band, k is the Boltzmann constant and T is the temperature of the crystal. Likewise, one can consider the mean free drift time of the charge carriers, written as

τ e,h = 1 σ e,h v th N t (2.36)
where N t is the level density in the forbidden band with energy E t . In the case of shallow impurities, charge carriers are de-trapped quite rapidly, with times < 100 ns. 4 Typically induced by neutrons. Coaxial detector are more aected by this phenomenon since they are designed to detect high energies gamma rays which is compensated for n-type detectors by the charge collection conguration. 5 Typically metallic atoms such as gold, zinc, cadmium.

IMPACT OF TRAPPING ON THE SIGNALS 33

Deep impurities, instead, trap the charges for longer times that range widely from microseconds to seconds. Finally, other types of deep impurities can act as recombination centers where both electrons and holes are captured causing them to annihilate. The time delay between trapping and de-trapping is often suciently long to prevent the trapped carriers from contributing to the shape and amplitude of the measured pulse, although this also depends on the main amplier shaping times used for pulse analysis.

Pulses can then be aected by trapping and three scenarios may arise that can be described taking a planar detector as example. In an interaction near the p + contact, the holes are immediately collected and one can set x = d in equation 2.26. If no trapping is considered, then

Q(t) = q 0 t t e (t ≤ t e ) (2.37)
where t e is the transit time of the electrons. In this case the pulse has the expected shape and amplitude as shown by signal (a) in gure 2.12.

If now it is assumed that an uniform concentration of electron traps is present along the charge carrier path, then, if the electrons are not de-trapped or are de-trapped after a time longer than the shaping time, one obtains

Q(t) = q 0 τ e t e 1 -e -t/τe (t ≤ t e ) (2.38)
where τ e is the mean free drift time of the electrons (equation 2.36). In this case trapping has an inuence on the leading edge of the signal and its nal amplitude, as exemplied by signal (b) in gure 2.12.

Finally, if the electrons are partially de-trapped in a fast enough time, a fast and a slow component will appear in the resulting pulse. The fast component consists in the leading edge of the pulse and is characterized by

Q(t) = q 0 Θ e t e t θ e + Θ e τ e (1 -e -t/Θe ) (t ≤ t e ) (2.39)
where θ e is given by equation 2. [START_REF] Lee | The GAMMASPHERE[END_REF] and [START_REF] Pullia | An advanced preamplier for highly segmented germanium detectors[END_REF] while the slow component don't have a simple analytic expression. The resulting signal is schematised by signal (c) of gure 2.12. To summarize, trapping can inuence both the timing and the energy reading of a signal. The latter is helped by de-trapping, but only if it occurs on a short time scale compared with pulse-shaping times in the subsequent electronics. Furthermore, trapping can cause a deterioration in energy resolution due to the variable amount of charges lost per pulse. The term W 2 X of equation 2.4, in fact, is not uniform inside the volume of the detector and depends on the interaction positions. An exact analytical form of W 2 X does not exist and experimental formulas are generally proposed starting from collimated beam measurements. In [START_REF] Raudorf | Eect of charge carrier trapping on germanium coaxial detector line shapes[END_REF], the following semiempirical formula is proposed for a n-type coaxial detector biased on the external p

Θ e = τ e θ e τ e + θ e (2.
+ contact W 2 X (r) = KE 0 [1 -η(r)] (2.41)
where K is a constant similar to the Fano factor related to the uctuation of the number of trapped charges, E 0 is the energy of the gamma-ray interaction, is the energy needed to produce an electron-hole pair and η(r) = η e (r) + η h (r), comprised between 0 and 1, is the total charge collection eciency as a function of the radius. The two terms η e (r) and η h (r) have the form

η e (r) = - e -r/λe ln(r 2 /r 1 ) ln r 1 r - 1 λ e (r -r 1 ) - 1 4λ 2 e r 2 -r 2 1 (2.42) η h (r) = e r/λ h ln(r 2 /r 1 ) ln r 2 r - 1 λ h (r 2 -r) + 1 4λ 2 h r 2 2 -r 2 (2.43)
where λ e (λ h ) is the mean free path of the electrons (holes) in the crystal and r 1 and r 2 are the inner and outer radii of the detector. The larger the charge carrier path, the wider the peak at position r in the case of a collimated irradiation.

As the resolution depends from the radius of the interaction (or the depth for a planar detector) if a collimated gamma beam would irradiate the detector at dierent radii, the FWHM of the resulting peaks would increase going towards one contact to 2.9. IMPACT OF TRAPPING ON THE SIGNALS 35 the other 6 . An example of this phenomenon is shown in gure 2.13. If a free source irradiates uniformly a detector, then the total peak can be seen as the sum of several Gaussian functions with dierent centroids and FWHMs. The centroid and FWHM of the total peak is inuenced by the ones of the many individual Gaussian functions obtained with collimated irradiation and its peak shape appears asymmetrical with a tail on the low-end. 60 Co source. The dashed line represents the sum of all the photopeaks and is compared with a photopeak obtained with a free 60 Co source (uniform irradiation). From [START_REF] Gutknecht | Phénoménes de capture des porteurs de charge dans les détecteurs au germanium compensé au lithium[END_REF].

Chapter 3

The AGATA detector

AGATA collaboration

The study of the nuclear structures far from stability through gamma-ray spectroscopy plays an important role in modern nuclear physics. Eorts are made into the production and investigation of nuclear system under extreme values of isospin, masses, angular momentum and temperature [START_REF] Korten | Physics opportunities with the Advanced Gamma Tracking Array: AGATA[END_REF]. These unstable nuclei exhibit peculiar structures (eg.

nuclear halo, nuclear skin, clusterization, hyperdeformation) and by exploring their level structure is possible to obtain data needed to improve existing nuclear models. Existing

Radioactive Ion Beams (RIBs) accelerator facilities, such as SPIRAL1 at GANIL and ISOLDE at CERN, are already capable to access a wide range of proton-and neutronrich nuclei and new generation facilities, currently under construction, like FAIR at GSI, SPIRAL2 at GANIL and SPES at LNL, will be capable of explore even more the exotic areas of the chart of nuclides.

Since the production rates of such exotic nuclei are very low, experiments involving these species require gamma-ray arrays with large detection eciency and excellent energy resolution. The Advanced GAmma Tracking Array (AGATA) is an European project that involves over 40 institutions from 11 countries. The aim of the collaboration is to design, build and develop a new generation HPGe detector array that delivers the required performances for the study of the nuclei far from the valley of stability. A parallel project is carried out in the USA by the GRETA/GRETINA collaboration [START_REF] Lee | GRETINA: A gamma ray energy tracking array[END_REF] with which the AGATA collaboration cooperates on technical developments of common interest.

In the coming sub-sections a description of the array, the single detector unit, pulseshape analysis, gamma-ray tracking and characterization will be given. AGATA is a mobile instrument, that will be moved between the major European laboratories to take advantage of the dierent beams, ancillary detectors and equipments available at the dierent facilities. Several experimental campaigns already made use of AGATA at LNL, GSI and GANIL.

38

CHAPTER 3. THE AGATA DETECTOR

The AGATA array

The previous generation of HPGe detector arrays covering a solid angle of 4π such as EUROBALL and GAMMASPHERE [START_REF] Beck | EUROBALL: Large gamma ray spectrometers through european collaborations[END_REF][START_REF] Simpson | The EUROBALL spectrometer[END_REF][START_REF] Lee | The GAMMASPHERE[END_REF] were already eciently developed and built respectively in Europe and USA during the 1990s. These arrays were equipped with escape-suppression shields which enhanced the peak-to-total ratio in gamma-ray spectra (see gure 3.1). In these kind of arrays the shields are generally composed of BGO detectors, which have low energy resolution but high intrinsic detection eciency. An event is rejected when a gamma ray Compton-interacts with a germanium detector of the array and then escape it interacting with the surrounding BGO. This technique has two main disadvantages. The rst one is that BGO shields occupy space, limiting the solid angle occupied by the germanium detectors and thus reducing the geometrical eciency.

The second disadvantage lays in the loss of intrinsic eciency due to suppression event.

This eciency loss could be avoided if, somehow, information on the escaped gamma rays could be recovered.

(a) (b) From [START_REF] Beausang | Measurements on prototype Ge and BGO detectors for the EUROGAM array[END_REF].

The AGATA detector array [START_REF] Akkoyun | AGATA-Advanced GAmma Tracking Array[END_REF] exploits the position sensitive properties of segmented HPGe detectors (see sections 2.8 and 3.4) to get the information on the position of a gamma ray for each of its interaction. The gamma-ray tracking feature make the use of Compton-suppression unnecessary and results in a gain of geometrical and intrinsic eciency of the detector with respect to the previous detector generation. Moreover, the direction of emission and scattering of each individual gamma ray can be determined with higher precision (rst interaction point within 5 mm) allowing better Doppler correction (see gure 3.2) and linear polarization determination (extracted from the knowledge of 3.2. THE AGATA ARRAY 39 the positions of the two rst interaction points). The completed AGATA array (in gure 3.3a) will consist in 180 segmented HPGe detectors arranged in a 4π conguration that will cover 82% of the solid angle. The array is currently in construction stage and is composed by 41 working detectors installed at GANIL, as shown in gure 3.3c. In order to maximize the covered solid angle (and thus the geometrical detection eciency) while minimizing the development and maintenance costs, AGATA is composed by few elementary shapes. The sphere is decomposed in 180 irregular hexagons 1 , grouped in clusters of 3 (triplet, see yellow contour in gure 3.3a), and 12 regular void pentagons that can be used for mechanical support, insertion of complementary detectors and beam pipes. Each triplet is formed by dierent hexagonal shapes named A, B, C (in red, green and blue respectively in gure 3.3a) which are arranged in the same triple cryostat, as shown in gure 3.3b. 1 The number of hexagons have been chosen based on GEANT4 simulations and the best response in eciency, peak-to-total and in-beam energy resolution is found for 180 capsules. In addition, this conguration leads to a large inner radius of 23.5 cm which enables the placement of large complementary detectors. See [START_REF] Farnea | Conceptual design and Monte Carlo simulations of the AGATA array[END_REF][START_REF]AGATA TDR (phase 1)[END_REF].

The AGATA detector unit

The AGATA detector units (gure 3.4) are segmented closed-end coaxial n-type HPGe crystals. The units of type A, B and C, which are used in triple clusters [START_REF] Wiens | The AGATA triple cluster detector[END_REF], have a tapered hexagonal geometry with an asymmetric shape. A fourth unit exists, the type S, which has a tapered hexagonal geometry with a symmetric shape. Three of such units were produced as a prototype and never integrated into the AGATA array.

The length of each crystal is 90 mm and the coaxial diameter is 80 mm. The central hole has a diameter of 10 mm and extends to 13 mm from the front end. The 6-fold sector-wise segmentation goes through the middle of each at hexagonal side. The 6fold longitudinal segmentation forms rings of 8, 13, 15, 18, 18 and 18 mm in thickness starting from the front face. Thus 37 signals are collected from each crystal: 36 segments signals plus 1 total energy signal collected by the central contact (core ).

Each crystal has a weight of 2 kg with an impurity concentration between 0.4 and 1.8×10 10 cm -3 . The crystals are encapsulated in hermetically sealed aluminum canisters with a 0.8 mm wall thickness. Thermal isolation is established by a vacuum with pressure values below 1 × 10 -6 mbar. The spacing between the crystal and the canister wall varies from 0.4 mm to 0.7 mm. At the back of the canister, ceramic feed-through connectors provide access to each of the 36 segment outer contacts and to the core contact. The latter is also used to apply the high voltage.

AGATA electronics

Due to their small amplitude, the current pulses coming from the electrodes of an AGATA detector unit need to be amplied and converted into voltage signals before being further processed. This is accomplished by 37 charge-sensitive preampliers the core signal is shown isolated. T 10 and T 90 mark the time at which the signal reach the 10% and 90%, respectively, of its maximum amplitude. The dierence between T 10 and T 90 , quoted as T 90 10 , corresponds to the rise time of the preamplier pulse. (c) Simple scheme of the MWD algorithm. The input signal is re-shaped into a trapezoid which characteristics are labeled in the scheme. The energy reading corresponds to the energy average for the samples in the peaking area window, highlighted in red. The sum τ of the rise time, the at top shift and the peaking area is called shaping time. [START_REF] Pullia | An advanced preamplier for highly segmented germanium detectors[END_REF][START_REF] Pascovici | Low noise, dual gain preamplier with built in spectroscopic pulser for highly segmented high-purity germanium detectors[END_REF][START_REF] Zocca | A time-over-threshold technique for wide dynamic range gamma-ray spectroscopy with the AGATA detector[END_REF] (one for each channel) with which AGATA units are equipped. The preampliers have a cold and warm stage, as it can be seen in gure 3.5. The cold stage is located in cold, under vacuum part of the cryostat and it is operated close to the liquid nitrogen temperature to ensure low noise performances 2 . The warm stage, instead, is situated outside the vacuum compartment and at room temperature, since it contributes less to the noise. The core preamplier is characterized by low noise and large dynamic range for energy detection. The board for the core signal delivers two energy-range outputs, 0 -5.7 M eV and 0 -20 M eV . Actually, it is possible to extend the 0 -20 M eV range of the preamplier up to 180 M eV , with a resolution of 0.2 % (FWHM), by applying the time over threshold technique [START_REF] Zocca | A time-over-threshold technique for wide dynamic range gamma-ray spectroscopy with the AGATA detector[END_REF]. The preampliers are characterized by a response time of ∼ 25 ns. A large bandwidth ensures good resolution for pulse-shape analysis (since the small transient signals are not deformed) and good timing properties.

The outputs of the preampliers are sent to digitizers that sample the signals with

14 bit resolution at 100 M Hz rate. between ∼ 150 ns and ∼ 400 ns. The rise time of a signal can be determined calculating the T 90 10 , dened as the time interval in which the amplitude of the considered signal goes from 10% to 90% of the maximum amplitude (see gure 3.6b).

Finally, the energy of a signal is measured with a pre-processing unit that applies a moving window deconvolution (MWD) algorithm (Jordanov trapezoidal lter) [START_REF] Valentin | Digital techniques for real-time pulse shaping in radiation measurements[END_REF][START_REF] Georgiev | An analog-to-digital conversion based on a moving window deconvolution[END_REF].

The algorithm transforms the incoming signal into a trapezoidal shape, as exemplied in gure 3.6c, and the energy reading is done by averaging the amplitude value in the peaking area. Dierent parameters of the trapezoid such as the rise and fall time (k), the at top window (m), the at top shift (s) and the peaking area (w) should be set in order to obtain the best energy resolution. Hereafter, the sum τ = k + s + w of the rising time, at top shift and peaking area of the trapezoidal signal is called shaping time.

Tracking and the importance of characterization

As the AGATA array doesn't use BGO shields to suppress Compton scattered gamma rays, a novel technique has been developed to reconstruct the trajectory of each detected gamma ray. The data processing is performed in three steps. In the rst step a pulseshape analysis (PSA) algorithm [START_REF] Venturelli | Adaptive grid search as pulse shape analysis algorithm for gamma-tracking and results[END_REF][START_REF] Schlarb | Pulse shape analysis for gamma-ray tracking (Part I): Pulse shape simulation with JASS[END_REF][START_REF] Olariu | Pulse shape analysis for the location of the gamma-interactions in gamma[END_REF][START_REF] Th | A genetic algorithm for the decomposition of multiple hit events in the gamma-ray tracking detector MARS[END_REF][START_REF] Crespi | A pulse shape analysis algorithm for HPGe detectors[END_REF] is used to determine the position of each interaction composing an event 3 . The algorithm compares the experimental pulse shape with a database of calculated pulse shapes associated with spatial coordinates within the volume of the detector. Table 3.1 shows the PSA algorithms tested by the collaboration with relative performances and position resolutions. Once all the interaction positions of a detected nuclear event are obtained, a clustering algorithm groups the interactions which most likely belong to the same gamma-ray and a tracking algorithm [START_REF] Venturelli | Adaptive grid search as pulse shape analysis algorithm for gamma-tracking and results[END_REF][START_REF] Lopez-Martens | Gamma-ray tracking algorithms: a comparison[END_REF][START_REF] Suliman | Fuzzy clustering algorithm for gamma ray tracking in segmented detectors[END_REF][START_REF] Didierjean | The Deterministic Annealing Filter: A new clustering method for gamma-ray tracking algorithms[END_REF][START_REF] Tashenov | Tango -new tracking algorithm for gamma-rays[END_REF] reconstructs the interaction history for each gamma ray. This last part is done by calculating, for each possible interaction combination, a factor of merit based on the energies, scattering angles and distances of each interaction. At the end of the procedure the reconstructed event associated to the best factor of merit is chosen and if this value is above a certain experimental threshold the event is accepted and stored, otherwise it gets rejected. The whole process is schematised in gure 3.7.

The spatial resolution achieved by the array after PSA and tracking is 5 mm FWHM at 1 M eV [START_REF] Recchia | Position resolution of the prototype AGATA triple-cluster detector from an in-beam experiment[END_REF][START_REF] Soederstroem | Interaction position resolution simulations and in-beam measurements of the AGATA HPGe detectors[END_REF]. Overview of the performance of dierent PSA algorithms tested using simulated data. The performances for single (multiple) interactions are relative to the grid search (particle swarm) algorithm.

Algorithm

The position resolution refers to the FWHM. From [START_REF] Akkoyun | AGATA-Advanced GAmma Tracking Array[END_REF].

The PSA step is fundamental to achieve the best tracking results and this requires accurate databases of pulses. In fact, incorrect spatial attribution of gamma-ray interactions could lead, on the one hand, to the rejection of events which would have contributed to the full energy peak resulting to the decrease of the overall array eciency and, on the other hand, to the selection of escaped gamma rays contributing to the background of the spectrum and degrading the peak-to-total (P /T ) ratio. Presently, the PSA in AGATA is performed with the grid search algorithm [START_REF] Venturelli | Adaptive grid search as pulse shape analysis algorithm for gamma-tracking and results[END_REF] which uses databases calculated via AGATA Detector Library (ADL) ( [START_REF] Bruyneel | Pulse shape analysis and position determination in segmented HPGe detectors: The AGATA detector library[END_REF], see section 5.1). ADL calculates the pulse shape at a certain point of the detector, given the values of the electric eld and the weighting potentials of the detector. Criticalities with the tracking algorithm arise for interaction points coming from the front and the back of the detector. In these areas the electric eld strongly depends on the local geometry of the detector and particular impurities distribution. Such factors are dicult to implement in the numerical methods for the calculation of databases. Another source of incertitude for the numerical methods is the behavior of charges along the segmentation lines or surfaces, which cannot be easily implemented. A dierent approach to these problems consists in obtaining the CHAPTER 3. THE AGATA DETECTOR pulse-shape databases experimentally. Such topic will be discussed in the next chapters of this work. Gamma emission properties AGATA 4π EUROBALL Full-energy eciency

Eγ = 0.1 M eV , Mγ = 1, 0 < β < 0.5 67 -70% ∼ 40% Eγ = 1 M eV , Mγ = 1, 0 < β < 0.5 34 -38% 9.4% Eγ = 10 M eV , Mγ = 1, 0 < β < 0.5 3.6 -5% //
Peak-to-total ratio (P/T) Eγ = 1 M eV , Mγ = 1, 0 < β < 0.5

-54% 53%

Eγ = 1 M eV , Mγ = 30, 0 < β < 0.5

-41% 45%

Table 3.2: Comparison between AGATA and EUROBALL characteristics for dierent gamma energies Eγ et multiplicities Mγ. From [START_REF] Korten | Annexe of AGATA white book[END_REF].

In table 3.2 the properties of the full AGATA array are compared to the ones of the previous generation array EUROBALL. The table shows that the eciency of AGATA at 1 M eV is a factor ∼ 3.5 times bigger than EUROBALL for multiplicities (M γ ) 1 and 30, although the P/T ratio appears to be 10% lower.

The performance parameters of a gamma-ray spectrometer in real experimental conditions (in-beam, background, etc...) are determined by two quantities, the resolving power (or background reduction factor, R) which indicates how well a peak can be isolated from the background and the total photopeak detection eciency P ph . The former is related to the P/T ratio and the energy resolution ∆E γ (FWHM) by the following

formula [58] R = 0.76 • SE γ ∆E γ • P/T (3.1)
where SE γ is the average separation of the peaks of the spectrum and the 0.76 factor

TRACKING AND THE IMPORTANCE OF CHARACTERIZATION

47 comes from the fraction of a Gaussian peak which is included in setting a coincidence gate.

Figure 3.8: Observational limit as a function of fold f for various values of R and P ph respectively. The observational limit is determined by the intersection of the R and P ph curves. From [START_REF]Upgrading to Euroball III[END_REF].

In high-spin studies, where long cascades of gamma rays are emitted, the resolving power can be estimated as R f where f is the fold of the cascade (f -1 gates are applied to obtain the specic spectrum). It can be seen that as f increases, the parameter R f increases. This is due to the fact that the background gets diluted in a f dimensions data analysis space [START_REF] Eberth | From Ge(Li) detectors to gamma-ray tracking arrays-50 years of gamma spectroscopy with germanium detectors[END_REF][START_REF]Upgrading to Euroball III[END_REF].

On the other hand, by rising the fold number, the counts in the peak of interest will decrease due to the lower probability to populate multi-fold events. The number of counts depends from the total photopeak eciency P ph [START_REF]Upgrading to Euroball III[END_REF].

The observational limit of a gamma-ray array as a function of f can be than extracted by considering the resolving power and the total photopeak eciency. Figure 3.8 shows the observational limit as a function of f for various values of R and P ph , respectively.

Since a peak can be observed if the resolving power is suciently high and the number of counts is statistically signicant, the observational limit is determined by the intersection of the R and P ph curves.

Finally, the array experimental sensitivity is dened as the inverse of the obser- Chapter 4

IPHC scanning table

As anticipated in the previous chapter, the pulse database of a detector can be alternatively obtained performing a full volume characterization. This operation can be performed by the use of the so called scanning tables.

CHAPTER 4. IPHC SCANNING TABLE

Darmstadt and Salamanca scanning tables [START_REF] Goel | Spatial calibration via imaging techniques of a novel scanning system for the pulse shape characterisation of position sensitive HPGe detectors[END_REF][START_REF] Hernandez-Prieto | Study of accuracy in the position determination with SALSA, a gamma-scanning system for the characterization of segmented HPGe detectors[END_REF] share the same technique implemented in a slightly dierent manner. A 22 N a source is placed between a position sensitive detector (PSD) and the scanned detector. The source emits, for each decay, two gamma rays in coincidence with the same energy (511 keV ) but opposite directions.

The coincidences between the PSD and the detector are measured and the direction of the gamma ray pair is calculated using the position information given by the PSD.

Subsequently, for the Darmstadt scanning table, the PSD detector is moved 90 Summarizing, the rst two tables have a clean selection but are quite slow in the data acquisition, while the second two tables have fast scanning times but are limited to scan the detector with 511 keV gamma rays. Strasbourg scanning table [START_REF] Sigward | Pulse-Shape Comparison Scan of germanium detectors using the IPHC scanning table[END_REF] was designed with the aim of small scan duration, good spatial resolution and variable scanning energy.

It relies on the pulse shape coincidence scan (PSCS) technique that allows to perform 3D scans, of the full crystal volume in times of the order of 15 days. In this chapter a description of the PSCS technique and the scanning table will be given, along with some preliminary results.

Pulse Shape Coincidence Scan method

The pulse shape coincidence scan (PSCS) [START_REF] Crespi | A novel technique for the characterization of a HPGe detector response based on pulse shape comparison[END_REF] method allows full volume characterization of a given detector starting from two sets of data obtained by shooting the detector with a collimated gamma ray source. The detector is put at rst in vertical position (see gure 4.1), then the collimated source is moved by regular steps in a plane perpendicular to the detector axis. For each position of the collimator all the pulses generated by the detector along the gamma ray beam are collected and a vertical beam dataset V is so obtained. The detector is then moved to horizontal position by rotating it by 90 • (see gure 4.1) and a horizontal beams dataset H is obtained by repeating the same scanning procedure. The positions of the beams of the V and H datasets are chosen so that they (virtually) cross forming a three-dimensional scanning grid.

For a position sensitive detector (such as AGATA) two identical gamma rays that interacts in the same point will produce the same signal. If V and H datasets are compared, their pulses will dier except where the beams intersect. The similarity between two pulses can be evaluated with the following χ 2 -like formula where v i and h i are the samples of two pulses v and h coming from V and H datasets respectively, N is the total number of samples of each signal (it is implied that v and h are sampled at the same rate) and σ is the measured noise level of the signals coming from the scanned detector. The lower the χ 2 value, the most alike are the two compared pulses. Unfortunately, it does not exist an absolute threshold for the χ 2 value under which two pulses can be considered identical. This value, in fact, also depends on the experimental conditions, so that only relative evaluations can be done. In this regard, the main disadvantage of the PSCS technique lays in the fact that multiple interaction events could give rise to small χ 2 and appear as fake single-interaction events originated at the crossing point. This kind of events could have a negative impact on the nal database quality and should be excluded if possible. As nal comment it is worth to mention that a recent study [START_REF] Lewandowski | Pulse-Shape Analysis and position resolution in highly segmented HPGe AGATA detectors[END_REF] showed that the use of an optimized exponential value in equation 4.1 (χ α instead of χ 2 ) could lead to better results for pulse selection and database quality. The table setup [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF][START_REF] Sigward | Pulse-Shape Comparison Scan of germanium detectors using the IPHC scanning table[END_REF] is shown in picture 4.2. A metal collimator, later described, sits on two motorized perpendicular axes that allow its planar movement in a range of 300 mm in both X T and Y T directions. The axes are designed to sustain and move the 170 kg heavy collimator with a precision of about 10 µm. Above the collimator level, two xed plates allow the placement of the detector in vertical and horizontal positions.

χ 2 = N i=0 (v i -h i ) 2 σ • N (4.1)

IPHC SCANNING TABLE SETUP

The detector is actually placed in an adjustment frame which is xed on the plates by two centering studs. The adjustment frame allows the adjustment between the detector and the table axes, by tilting it using micrometric screws and by freehand rotating it (a ne bearing scale is used for measuring rotating angles). Finally, a laser alignment system is set on the mechanical support of the collimator and is used to keep the relative alignment of the detector when going from vertical to horizontal position.

The collimator

The collimator consists of a metallic cylindrical block, 189 mm high with a diameter of 220 mm, made by the mechanical union of dierent components. These components are made of iron, lead and tungsten, materials that absorb the gamma rays which are not traveling through the central hole [START_REF] Sigward | Pulse-Shape Comparison Scan of germanium detectors using the IPHC scanning table[END_REF]. A simple representation of the section of the collimator is shown in gure 4.

The sources

Three sources are used for scanning. Each emits gamma rays of dierent energies that can be used accordingly to their penetrating power (see section 1.5). An 241 Am source, which emits monochromatic gamma rays with an energy of 59.5 keV , is used for surface (2D ) scans. A 137 Cs source, which emits monochromatic gamma rays with an energy of 661.7 keV , is used for deep scanning as well for the full volume characterization (3D ) scans. Finally, a 152 Eu source, which emits gamma rays of several energies in the range of 122 keV ÷ 1408 keV , is used to perform several advanced tests on detectors. The source emits some of its gamma rays in cascade and there's a negligible probability that two gamma rays pass at the same time through the collimator. For example, the 779 keV gamma ray is always followed by the 344 keV gamma ray but, following Geant4 simulations, the two have only 0.06% chance to come out of the collimator simultaneously 2 .

For the work here presented, two sets of sources where used. The rst set was used with the collimator in the original conguration, while the second set was used mostly with the upgraded conguration.

Data acquisition (DAQ)

The data acquisition (DAQ) is done with TNT2 cards [START_REF] Arnold | TNT Digital Pule Processor[END_REF], developed at IPHC. These

Tested detectors

Two detectors were involved in the work here presented: a S-type AGATA detector and a planar 3 × 3 pixelated HP Ge detector (which will be referred from now on as 3 × 3 pixelated detector). The former was used in both simulations and real measurements while the latter was used exclusively in simulations. The geometrical features of the two detectors were faithfully replicated in the simulations.

The S-type detector is, to be precise, the S001 unit, the rst prototype unit commissioned from the collaboration, and its geometry was already discussed in section 3.3.

When mounted on the table, the distance of the front face of the collimator from the center of the detector in both vertical and horizontal conguration is 54 mm and 95 mm, respectively. A render of the detector as it appears in the simulations is shown in gure 4.4. The 3 × 3 pixelated detector is also a prototype, owned by the IPHC AGATA group. The detector (in gure 4.5) has a rectangular shape with an active volume of 51 × 51 × 19.9 mm 3 . One side of the active part is segmented by nine 17 × 17 mm 2 boronimplanted electrodes arranged in a 3 rows, 3 columns matrix, while on the opposite side lies the core contact realized with a 0.3 mm thick lithium layer. A guard ring of inactive germanium with a thickness of 4.5 mm is placed around the active area and helps to regularize the electrical eld at the edges of the detector. The total volume of the germanium crystal is then 60 × 60 × 20.2 mm 3 . The average impurity concentration of the germanium, specied by the manufacturer, is comprised between 0.90 • 10 10 cm -3 and 0.95 • 10 10 cm -3 . Finally a FR-4 board facing the segmented contact (see gure 4.5) holds the nine cold preampliers of the detector on the segmented side.

The detector is mounted in a dedicated cryostat with a cylindrical aluminum endcap. The cylindrical walls of the cap are 0.8 mm thick, while its front face is 2 mm thick. The detector central axis is not collinear to the cap axis, but is shifted by 10.25 mm, so that the cap axis lays along the Li-diused contact of the detector. When the detector is put on the scanning table in vertical conguration, the distance between the front of the aluminum cap and the top of the collimator is 110 mm. The distance between the center of the detector and the face of the collimator is 159 mm. With the detector in horizontal conguration the segment contacts face the collimator and the distance of the top of the collimator is 39 mm from the side of the cryostat cap and 80.55 mm from the center of the detector.

TESTED DETECTORS

Response function

In real measurements, the actual signals coming from the acquisition system have different shapes with respect to the theoretical ones. This is due to the fact that the detector-plus-preamplier system has a limited bandwidth which slows down the output charge pulse. The result is that the leading edge of the real pulses are altered with respect to the expected ones. The output signal V (t) is, in fact, convoluted with a response function R(t) so that

V (t) = ˆt 0 I(t -t ) • R(t ) dt

Realistic noise extraction

Noise characteristics were extracted from real measurements from both the S001 detector and the 3 × 3 pixelated detector with the following procedure (schematized in gure 4.9). An uncollimated 137 Cs source was used to irradiate the detector. Then, the signals coming from events in which a 662 keV gamma ray was absorbed in a single segment were selected for each segment (including the core). For each pool of signals the samples of the baseline were put on histograms after being normalized as follows.

The signal is shifted so that the baseline is centered at zero. Then the amplitude of the signal (dierence between the baseline and the plateau) is considered to have a value 4 of 661.7 keV and the samples of the baseline are scaled proportionally to this value. In average, ∼ 2000 pulses per segment were used to extract the noise characteristics for the 3 Since the segment preampliers of the 3 × 3 pixelated detector are of the same type and similarly tuned, only one response function was measured. 4 The unit here used is arbitrary. Electron-volt where used for the sake of simplicity. 4.2. It is worth to note that the noise amplitude for the core is higher than the amplitude for the segments for both the S001 and 3 × 3 pixelated detector.

Beam simulations and measurements

The gamma ray beam output of the collimator was the object of a preliminary study performed with the use of Geant4 [67], a Monte Carlo software that simulates the interaction of radiation with the matter (see section 5.1). Both the geometry and materials

     x = (z -z p ) • (v x /v z ) + x p y = (z -z p ) • (v y /v z ) + y p z ∈ [0; ∞] (4.3)
where the variable z is used as a parameter and v z > 0.

The beam proles for 241 Am and 137 Cs with the collimator in the original conguration are shown in gure 4.10. Projections on the x axis for dierent z values5 are shown in gure 4.11. As it can be seen the beams haven't a sharp pencil-like output and their spots become larger as the distance Z = z -z p from the hole of the collimator increases. The beam diverges with a maximum angle of ±0.5 • (±0.3 • ) for the 1.5 mm (1.0 mm) diameter collimator. Further it can be seen that the americium beam is slightly sharper than the cesium one. That's because the gamma rays emitted by americium are less energetic, thus they are more likely to be absorbed inside the tungsten of the very last segment of the collimator hole, while the gamma rays emitted by the 137 Cs source can easily pass through the corner of the collimator hole.

The beam prole of the sources for the dierent congurations of the collimator was measured with an IPIX sensor (see gure 4.12). The sensor is a pixelated CdT e detector.

It is made by 256 × 256 pixels each with an area of 55 × 55 µm 2 and a thickness of 1 mm.

The detector is generally used for imaging purposes and is very compact and easy to handle. The detector was mounted on an adjustable stand and put perpendicularly to the beam at various heights.

(a) (b)

y = A • Erf x -µ + r √ 2 • σ -Erf x -µ -r √ 2 • σ (4.4)
where A is an amplitude constant, µ and σ are the mean value and the standard deviation, respectively, of the Gaussian part and r is the half-width of the plateau. 4.6 further in the section). This shifts the measured beam widths to a value closer to the ones of the americium. On the other hand for the simulation of the europium beam, only events with 1408 keV were considered, leading to a larger beam width as expected.

From the simulation it is also possible to evaluate the yield of the source-collimator system, that is the ratio R yield = γout γtot of gamma rays that exit the collimator on the total number of gamma rays emitted. These evaluations are important to be able to determine the time duration of the data acquisition at each point of the scan, in order to have enough statistics in the photopeak of interest. For this purpose, the geometrical dimensions of the various sources were taken into account (see table 4

Absorption rate simulations

In the previous section the yield of the collimator for a given source was calculated, as well as the relatives c.p.s.. From this, the rate of absorption in a single segment of gamma rays of a given energy can be calculated. This information is useful to set (and predict) the duration of a scan, since it gives an indication on how many events of interest will be measured per unit of time.

A Geant4 simulation was run to estimate the absorption rate for the segments of an AGATA detector. The simulation was performed for the new 137 Cs and 152 Eu sources with the 1 mm hole collimator. The detector modeled for the test is an S-type detector (see section 3.3). ADL (which will be be widely presented in section 5.1) was used to determine if a gamma ray is fully absorbed and in which segment.

A monochromatic beam of 2 × 10 5 gamma rays hit the detector in vertical position. The beam hits the detector in sector D (see gure 3.4 and 4.14) as the collimator is positioned at coordinates x c = -20 mm and y c = 0 mm in the frame shown in gure 4.14. The absorption rates are shown in tables 4.7, 4.8 and 4.9. As expected from gure 1.9, low energy gamma rays (122 keV , 245 keV and 344 keV ) are most likely to be fully absorbed in the rst segments of the detector. It is worth to note that in the case of gamma rays with 122 keV the rate drops to zero due to the fact that the photons are completely absorbed in the rst four segments. Going towards higher energies, gamma rays gain penetrating power but the probability to be absorbed in a single segment drops since now Compton scattered gamma rays have more energy and may travel further in the germanium due to the lower interaction cross section. Absorption rates also depend on the dimensions of the segment in which gamma rays interact. For example, for energies ≥ 662 keV the rate in segment 20 is smaller than in segment 21 since its larger volume compensates for its backward positioning. Finally, tables 4.8 and 4.9 show, respectively, the counts per second (c.p.s.) and the counts per minutes (c.p.m.) of gamma rays absorbed by a segment, calculated for the 137 Cs and the 152 Eu source. It can be noticed that the 137 Cs source can deliver enough statistics in a ∼ 2 min interval, while the same cannot be said for the 152 Eu source. It is not possible, in fact, to perform full volume Chapter 5

Simulation tools and methods

A simulation of the PSCS technique applied to the 3 × 3 segmented detector and a Stype AGATA detector is carried out using three software tools: Geant4, SIMION and the AGATA Detector Library (ADL). The simulation includes the gamma-ray propagation, the pulse shape generation and χ 2 selection with the database creation. A simple scheme of the procedure is shown in gure 5.1. In the following sections, a description of the previously mentioned tools will be given, along with the explanation of the data treatment and analysis procedure. [START_REF] Bruyneel | Pulse shape analysis and position determination in segmented HPGe detectors: The AGATA detector library[END_REF]). In blue and red are represented the parameters or inputs to be set in the code while in green are represented the dierent routines that form the code.

ADL operates on the theoretical basis described in section 2.8 with the addition of the following supplementary assumptions. The rst assumption is that the charge cloud generated by the interaction of the gamma ray in the detector is considered point-like since the range of the electrons in the charge cloud can not be resolved. This is justied by the fact that a single interaction of a gamma ray of 1 M eV in germanium generates a charge cloud with a radius of 0.5 mm [START_REF] Schlarb | Pulse shape analysis for gamma-ray tracking (Part I): Pulse shape simulation with JASS[END_REF] which is much lower than the PSA position resolution [START_REF] Recchia | Position resolution of the prototype AGATA triple-cluster detector from an in-beam experiment[END_REF][START_REF] Soederstroem | Interaction position resolution simulations and in-beam measurements of the AGATA HPGe detectors[END_REF]. Diusion eects are also neglected in ADL. Under action of diusion, initial delta distributions of charges will be transformed into a Gaussian distribution with σ = √ 2Dt, where D is the diusion coecient and t the time. For AGATA detectors at liquid nitrogen temperature, D is typically lower than 300 cm 2 /s and collection times will not surpass 0.6 µs, giving an upper limit of σ max < 0.2 mm. Thus, having in mind the considerations previously made, the image charges induced by such Gaussian prole will not dier from the image charge induced by a delta distribution and diusion eects can be neglected. Finally, the quasi-static eld approximation is used, meaning that the The second group of parameters to be set are the mobility parameters for the electrons and holes in the crystal and its axis orientation. For the AGATA detectors these values were measured in [START_REF] Bruyneel | Characterization of large volume HPGe detectors. Part I: Electron and hole mobility parameterization[END_REF] and are listed in table 5.1.

Electron mobility parameters

Mobility along 100

Inter valley scattering rate

E 0 [V /cm] 507.7 E 0 [V /cm] 1200 β 0.804 ν 0 0.459 µ 0 [cm 2 /V s] 37165 ν 1 0.0294 µ n [cm 2 /V s] -145 ν 2 0.000054

Hole mobility parameters

Mobility along 100 Mobility along 111

E 0 [V /cm] 181.9 E 0 [V /cm] 143.9 β 0.735 β 0.749 µ [cm 2 /V s] 62934 µ [cm 2 /V s] 62383
Table 5.1: Mobility table. Values taken from [START_REF] Bruyneel | Pulse shape analysis and position determination in segmented HPGe detectors: The AGATA detector library[END_REF].

With the elds and the mobility parameters set, it is possible to calculate the pulse shape generated by an event giving the positions and the deposited energies as input.

These are obtained, for the the simulations presented in this work, via Geant4 and in particular it is considered that the energy is released at the gamma-ray interaction point 1 .

The simulation uses the FTFP_BERT physics list, although the coherent scattering is not taken into account as it has no inuence on the PSCS technique The Geant4 generated les are then cleaned from events in which gamma rays are not completely absorbed by the detector and prepared to be inputted into the ADL application which will calculate the pulse shapes. During calculation only the events generated by gamma rays that are fully absorbed in a single segment are saved in the output le. For a typical simulated scan of an AGATA detector 2975 beam les are converted (1257 in vertical and 1718 in horizontal conguration). The average running time to convert 6000 events is ∼ 200 s, which means that the total calculation time is of about one week (on a 2.60 GHz processor machine) that can be halved if two conversion processes are run in parallel on more than one CPU. The next step is the pulse-shape comparison, performed with a code that implements the PSCS algorithm presented in section 4.1. The overall code design follows the one described in [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF] with several changes in the handling and selection of the traces. The path of the couples of les that have to be compared and the coordinates of the corresponding crossing point are listed in a script that is read by the program. At the beginning, the two les with the traces to compare are loaded in memory. This decreases the running time, since it was observed that accessing directly the original les (.root extension) is ∼ 200 times faster. The typical amount of events that are treated for each le is 6000 (this parameter can be set at the beginning of a run). This mean that 3.6 • 10 6 couples of signals must be compared for each point of the scan grid. Actually, only the signals produced by events happening in the same segment are compared and this reduces the total amount of couples to compare.

The comparison between two pulses is performed by calculating the χ 2 value with equation 4.1, written in the form

χ 2 = M seg∈M i f i=i 0 (v seg,i -h seg,i ) 2 M • (i f -i 0 ) (5.1)
where seg is the segment index, M is the M dimensioned ensemble of segments formed by the Core segment, the hit segment and the neighboring segments of the hit segment (4 segments if the hit segment is in the middle of the detector or 3 segments if the hit segment is at the top or bottom of the detector) and v i and h i are the samples of the vertical and horizontal signals, respectively. Finally, the comparison can be performed on a subset of contiguous samples in the window [i 0 , i f ], e.g. the window containing the leading edge.

A list with the IDs of the two compared pulse shapes and their calculated χ 2 value is updated after every comparison. The list of N 1 pairs of pulse shapes is sorted in increasing order of χ 2 . The number N 1 is set before running the code. A couple of pulse shapes is entered into the list if its χ 2 value is lower than a threshold, otherwise it gets rejected. The threshold value is set high at the beginning of the run and then it self-adjusts, taking the value of the highest χ 2 value of the list. This sliding threshold CHAPTER

SIMULATION TOOLS AND METHODS

technique is necessary because the average value of the χ 2 varies widely within the scanned points, making impossible to set a global threshold. The sliding technique ensures that only the N 1 best matching couples of events are selected.

Once all the couples have been compared, it is possible that in the list of N 1 pairs of pulse shapes some leading edges have been selected more than once. These extra events are removed so that just one copy for each event ID is considered. The elements of the list are then decoupled forming a new list of N 2 events ready for the next step of the algorithm which is the mean pulse-shape renement. The renement rejects the most diverging pulses giving a more coherent nal selection of events, since the χ 2 procedure just described don't assure that the selected pairs are similar within each others 3 . The procedure is schematised in gure 5.6. At rst the mean pulse of the N 2 events of the list is calculated. Then each pulse is compared with this mean pulse and the respective χ 2 is calculated with equation 5.1. The 5% of the N 2 pulses with the higher χ 2 are rejected and the procedure is repeated several times (usually 10 times). The remaining N f inal = N 2 (1 -0.05) i (where i is the number of iterations) signals are averaged and the resulting signal will be part of the nal database. A rejection rate of 5% was chosen to insure that the nal pulse would be obtained by the average of more than 100 selected pulses. Finally, all the information related to the nal selection of events is saved in an output le that will be further analyzed. The running times for the selection procedure are of the order of ∼ 7 s per grid point (this is highly inuenced by the number of couples to be compared) leading to a global running time of ∼ 4.7 days for a typical full scan of an AGATA detector (simulated or measured) of ∼ 60000 points which produces (considering the tapering) a database of ∼ 45000 points. 3 This is specially true with experimental data, as explained in [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF]. In fact it can happen that an event coming from the natural radioactive background can be accidentally selected even if its pulse shape is totally dierent from the expected one.

Chapter 6

Simulations of PSCS technique

The simulations for the evaluation of the PSCS technique performance were carried out on the 3 × 3 pixelated detector and a S-type AGATA detector presented in section 4.3.

The simple geometry of the former helped designing the simulation and the analysis procedure. The same approach is then used to analyze the simulation results of the more complex S-type detector. In particular the simulations are performed modeling the S001 detector with which a real scan was performed as it will be shown in the next chapter. In this chapter the analysis on the simulated PSCS data for both the 3 × 3 pixelated and the S001 detectors will be presented.

Simulations of the PSCS technique on the 3×3 pixelated detector

A full scan of the 3 × 3 pixelated detector was simulated with the tools described in chapter 5. The simulated scan was performed with a pitch of 2 × 2 mm 2 , a collimation diameter of 1.5 mm (which corresponds to the collimation diameter before the scanningtable upgrade) and a gamma-ray energy of 662 keV ( 137 Cs source). For each vertical and horizontal scan line, 6000 events were used for the PSCS selection. Figure 6.1 shows the labeling of the segments of the detector and the reference frame used to present the results of the simulated scans. The dierent parameters extracted to quantify the quality of the PSCS technique are presented in the next sections.

Single-interaction events selection

The rst parameter that is extracted from the simulated scan is the percentage of pulses generated by single interacting gamma rays (or single-interaction events) selected by the pulse shape comparison (PSC) algorithm. As mentioned at the end of section 4.1 multiple interaction events can be selected by the PSCS technique and may pollute the nal database. Unfortunately there is no way to completely get rid of multiple interaction events and they can only be reduced by taking some precautions. One straightforward method is to apply the PSCS technique only to the pulses which are 77 generated by gamma rays which are fully absorbed in one single segment. To verify that hypothesis, some preliminary tests were made. A gamma-ray beam is shot in the middle of the detector placed both in vertical and horizontal congurations. The histogram of the total number of interactions of each gamma ray fully absorbed in segment 5 (shown in gure 6.2a) shows that the majority of events (∼ 91%) get absorbed after a maximum of 4 interactions, with an average of 2.77 interactions. By analyzing the energy spectrum of the rst interaction of each gamma ray (in gures 6.2b and 6.2c) it can be noticed that only ∼ 2% of the totality of gamma rays undergo a single-interaction photoelectric absorption. This percentage increases to ∼ 15% if only events that are fully absorbed in a single segment are selected (see table 6.1). (b,c) Compared rst-interaction energy spectra for both vertical (b) and horizontal (c) congurations of the system. The spectra in blue line are obtained considering only the gamma rays that are fully absorbed in segment 5. The peak at 661 keV belongs to both the blue and red spectra (even if only the blue line appears). (fourth column). The two lines refer, respectively, to horizontal and vertical congurations of the system. A dierence in the values of the fth column can be noted. This is due to the fact that when the detector is in vertical position the beam crosses segment 4 before entering segment 5 getting attenuated.

It is expected that the use of the PSCS technique will increase further the fraction of the selected single-interaction events. The graphs in gure 6.3 show the percentage of single events selected by PSCS. The graphs show dierent slices with a thickness of 1 grid unit (2 mm) at dierent depths (Y C ) of the detector. As it can be seen the values vary from point to point in a range that goes from 5% to 57% with an average of 21%.

The graphs in 6.3 also show that these values are overall homogeneous in the volume of the detector.

Figure 6.3: Percentage of single-interaction events selected by the PSCS technique over the total number of fully absorbed events. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for YC =4 mm, 10 mm and 16 mm.

Finally the PSCS has not substantially increased (in average) the fraction of selected single-interaction events as expected. Moreover these values are far from the ones obtained by using the Liverpool scanning technique (taken as reference point for single interaction selection as stated in the introduction of chapter 4). In fact, a Geant4 application was designed to reproduce the Liverpool scanning technique on the 3×3 pixelated detector and it showed that the system is capable to get a single-interaction selection that ranges from 83% to 92%.

Interaction points parameters (IPP) search algorithm

In an attempt of improving the single-interaction event selection a complementary method, described in [START_REF] Crespi | A pulse shape analysis algorithm for HPGe detectors[END_REF], was tested on the simulated PSCS 3 × 3 detector PSCS CHAPTER 6. SIMULATIONS OF PSCS TECHNIQUE dataset. The new method allows to extract the following three interaction points parameters (IPP) of an interacting gamma ray by analyzing the signal it generates: number of interactions of the incident gamma ray (IPn), coordinates of each interaction point and the energy deposited at that point. The procedure was designed to pre-process data for more complex PSA routines in the AGATA PSA analysis. The IPP search algorithm exploits the feature that the slope of the net charge signal induced at the electrode of a segmented HPGe detector changes signicantly as the charge is collected. These slope changes can be seen as peak shaped structures (PSS) in the current pulse 1 shape of a true coaxial detector, as exemplied in gure 6.4 (the following examples are taken from [START_REF] Crespi | A pulse shape analysis algorithm for HPGe detectors[END_REF] and refers to a MARS detector [START_REF] Th | A genetic algorithm for the decomposition of multiple hit events in the gamma-ray tracking detector MARS[END_REF]). From the gure, it can be seen that, in the appropriate time window, each PSS can be isolated and treated as a signal with IP n = 1. Moreover, the example shows also that the number of PSSs is proportional to the number of interactions, their position depends on the radius of the interaction (related to the diusion time) and their amplitude is proportional to the energy released. The whole signal can be then decomposed and its IPP extracted by comparing each PSS with the pulses of a pre-calculated database. 1 The current pulse is the derivative of the voltage signal at the output of the preamplier.

CHAPTER 6. SIMULATIONS OF PSCS TECHNIQUE

By determining the IPn for each event it would be possible, then, to raise the fraction of selected single-interaction events. For a 3 × 3 pixelated detector, the peaks structures are replaced by plateau-like structures which position depends on the depth of the interaction (Y C ) as can be seen in gures 6.5 and 6.6. The plateau-like structures are due to the over all linear trend of the potential of the planar detector. However the space charges in germanium bulk introduce a non-linear trend in the potential, making the plateaus not perfectly straight (in the ideal case).

From gures 6.5 and 6.6 it is seen that it is possible to disentangle (determine the IPn) a double interaction in a segment when no response function nor noise is applied and if the two interactions are well separated along Y C direction. The task gets nearly impossible when the preamplier response function and noise are added, as the signal lose denition with respect to its pure theoretical counterpart.

As a nal test, lets consider an average pulse from a given database grid point. It is composed of single-interaction events and multiple-interaction events. In the latter there exist two-fold events exhibiting very similar voltage and current pulse shapes than single-interactions pulse, both being selected by the PSCS technique for the same grid point. From gure 6.7, it is clear that it is not possible to distinguish both types of interactions from the two current signals. In conclusion, the proposed algorithm is not eective for the purposes it was chosen for. Some explanations that help to understand why the algorithm fails will be given in the following section. Comparison between two current pulses selected by the PSCS technique for the same grid point. The signal on the left is generated by a gamma ray interacting twice, while the signal on the right is generated by a single-interacting gamma ray.

Impact of multiple-interaction events on PSCS results

At the end of the previous section it was shown that the current signals coming from the PSCS selection at a given point of the database grid are basically indistinguishable.

This, of course, is also true for the corresponding charge signal from which they were derived. This should come with no surprise, since the χ² algorithm is designed to select pulses that share the most similar shape.

To better show this feature, for each point of the database the average of all the signals generated by single-interacting gamma rays was compared with the average of all the signals generated by multiple interacting gamma rays, as shown in gure 6.8. is around 2 ÷ 4% of the main signal amplitude. In gure 6.8a the maximum dierence is between the main pulses, while in gure 6.8b the maximum dierence is between two corresponding induced pulses. It has been seen that the case shown in gure 6.8b occurs tendentially near the segmentation lines where the transient-signal amplitude changes rapidly with the position of the interactions. In the bulk of the segments, instead, the case shown in gure 6.8a is more likely to happen. Another meaningful parameter to take into account is how far, in average, are the interactions of the PSCS selected events from the position of their corresponding database point. Figure 6.10 shows the average distance values for each point of dierent slices 2 The dierence is performed sample by sample since all the signals calculated in the simulation by ADL are time aligned. One factor that can eventually disturb the PSCS procedure, in fact, is the time misalignment among the signals coming from a real scan. This aspect was not investigated in the simulation. This average distance can be compared with the spatial resolution of the detector.

Although there are no data on the spatial resolution of the 3 × 3 pixelated detector, it is assumed to be worst than the spatial resolution of an AGATA detector, which is of ∼ 5 mm FWHM at 1.382 M eV after PSA and tracking [START_REF] Recchia | Position resolution of the prototype AGATA triple-cluster detector from an in-beam experiment[END_REF][START_REF] Soederstroem | Interaction position resolution simulations and in-beam measurements of the AGATA HPGe detectors[END_REF]. Since it was shown that the average of the interactions of the PSCS selected events from the position of their database point is of 6.2 mm, one can conclude that, in average, the interactions of the selected events take places within the spatial resolution of the detector. Moreover, for multiple-interaction events, the furthest interaction of an event from its rst interaction position generally releases the least energy, as exemplied in gures 6.11. This means 3 that these far interactions contribute less to the signal formation and that the bulk of the signal is formed near the considered rst interaction position. As nal test, the database obtained by simulating the PSCS technique was compared with the theoretical database, obtained using ADL to calculate the pulse shapes at the exact scanning grid-point positions. These theoretical pulses where convoluted with the response function of the preampliers. As previously done, the dierence between each PSCS calculated database signal and the corresponding theoretical signal was evaluated (see gure 6.12) and the maximum value of the residual signal was extracted. The results for each point of dierent slices with a thickness of 1 grid unit (2 mm) at dierent given depths (Y C ) in the detector are reported in gure 6.13. The values are homogeneous in the bulk of each segment, having an average value of 3% but they increase rapidly 3 It is worth to remind that for multiple-interaction events, the signal is generated as the sum of single-interaction pulses calculated for each interaction position and weighted by the energy released at that point. The results shown in gure 6.11 help understanding why the selected multiple-interaction event pulses are similar to selected single-interaction pulses. Figure 6.11: Furthest interaction distance of a multiple-interaction event from its rst interaction position versus its respective released energy. Each graph gathers the interactions of all the points for a slice of the database with a thickness of 1 grid unit (2 mm). The slices considered are at YC =4 mm, 10 mm and 16 mm from left to right. The events concentrated around the line at 0.18 M eV corresponds to the backscattering in case of 2-fold events (the large majority of multiple events). The events around 0.12 M eV and 0.08 M eV correspond to 3-fold and 4-fold events.

towards the segmentation lines where the average maximum residual is 16%. Moreover, right in correspondence of the segmentation lines the values spike, getting over 40% and in some cases reaching 100%. When the maximum residual amplitude reaches 100%, the main signal of the PSCS selected trace is generated in the neighboring segment with respect to the main signal of the corresponding ADL trace (as it can be seen in gure 6.14). This is due to the fact that when the gamma ray beam overlaps the border of two neighboring segments, the PSCS technique can select, somehow, pulses which are generated by interactions taking place in the wrong segment with respect to the segment in which the database point lies geometrically. This is especially true if the collimated beam hits one segment more than the other. This is indeed a problem of the PSCS technique that can be solved by carefully choosing the scanning grid alignment and pitch, in order to minimize the number of database points overlapping the segmentation lines. This is easy to do for a simple geometry like the one of the 3×3 pixelated detector, but less trivial for a complex geometry like the one of an AGATA detector.

In conclusion, the extracted parameters suggest that the PSCS selection, for the 3×3 pixelated detector, is reliable. It was shown that the χ 2 algorithm selects correctly similar pulses and that even if a large part of the selected events are multi-folded this doesn't aect the shape of the PSCS calculated signal due to the fact that the interactions of the selected events are in average within the spatial resolution of the detector and that the furthest interactions tendentially release the least energy contributing less to the signal formation. Moreover, the dierence between the PSCS calculated database signals and the corresponding ADL signals is minimal, with the exception of some anomalies saw along the segmentation lines. A detector with a more complex geometry, like an AGATA unit detector, could lead to a better performance on the PSCS. This will be discussed in the next section.

Simulations of the PSCS technique on the S001 detector

As anticipated at the beginning of this chapter, the PSCS technique was tested on the S001 detector by simulating various scans. The tests aim to conrm the results obtained in section 6.1 and to explore the dependence from the energy and from the number of input events on the PSCS technique. A list of the performed simulated scans is given in table 6.2. For all the scans a collimator of 1 mm diameter was used, which correspond to the upgraded version of the scanning table. Finally, in gure 6.15 the reference frame in which the results of the analysis will be presented is shown.

Description

Full volume 137 Cs scan

The PSCS technique applied to the S001 detector was at rst tested with a simulated full volume 137 Cs scan. As done for the 3 × 3 pixelated detector in section 6.1, the rst parameter extracted from the PSCS data of the full volume scan is the percentage of selected single-interaction events. It can be seen that this value is quite homogeneous across each transversal (with respect to the Z C direction) slice of the database, as shown in gure 6.16. However, gure 6.17 shows that the average value per 2 mm slice varies .17: Percentage (pct.) of selected single-interaction events along the ZC direction. The bars show the standard deviation for slices at the front, center and back of the detector.

SIMULATIONS OF THE PSCS TECHNIQUE ON THE S001 DETECTOR

along the depth of the detector, decreasing as Z c increments. The maximum average value of single-interaction events is of about 60% at the front of the detector while the minimum average value is of around 40% at the back. The reasons for this trend can be found in two factors. The rst one has to do with the geometrical properties of the segments: the active volume of the segments of the S001 detector increases from the front to the back of the crystal and this increases the fraction of selected multi-interaction events among the considered events that release all their energy in a single sector. The second factor concerns the absorption of gamma rays in the germanium: as the beam dips deep in the detector, the available number of events for the χ 2 selection is reduced (beam absorption) and this leads to a less ecient selection of single-interaction events (the impact of the number of events used for the χ 2 selection will be described later in section 6.2.3). These two factors were negligible for the 3 × 3 pixelated detector which has segments with smaller volume which are geometrically identical. In conclusion, the selection of single-interaction events for S001 detector is better than the one for the 3 × 3 pixelated detector but still not comparable with the values obtained by the Liverpool scanning table.

Nevertheless, as for the case of the 3 × 3 pixelated detector, the PSCS technique selects, for each given database point simulated, single-interaction and multiple-interaction events which are quite similar. This can also be simulated for detector S001. The average pulses of single-interaction events and multiple-interaction events, for each database point, are calculated as well as the residual supertrace (see section 3.3). The maximum residual values, in percentage with respect to the amplitude of the main signal, is shown for several database slices at dierent depths of the detector, in gure 6.18. The values are quite homogeneous in the volume of the detector with a global average < 5%. Some anomalous high values can be registered for points that are towards the segmentation lines due to the border eects mentioned in section 6.1.3.

The similarity between the pulses generated by single-interaction events and multipleinteraction events can be understood, once again, by considering the average distance of the PSCS selected events from the position of their corresponding database point.

The values for dierent transversal database slices at dierent depths of the detector (in gure 6.19) show that the average distance is homogeneous across each individual 2 mm slice. The graph in gure 6.20 shows a moderate growing trend along Z C for the values of each slice. The average distance, in fact, has a value of ∼ 2 mm in the front of the detector and then rises slightly until it reaches ∼ 2.5 mm at its back. These values, nevertheless, are below the nominal position resolution of an AGATA detector of 5 mm (after PSA and tracking) and lower with respect to the corresponding values for the 3 × 3 pixelated detector (as anticipated in section 6.1.3).

A second reason that explains the similarity between the selected single-interaction events and multiple-interaction events pulses comes by considering, for multiple-interaction events, the energy released by the furthest interaction from the rst interaction point related to this distance. Some examples, in gure 6.21, show that generally the furthest interaction releases the least energy and thus, as already stated in section 6.1.3, it contributes less to the signal formation. In other words the bulk of the signal is formed near the position of the rst interaction. Maximum residual value, in percent with respect to the maximum amplitude of the main signal, between the averaged signals of single-interaction events and the averaged signals of multipleinteraction events. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm. In the top-left panel, the segment labeling is shown while in the top-center panel the red arrow shows the horizontal beam direction.

SIMULATIONS OF THE PSCS TECHNIQUE ON THE S001 DETECTOR

The nal test is the comparison between the database obtained by simulating the PSCS technique with the one calculated using ADL (and convoluted with the response function of the preampliers). For each database point the residual supertrace between the PSCS technique and the ADL calculated signals was evaluated and its maximum extracted. Figure 6.22 shows the values for several database slices along the depth of the detector. The values are, as for the case of the 3 × 3 pixelated detector, homogeneous in the bulk of the segments but increase rapidly towards the segments boundaries. The maximum residual can reach values of 100% (with respect to the maximum amplitude of the main signal) when the database points lay on the segmentation lines. The main reason for the anomaly, already explained in section 6.1.3, is that in these cases the PSCS technique selects in majority signals that are generated in a neighbor segment with respect to the actual segment in which the main signal should be generated. Thus the maximum dierence between this miss-selected signal and the ADL one is the full amplitude of the main signal, as exemplied for the 3×3 detector in gure 6.14. The average value of the maximum residual varies with the depth of the detector as shown in gure Furthest interaction distance of a multiple-interaction event from its rst interaction position versus its respective released energy. Each graph gathers the interactions of all the points for a slice of the database with a thickness of 1 grid unit (2 mm). The slices considered are at ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm.

< 5%. This can be explained by the irregular geometry of the segments in the front of the detector which generates fast-changing electrical elds with respect to the one generated by the quasi-coaxial geometry of the back segments. Consequently, for the front of the detector a small variation in the position of a gamma-ray interaction can generate a big change in the resulting signal, both in the main pulse and in the induced pulses.

As a nal remark, the high values at Z C = 14 mm, 22 mm, 36 mm, 56 mm, 74 mm are due to the presence, in those positions, of the boundary surfaces between segment slices.

This eect is magnied by the fact that the surface of the segment-slice separation cross several 2 mm slices as shown in gure 4.14. With similar argumentations given at the end of the previous section, one can conclude that the analysis of the selected parameters suggests that the PSCS technique is reliable when applied on an AGATA detector.

The χ 2 algorithm selects similar pulses and even if a large part of them are generated by multiple-interaction events, this doesn't aect the nal pulses that will compose the database. This is due to the fact that the interactions of the selected events are in average within the spatial resolution of the detector and that the furthest interactions tendentially release the least energy contributing less to the signal formation. Moreover the comparison between the PSCS calculated database and the ADL calculated one shows little dierence with some exceptions at the boundaries between the segments of the detector.

SIMULATIONS OF THE PSCS TECHNIQUE ON THE S001 DETECTOR 95

In the next two sections the PSCS technique will be further tested with scans performed with dierent values for the gamma-ray energy and dierent number of pulses used as input of the χ 2 selection.

Dierent energies scans

As a rst further test of the PSCS technique, the impact of the gamma-ray energy used for the scan was evaluated. Four simulated partial scans (only one sector of the detector was scanned) were performed with energies 122 keV , 344 keV , 779 keV and 1408 keV which correspond to four of the various energies of the gamma rays emitted by a 152 Eu source (see table 6.2). As the activity of the 152 Eu source is about three times smaller than the one of the 137 Cs source and as the branching ratio of the main 152 Eu gamma rays are rather low, a full scan of the S001 detector would be too long. Therefore a scan of only one sector will be performed and the results will be shown in chapter 7. The simulations here presented will be performed accordingly. The parameters considered for the present analysis are:

the percentage of selected single-interaction events; the average distance of the selected events from the position of their corresponding database point;

the maximum value of the residual signal between the simulated PSCS and ADL supertraces.

Figure 6.24a shows the percentage of selected single-interaction events at dierent depths of the detector for the dierent scanning energies. Data from the 662 keV gamma-ray energy scan is added for reference. Since in the previous section it was shown that the values of the considered parameters are homogeneous in each database slice, the data represented in 6.24a refers to the average value per 2 mm slice. The graphs show that data series are comparable with one another and follow the same trend. The gamma-ray energy has an impact on the PSCS results. For low energies (122 keV and 344 keV ), the percentage of selected single interaction is sensibly larger with respect to the remaining energies above 500 keV which have similar values. This result is due to the fact that at lower energies gamma rays are more likely to undergo photo-absorption as shown in section 1.1. This means that for each pool of events for a given scanned position, the fraction of single-interaction events is already larger before the χ 2 selection than for higher energies. Also, since low energy gamma rays are more likely to be absorbed in few centimeters of germanium (see section 1.5), no data is available after Z C = 34 mm for the 122 keV scan.

The average distance of the selected events from the position of their corresponding database point exhibits a tiny energy dependence, the higher energy gamma rays having the largest average distance values (gure 6.24b). However, the overall values are quite comparable, following the same trend, and range mainly between 1 mm and 3 mm. At positions around Z C = 14 mm, 22 mm, 36 mm, 56 mm and 74 mm the average distance peaks at ∼ 4 mm due to the presence of the segment boundaries (see gure 6.25 in the next section). This generates anomalous data values as already explained in 6.1.3. For all the graphs, the bars show the standard deviation for slices at the front, center and back of the detector.

Finally in gure 6.24c the maximum value of the residual between the simulated PSCS and ADL supertraces is plotted for the dierent energies used. The data series are once again similar and the results of the PSCS technique are not aected in an appreciable way by the gamma-ray energy used. The energy independence of the parameters can be justied by the fact that the shape of the signal is in principle independent from the energy of the interacting gamma ray. This hypothesis will be tested in chapter 7 by scans of one segment sector of the S001 detector using the 152 Eu source.

SIMULATIONS OF THE PSCS TECHNIQUE ON THE S001 DETECTOR 97 6.2.3 Impact of the statistics on the PSCS technique performance

The impact on the PSCS technique of the number of pulses used as input for the χ 2 selection is evaluated. A scan of six points along the Z C direction was performed, as shown in gure 6.25, so that each point is roughly in the center of the each segment of sector D. The χ 2 selection was performed by comparing 1000 × 1000 (low statistics), 6000 × 6000 (regular simulation statistics) and 60000 × 60000 (high statistics) pulses for each point of the scan. Two gamma-ray energies were used, 779 keV and 1408 keV and, as in the previous section, the three main parameters considered for this analysis are:

the percentage of selected single-interaction events; the average distance of the selected events from the position of their corresponding database point;

the maximum value of the residual signal between the simulated PSCS and ADL supertraces.

Figure 6.25: ZC positions of the six scanned points at XC = -20 mm and YC = 0 mm analyzed in this section. In the gure a lateral view of the segments boundaries is also shown.

The results, plotted in gure 6.26 for the 779 keV gamma-ray energy scans and gure 6.27 for the 1408 keV gamma-ray energy scans, show that statistics plays an important role in the PSCS selection. In fact, although the trends of the data series of the rst two parameters previously listed is identical, their values are noticeably aected. The percentage of selected single-interaction events increases substantially and the average distance of the selected events from the position of their corresponding database point decreases, respectively, with an increasing number of pulses used for the χ 2 selection. It is clear that for these two parameters the PSCS technique performs better when higher number of pulses are used for the χ 2 selection. Moreover it seems that there is no correlation between statistics and gamma-ray energy. However the maximum value of the residual between the simulated PSCS and ADL calculated supertraces doesn't seem to be signicantly aected on contrary to the two previous parameters. There isn't, in fact, a noticeable change in the values except a small eect at the point of the rst slice of the detector. As this third parameter is very indicative of the similarity between the simulated PSCS and ADL database pulses and as dierences have been evidenced in sections 6.2.1 and 6.2.2 at the front of the detector, one can conclude that the number of events used as input for the χ 2 selection, comprised between 1000 and 60000 events, does not result in sizable changes in the construction of the database. As a further analysis it would be worth to extend the range of the test to even lower statistics (few hundreds of events) and higher statistics (orders of magnitude > ). Chapter 7

Real scan of the S001 detector

Along the simulation analysis, complementary work was done on the real scanning table system, a part of which was already presented in chapter 4. In this chapter the results of several 2D and 3D scans, performed on the S001 detector, will be presented. All the measurements are performed with the scanning table in the upgraded conguration. At rst, the alignment procedure will be described. Afterwards, a 2D characterization of the detector, made with the 137 Cs and 152 Eu sources, is presented analyzed and discussed. Finally, the results of the 3D scans made with the 137 Cs and 152 Eu sources are shown and preliminary conclusions drawn.

Detector alignment procedure

The PSCS technique will always give a result from the comparison of two series of data regardless of the crossing precision. It is, then, of highest importance that the detector is well positioned and geometrically referenced on the scanning table in order to minimize the errors due to miss-alignment of the virtual scanning grid. A rough detector alignment along X T and Y T axes (see gure 4.2) is carried out using a square and by adjusting the micrometric screws of the adjustment frame. Then, dedicated local scans are performed to determine the position of the crystal in the scanning table reference frame. The alignment procedure is described in the following sections.

Vertical rotation

The scanning procedure starts by aligning the detector vertically. This means that the central axis of the detector is perpendicular with respect to the collimator moving plane.

Also, in the specic case of an AGATA detector, it is required that the segmentation line between segments E1 and F 1 of the detector is parallel to the Y T axis (see gure

f (x) = C + A (2 • Acos (B • (x -x 0 ))) -sin (2 • Acos (B • (x -x 0 ))) (7.1)
where A, B, C and x 0 are the t parameters. In particular, x 0 is the abscissa of the point at half height of equation 7.1 and this value is taken as segment edge. This tting procedure is repeated for each scan line acquired and a graph with the coordinates of the segmentation-line edge coordinates is built as in gure 7.2. From these data it is possible to extract the value of the angular correction that has to be applied to the detector in order to align it. For the S001 detector, scans at 11 dierent radius values, reported in table 7.1, along the E -F segmentation line were performed with a collimator diameter of 1.0 mm and a pitch of 100 µm. It showed a misalignment between the segmentation line and Y T axis of 0.039 • ± 0.002 • which is an acceptable value to consider the detector aligned, since it is below the correction precision of the adjustment frame (along the Z T rotational direction). It corresponds to a displacement of 14 µm between the two extreme scanned points which are spaced by 20 mm. This scan also allows to determine the width of the segmentation line, as exemplied in gure 7.3a. The segmentation line is measured to be in average 0.668±0.006 mm (see table 7.1). An additional single scan, 1 For simplicity the counts in the photopeak are called local photopeak eciency. with a collimator diameter of 0.5 mm and a pitch of 50 µm, was performed to cross check this result. As it is to be expected, a ner scan allows for a more precise determination of the segments edges 2 . Figure 7.3b shows that the edges of the eciency graphs are (a) (b) 7.2) to determine its width. The graph in (a) refers to the scan performed with a 1.0 mm diameter collimator and a 100 µm pitch at YT = 158 mm (see table 7.1). The graph in (b) refers to the scan performed with a 0.5 mm diameter collimator and a 50 µm pitch at the same position.

For both the graphs the red line refers to the data taken in segment E1, while the blue line refers to the data taken in segment F 1. Note that the measurement duration was 120 s for (a) and 2000 s for (b).

In the latter case, background from the detector-laboratory environment lead to a minimum of about 1000 counts in the energy gate.

sharper and moreover they don't overlap as for the case of gure 7.3a. This second scan gives a value for the segmentation width of 0.626 ± 0.004 mm which diers by 7% from the respective value measured with the 1.0 mm diameter collimator (see table 7.1).

However, a real comparison between the two values can not be done because, in order to obtain a statistically rigorous result, the measurement with the 0.5 mm diameter collimator should be repeated several times. This was not done by lack of time.

Vertical axis alignment

Once the face of the detector is correctly oriented, the vertical alignment of the detector axis is performed. The 137 Cs source is used to perform ne pitch scans (of 100 µm) across the central hole of the detector. Two crossing linear scans are performed as shown in gure 7.4a. For this analysis the spectra at each scanned point were build considering only the events of total gamma-ray absorption in a single slice. Graphs of the segments eciency as a function of the scanned points along X T and Y T are drawn for each of the 6 slices of the detector (right panel of gure 7.4a). As for the previous case, the eciency stays constant when the gamma-ray beam is in the segment bulk and drops when the 2 A study of the progressive penetration of a gamma ray beam inside the active area of a detector is presented in [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF]. Note that in this graph the ordinates refer to the scanning table reference frame (YT ) while the abscissas refer to the crystal reference frame (ZC). In this particular case, slice 6 was not considered for the t. See text for more details.

beam crosses the hole. For the last 5 slices 3 , the positions of the hole boundaries are determined in the following way. The positions of the hole boundaries are determined by linear tting the edges of the eciency graphs (see the red lines in the right panel of gure 7.4a). The linear ts are performed in the range for which y is comprised between 0.2 • h and 0.6 • h, where h is the height of the plateau 4 . The left (right) boundary of the hole is taken as the abscissa x l (x r ) of the point laying on the left (right) t line with an ordinate y = y 0 • h, where y 0 is a value taken as much closer as possible to the mid-height of the eciency prole (y 0 = 0.3 in the current analysis since, to obtain a good t, the t ranges between the slices dier). Knowing the boundaries of the hole, its center x 0 is calculated and plotted as a function of the height of the respective slice. A linear t of the hole boundaries in the 5 slices enables to deduce the tilt of the crystal 3 The rst slice of the detector has no hole. 4 Generally the eciency graphs are renormalized so that h = 1.

CHAPTER 7. REAL SCAN OF THE S001 DETECTOR

along X T and Y T axes. This gives the value of the two angular corrections (around the X and Y rotational axes of the adjustment frame) that have to be applied (using the micrometric screws) to the detector in order to properly align its axes on the scanning table axes (gure 7.4b).

For the S001 detector, a crossing lines scan was performed, across the bored hole, with a collimator diameter of 1.0 mm and a ne pitch of 100 µm. The scan revealed that the detector had a tilt of 0.02 • ± 0.02 • on the X T axis and a tilt of -0.42 • ± 0.03 • on the Y T axis. The detector was considered aligned on the X T axis while the tilt on the Y T axis was corrected. A new, similar, scan conrmed the good alignment of the detector which presented a tilt of 0.05 • ± 0.02 • on the Y T axis after correction. Finally, the shift along X T (Y T ) between points at the front and the back of the crystal is 32 µm(79 µm)

only.

Such scans give also information on the diameter of the central hole of the detector that was obtained by making the dierence of the values of the boundaries of the hole for each slice. The value obtained is around 14.1 ± 0.2 mm which is in agreement with the same measurements performed on the B006 detector [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF]. The measured diameter is larger than expected (10 mm) which is due to a combination of causes such as the width of the beam and the dead layer of the hole contact that produce a smearing eect (see discussion in chapter 4 of [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF]).

Once the detector is vertically aligned, all the needed vertical scans are performed, after which the detector is prepared for horizontal positioning.

Horizontal alignment

While the detector is still in vertical position, the gamma source is replaced by a laser beam in order to set up the optical alignment system. The optical module consists of a pair of pin holes, spaced by 16 cm, attached to the side of the cryostat along its symmetry axis. The diameters of the rst and second holes are 200 µm and 50 µm, respectively. The collimator is opened, the source removed and replaced by a prism.

The laser beam passes through the collimator from the bottom to the top, following the gamma-ray path. Beyond the collimator, the laser beam passes through the two holes which positions can be adjusted. The laser beam intensity is rst maximized at the exit of the rst hole (using a wattmeter which operates in the nW to mW range) by adjusting the pin hole position in X and Y . A similar operation is performed with the second pin hole. When the laser delivers the maximum intensity at the exit of the second hole, the optical system is set and the two holes dene a direction parallel to the laser beam, i.e. the gamma-ray beam. The detector is put in horizontal position and the optical module is used to adjust its alignment with the aid of a second prism.

Again the laser beam should deliver the maximum intensity at the exit of the second hole of the optical system. Since the detector is considered horizontally aligned when the axis of the detector is collinear to the X T axis of the scanning table, the optical alignment is veried through dedicated scans with the 137 Cs source. The scans run transversally through the bored-hole of the detector as shown in gure 7.5a, one line for each slice. An eciency graph is then build for each slice of the detector as shown in

Two-dimensional scans

With the Strasbourg scanning table it is possible to characterize a detector by performing two-dimensional (2D) scans. In the following sections the results of various 2D scans of the S001 detector, will be shown. The scans, a list of which is given in table to obtain various informations on the behavior of the detector and show the versatility of the Strasbourg scanning technique. For the rst time in the AGATA and GRETA collaborations a scan with a 152 Eu source was performed. It is worth mentioning that the yield of the collimator (i.e. the number of gamma rays that exit the collimator with respect to the gamma rays emitted by the source) for the 152 Eu source is lower (due to a lower activity by a factor 2.5) than the 137 Cs (see chapter 4). Moreover, the yield is divided among the dierent energies of the gamma ray emitted which have dierent branching ratios. This means that in order to have a satisfactory amount of statistics for a given energy, the time spent to acquire data for a single point should be longer, with respect to the 137 Cs source, leading to time consuming scans about a factor 20 or longer. For example, a single point acquisition with a 137 Cs source requires, generally, 150 sec while 1 hour is required for the 152 Eu source in order to have the same number of events that are in the photopeak of the cesium for the less intense transition considered of the 152 Eu source. A complete scan of S001 detector, with the 152 Eu source, would then last about two months.

In the following a study on the local detection eciency, on the charge carriers behavior and imaging will be presented. The local detection eciency is dened as the spectrum area around the photopeak of the energy of interest obtained at each scanned point (collimator position). The energy window is generally taken as ±5 keV but may be adjusted when needed. Figure 7.6 shows the results for a vertical scan realized with the 137 Cs source. The gures refer to the spectra obtained on the core contact requesting full absorption in the full crystal volume (gure 7.6a) and the segment contacts requesting full absorption in a single segment (gure 7.6b), respectively. Figure 7.6a shows that the core local eciency is not homogeneous as it is larger in the bulk of the detector with respect to the borders (see color scale). This eect is due to Compton scattering, as gamma rays interacting near the border of the detector have, geometrically, a larger probability to be scattered outside the detector thus reducing the number of fully absorbed events (the photopeak area). Another drop of eciency, located in the central part of the detector, is caused by the presence of the bored hole which reduces the active part of the crystal. A particular eect can be noted where a darker blue point marks the center of the bored hole area.

TWO-DIMENSIONAL SCANS

This point corresponds to the position of segmentation lines crossing on the front face of the detector. The regions between the segmentation lines have very low electrical elds that lead to an incomplete charge collection. The charges will drift slowly towards the contacts increasing the probability to recombine and these areas can be thus considered inactive. This explains the sudden eciency drop in correspondence to that specic point of the scan. As a nal remark, the hexagonal shape of the front face and the tapering of the detector can be guessed by looking at gure 7.6a as the eciency prole is directly linked to the active volume of the crystal.

Figure 7.6b shows the local eciency of the segments of the six detector slices. For the rst four slices of the detector, the hexagonal shape of the tapering is clearly visible while slice 5 exhibit a rounded hexagonal shape and slice 6 shows the overall cylindrical shape of the detector back end. The eciency in the rst slice is higher in the bulk of the segments while it decreases, towards the borders of the detector. This can be understood by looking at the horizontal prole of the slices electrical elds, schematically presented in gure 6.25. The gure shows that the rst slice of the detector has a larger active volume towards the center, hence enhancing the photopeak eciency in this area. For the second slice of the detector, the opposite phenomenon occurs, as in the same region the active volume is smaller, leading to a lower eciency. In general, the average eciency decreases as the slice number grows due to gamma-ray absorption along the germanium, with the only exception on the border of the slices where the beam can enter directly in the segments due to the tapering of the crystal. Finally, a signicant drop in eciency is located along the segmentation areas.

(a) (b) The results for the 122 keV photopeak are shown in gure 7.8 for each one of the six slices of the detector. It can be seen that, as expected, at this energy the gamma rays are totally absorbed in the rst two slices of the detector, while for the other slices events are registered only when the beam hits the tapered border of the detector. In particular, in the second slice of the detector, the only area where the local eciency isn't zero is for R 20 mm. As explained in the previous section, this is due to the fact that the active volume of the rst slice, around the center of the detector, extends toward the Z C direction, while the active volume of the second slice diminishes in the same radial range. Thus the gamma rays emitted by the collimator at this scanning positions are most likely to be absorbed by the rst slice. Finally, in the rst slice it is hard but possible to see the shadows of the contacts of the six front segments, as the material in which they are made absorbs of low-energy gamma rays. See for example the vertical line at X C = 8 mm and -20 mm < Y C < -10 mm.

For the next higher energy gate at 334 keV , the local detection eciency is non zero for the third, the fourth and the fth slices, as shown in gure 7.9. For the sixth slice The results obtained gating on 779 keV gamma-ray energy, in gure 7.10, should be similar to the ones obtained for the 662 keV scan. However the dierence in intensity between the 137 Cs source and the 779 keV emission rate of the 152 Eu source (see sections 4.4 and 4.5) causes a substantial dierence in the values of the local eciency (a maximum of 5 × 10 2 cpp, count per pixel, for the 779 keV versus 6 × 10 3 cpp for the 662 keV in the rst slice). This leaves some empty spots around the central contact of the sixth slice as the gathered statistics in that region is poor.

Finally, the results for the 1408 keV gate are shown in gure 7.11. The overall eciency is lower than in the previous cases, but it is more homogeneous in the volume of the detector. This comes from the higher mean free path of high energy gamma rays.

In conclusion, the technique based on a multi-chromatic source seems to be eective and the method can be exploited to make 2D characterization of the detector and extended to perform 3D scans.

Crystal orientation

The orientation of the germanium crystal can be determined by measuring the rise time of the pulses generated for each position of the collimator. The rise time depends on the charge carrier velocity which, as said in section 2.3, depends from the orientation of the crystal. One can determine the rise time of a pulse by calculating the T 90 10 as shown in section 3.3.1. For this study a 137 Cs scan is analyzed and, in particular, only the photopeak events absorbed in a single segment (1-fold events) are considered. For each collimator position, the T 90 10 corresponds to the average of the T 90 10 values of the events acquired at a scanned point for a given segment. Figure 7.12 shows the T 90 10 distribution for the core and the segments. AGATA crystals are grown by slowly pulling it from a hot germanium bath along the < 001 > crystal axis (see gure 2.2b) which is collinear to the Z C axis. This mean that the < 100 > direction lays in the X C Y C plane and its direction can be determined from the distributions presented in gure 7.12. As charge carriers are faster along the < 100 > crystal axis (see section 2.3), the corresponding T 90 10 has the minimum value. For each segment slice and the core, the T 90 10 values along a xed radius are plotted as a function of the angle θ between the X C axis and the radius direction, as shown in gure 7.13. These plots can be tted with the function proposed in [START_REF] Bruyneel | Pulse shape analysis and position determination in segmented HPGe detectors: The AGATA detector library[END_REF] T 90 10 (θ

) = A • (1 + R 4 • cos(4 • (θ -θ 4 ))) • (1 + R 2 • cos(2 • (θ -θ 2 ))) (7.2)
where θ 4 denes the crystal orientation relative to the detector axis X C , the R 2 term corrects for the deviation of the 4-fold symmetry when the 6-fold geometry of the tapering is taken into account. The results of the ts are listed in table 7.3 along with the radius value for each slice at which the data are extracted. An average value for θ 4 = -16.7 • ± 0.4 • is obtained. 10 of the signals generated by the core gated on 1-fold events. Figure (a) shows the orientation of the < 100 > and < 110 > crystallographic axes and the angle θ4 between the crystallographic axis < 100 > and the detector axis XC (see text for more information).

[rad] θ 3 - 2 - 1 - 0 1 2 3
[ns] 7.3). The curves are t using equation 7.2 and θ is in radians. See text for more details.

-17 • ± 1 • r = 31 mm Slice 4 -16 • ± 1 • r = 35 mm
Slice 5 -17.0 • ± 0.8 • r = 37 mm Slice 6 -16.9

• ± 0.8 • r = 35 mm AVG -16.7 • ± 0.4 • Table 7
.3: Orientation of the crystal for the core and each slice (see text for more information). The right column displays the radius at which the data were extracted. The average (AVG) of the seven θ4 values is given at the bottom line.

Core-contact charge collection

It was already observed that along the segmentation lines the charge carriers collection from the electrodes is not optimal leading to drops in the eciency of the detector.

Apart from these areas, the charge carriers collection inside a detector is generally nonhomogeneous due to factors such as the non-uniformity of the electric eld, trapping impurities and defects concentrations of the crystal. This is more evident for large volume crystals, such as S001, which generally present a slightly worse energy resolution compared to small volume detectors. Charge carrier collection eects can be probed by looking at detector characteristics, such as the centroid position and the full width at half maximum (FWHM), of the energy photopeak acquired at a given scan position. For this purpose a 137 Cs 2D vertical scan is analyzed. For each position of the collimator, the photopeaks are tted with a Crystal Ball function [START_REF] Oreglia | A study of the reactions psi prime[END_REF] which consists of a Gaussian function joint with an exponential low-end tail. The function can be written in the form

f CB (x) =      n |α| n exp -a 2 2 n |α| -|α|-x n ∀ x < -|α| exp -1 2 x-µ σ 2 ∀ x > -|α| (7.3)
where µ and σ are, respectively, the mean and the standard deviation of the Gaussian function, α is the point in σ units where the Gaussian function joints the exponential part and nally n is the slope of the exponential part. As opposed to a simple Gaussian function, the exponential tail of the Crystal Ball function ts better the low end part of the photopeaks that are populated by events for which incomplete charge collection lead to an energy loss. In the large majority cases, the peaks are Gaussians, as expected, and the tail is negligible. An example of a photopeak tted with the Crystal Ball function is shown in gure 7.14. The photopeaks are tted in a ±10 keV range in order to take into account long tails. In gure 7.15 the centroid-position distribution of the photopeaks from the core contact is shown. The plot shows values of 661.7 keV around the bored hole of the detector, which decrease toward the edges, with a dierence between the maximum and the minimum values of about 1.3 keV . This behavior is due to the presence of trapping centers which capture the charge carriers without de-trapping them 5 . These centers are normally distributed uniformly inside the crystal, so that the probability for a charge to be trapped is mainly due to the length of drifting path. The core contact of the S001 detector collects negative charge carriers and thus, based on the Shockley-Ramo theorem, the core signals are mainly inuenced by electron collection. The electron 5 or de-trapping them after a time much larger than the shaping time of the digital ampliers, 5.95 µs for this scan (see section 4.2.4). trapping leads to lower signal amplitudes (see section 2.9) which in turn leads to a systematic peak shift which is larger as the distance of the interactions from the core grows. This phenomenon is well known in HPGe detectors [START_REF] Raudorf | Eect of charge carrier trapping on germanium coaxial detector line shapes[END_REF][START_REF] Bruyneel | Correction for hole trapping in AGATA detectors using pulse shape analysis[END_REF].

The core charge collection can be better investigated by gating the core energy on 1-fold events in the segments. The centroid distribution for the six slices of the detector is shown in gure 7.16a. Segments A2, A3 and F 6 present higher values compared to the other segments. This behavior can't be explained by trapping and it has most likely an electrical nature. The segment distributions are uniformed by normalizing the centroid value of each segment to 661.7 keV . The new distributions are shown in gure 7.16b.

As for the case of the core contact, the centroid position shifts toward the low end of the spectra as the collimated beam moves from the bored hole toward the edges of the detector. Figure 7.17a shows the centroid position as a function of the radius for the six slices of the detector and the core. The graphs are renormalized so that the nearest point to bored hole has a value of 661.7 keV . The behavior of the dierent slices is quite similar and matches with the one of the core. The dierences among the slices are due to their slightly dierent dimensions and shape. In the rst slice, for example, the shift of the centroid position is more pronounced because the electric-eld intensity varies rapidly with the radius and the path of the charge carriers becomes longer, out of plan, approaching the slowest < 111 > crystal axis (see section 2.3). The plot shows a maximum shift of ∼ 1.6 keV for the centroid values of the back slices of the detector. with examples found in literature ( [START_REF] Gutknecht | Phénoménes de capture des porteurs de charge dans les détecteurs au germanium compensé au lithium[END_REF][START_REF] Raudorf | Eect of charge carrier trapping on germanium coaxial detector line shapes[END_REF]) and shows how trapping also aects the resolution of a large volume detector (see section 2.9 and gure 2.13).

Segment-contacts charge collection

The distributions of the centroid values obtained from segment energy spectra is investigated by gating on 1-fold events. The results are shown in gure 7.18. Once again the distribution of each segment is standardized by normalizing the centroid values at the bored hole to 661.7 keV . The gure shows a behavior similar to the one found for the core contact (see gure 7.19a) with decreasing centroid values as the radius grows. This behavior diers from that expected. As the segment contacts collects positive charge carriers, the ballistic decit should be mostly determined by the trapping of holes and the centroid shift should have an opposite trend than what observed or be at when no hole trapping occurs. For example, the AGATA detector B006 was characterized in reference [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF] and it was observed that the centroid position of the segment energy photopeaks is quite constant along the radius of the detector. The algorithms used to analyze the data for the detector S001 were tested on the B006 detector data and reproduced the results described in [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF]. The only experimental dierence between the two scans are the TNT2 trapezoid lter settings (see section 3. The value of the FWHM as a function of the radius for sector A is shown in gure 7.19b. The values are rather constant for R smaller than 25 mm and an increase is observed for radii larger than 25÷30 mm depending on the segment slice considered. The growing is unexpected and conrms the anomalous trend previously described suggesting a larger inuence of the electron trapping instead of hole trapping.

Further analysis on the charge collection is done by examining the area of the exponential tail in the low end of the tted Crystal Ball function. In fact, a large tail area could denote an anomaly in the charge collection. If A CB is the total area of the tted Crystal Ball function and A Gauss the area of the Gaussian part, then the gure of merit F oM written as

F oM = A CB -A Gaus A CB (7.4)
can be used to quantify the trapping eects. The closer is F oM to 1, the largest will be the exponential component of the Crystal Ball. For a perfect Gaussian peak, F oM = 0. The macroscopic models of trapping make the assumption that the peak measured at a given position is a Gaussian which centroid is shifted and width widen in case of trapping. The present shapes of the peaks along the trail lead to the belief that the charges that will follow paths avoiding the defective zone and will be collected normally.

Another part of the gamma rays, instead, will produce charges that will follow paths crossing the defective area. For the former case the photopeak will exhibit the observed electron trapping (see gure 7.19a). In the latter case, instead, additional charges are In conclusion, the plots shown previously in gure 7.23 suggest that the defective zone has a big impact on the electron collection and extends along segments F 2, F 3 and F 4 from the center of the crystal to around R = 20 mm with an approximative shape of a plane of thickness smaller than the gamma beam spot (< 1.5 mm). Hypothetically the crystal can be defective in that part for some structural reasons such as a major crystal-defect concentration, an anomalously large trapping center concentration or a cleavage area. More tests should be made to fully understand the phenomenon and fully characterize the properties of the defective zone.

7.2.6 2D scans with 241 Am source: imaging

The rst layers of a detector can be explored by performing scans with low-energy gamma rays such as the ones emitted by the 241 Am source. In particular an imaging analysis can be performed by looking at the local eciency prole, as already seen in the previous chapters. Hardware features of the crystal can be extracted such as the position of the segmentation lines, the position of the segments contacts and even the wiring. These kind of measurements are generally performed at the very beginning of a characterization in order to better understand the detector position on the reference frame of the table.

Three-dimensional scans

As stated in chapter 4 the main feature of the Strasbourg scanning table is the possibility to perform full volume characterization of a detector using the PSCS technique. In the following section, a description of the raw data treatment will be given and then the results of the P SCS technique applied to real three-dimensional 137 Cs and 152 Eu scans will be presented.

Treatment of raw data

As shown in table 7.2, the cesium scan had a duration of 2.5 minutes per point, leading to a total duration of 6.7 days (2.5 days for the vertical acquisition and 4.2 days for 7.3. THREE-DIMENSIONAL SCANS 127 the horizontal acquisition, including the nitrogen rell pauses 6 ). This duration assure a sucient number of events, in the photopeak window of 662 ± 2.0 keV , per point for the χ 2 selection algorithm. On the other hand, as already stated in section 7.2, acquisition times for the europium scan must be longer in order to obtain similar statistics for each one of the four photopeaks of interest (121.8 keV , 344.3 keV , 778.9 keV and 1408.0 keV all gated in a ±2.0 keV window). A duration of 60 minutes per point was used and in order to limit the total scanning time it was chosen to scan only one single sector (sector B). Nevertheless the scan duration lasted 54 days in total (14 days for the vertical acquisition and 40 days for the horizontal acquisition, including the nitrogen rell pauses).

Before being treated with the χ 2 selection algorithm described in section 5.2, the acquired datasets are sorted and prepared. For each dataset, only 1-fold events are selected. Moreover each pulse shape is normalized and then aligned to their T 10 (see gure 3.6b). In particular the transient pulses are normalized and aligned with respect to the signal of the hit segment 7 . The europium events, which are acquired in a single scanning procedure, are sorted in four separated datasets, one for each energy, and treated independently with the χ 2 selection algorithm, leading to the construction of four dierent databases.

In the following the results of the 137 Cs scan will be presented. They will be used as reference and will be further compared to the results obtained for the europium scan.

Cesium 3D scan

A full volume characterization using the PSCS technique implemented by the Strasbourg scanning table was performed and described in [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF]. For that analysis, a B-type AGATA detector was scanned with a 137 Cs source using the 1.5 mm diameter collimator (original conguration, see section 4.2). The 137 Cs scan presented here, instead, is realized using the new sources and the 1.0 mm diameter collimator (updated conguration). In both measurements, a pitch of 2 mm was used.

Once the database is created, it is important to note that some of the pulses selected by the algorithm are associated to points that lay outside the volume of the detector.

Such cases can exist because the χ 2 selection algorithm is blind of the geometry of the detector 8 . It is, thus, important to clean the database from these events. Since on average the χ 2 value of these pulses is higher than the χ 2 value of the events selected inside the detector, it is possible to set a threshold in order to lter the database. A rst test to verify the PSCS results is to check the segment map. Despite the 6 During the nitrogen lling the scanning procedure is paused for the ll duration plus 15 minutes of waiting time after the ll (about 25 minutes in total) in order to avoid eects on the acquisition due to the bubbling of the liquid. An automatic rell is done every 8 hours. χ 2 selection algorithm being blind to the geometry of the detector, each averaged pulse shape its associated to the segment in which they are selected. The map, relative to a longitudinal slice of the database at Y C = 0 mm is shown in gure 7.25 compared to the ADL counterpart. Even if the mesh used for the two maps is dierent (2 mm for the real measurements and 1 mm for the ADL map) the two geometries are very similar. horizontal at its top. Consequently, the charge carrier velocities at the segment bottom are aected partially by the slower axis < 111 > which is not the case for the segment top, leading to the slight changes observed. While the amplitude of the transient pulses of segments F 5/B5 don't change, the amplitudes of pulses of segments A6/A4, as for the case in gure 7.28, increase or decrease depending on the distance of the interaction from the respective segment.

Europium 3D scan

For the rst time a three-dimensional scan was performed using an 152 Eu source. The aim of this measurement is to explore the new technique and to demonstrate that the pulse shapes are independent from the energy of the gamma ray interaction that generates them. This principle is asserted by the Shockley-Ramo theorem and it's at the base of the AGATA PSA algorithms implementation.

Unlike the 241 Am and 137 Cs source, the photopeaks of interest of the 152 Eu source are not isolated. In fact low energy photopeaks are build on top of a background produced by the Compton scattering of high energy gamma rays. In addition, an anomalous background bump is observed between 0 and ∼ 250 keV (see gure 7.7) which is due to multi-scattered gamma rays on the wall of the collimator. Therefore an analysis of the peak to total ratio (P /T ) is performed to estimate the purity of the datasets used for the χ 2 selection algorithm. The spectra generated by a vertical beam irradiating the detector in the center of sector B (X C = 10 mm Y C = 20 mm) are build for each segment of the sector. The spectra, represented in gure 7.31 are built with 1-fold events only.

Each of the photopeak of interest is tted with a Gaussian function built on a rst order polynomial background. The peak is then integrated in a window of ±3 • σ keV (where σ is the standard deviation of the integrated peak) and the ratio between the Gaussian component and the full area is calculated. The results, in table 7.4 give the fraction of good events over the total number of selected events. The 1408 keV photopeak doesn't have a meaningful background component since, being the highest energy photopeak of the source, it is isolated (contributions of the 1460 keV of 40 K and some high energy cosmic background generate a very small background). The 779 keV photopeak, on the other hand, lays on a ∼ 15% background level. This is true for each slice of the sector and it's due to the relatively low branching ratio of the 779 keV emission. In fact, the 344 keV photopeak has a large peak component (∼ 95%) due to the higher branching ratio and detection eciency despite the fact that it lays on a background level which is two times larger. This is true for the rst four segments of the sector, since, due to gamma-ray absorption, the value reach 87% and 67% levels in the fth and sixth slices.

Finally the 122 keV photopeak has a large P/T ratio in the rst two slices, but the value decreases rapidly to 66% in the third slice, due to gamma-ray absorption, and nally the peak disappears in slices 4, 5 and 6. Thus, for the 122 keV energy it is meaningful to reliably build a database only for the rst two slices.

With this premise, four databases for the four energies of interest were produced.

As a rst test the 779 keV database is compared with the 662 keV database, since they are close in energy. It is possible to make a rst comparison of the two databases by looking at the distribution of parameters such as the T 90 10 (dened in section 7.2. Indeed, if two pulses with the same coordinates are compared, as in gure 7.35, it can be seen that they are almost identical. The comparison can be extended to all the points of the two databases and, as done in sections 6.1.3 and 6.2.1, the residuals of two pulse shapes, taken at the same point of the two databases, is calculated and the maximum residual value is used as comparison index (see the green signal in gure 7.35). The distribution of the residuals for some slices are shown in gure 7.36. They are quite homogeneous in each slice despite some points having high values (dark red) which appear to be concentrated near the core contact and the segmentation lines.

The average value for each slice can be calculated and the results plotted as a function of Z C as in gure 7.37a. The graph shows that the average maximum residual per database slice has a value of 2% to 3% toward the front of the detector that increases slightly towards the back of the crystal where it reaches values up to 6% at the very back. Moreover, in correspondence of the segment separation surfaces (Z C = 14 mm, 22 mm, 36 mm, 56 mm, 74 mm) a slight value increase is observed. The same analysis can be redone by just taking into account the transient pulses. The graph, in gure 7.37b, shows that the average maximum residual between transient pulses is lower with respect to the main signals, ranging in the interval 1% ÷ 3%. It has to be said, however, show the comparison between the 122 keV and the other energies databases and as it can be seen, these data series don't follow any of the trends previously discussed. The total average maximum residuals have values of ∼ 5% percent in the front slices of the database and then increase to ∼ 10% toward slice 2 of the detector.

The causes of these discrepancies are most likely to be searched in the PSCS implementation or the χ 2 selection rather than in the physics of the system. However at the present state of the analysis no solid elements are found indicating where the PSCS, for low energies, lead to divergent databases. As a rst hypothesis one can think that the discrepancies are due to the statistics. For example, for the series relative to the 344 keV database, it can be noted that the most divergent points in slice 5 are concentrated around the core contact extending in the bulk of the detector (see gure 7.39), hinting that the discrepancies may be related to the gamma ray absorption that lowers the statistics of vertical datasets. However this hypothesis can be rejected by looking at table 7.5 where the area of the photopeaks of interest, with the background subtracted, is shown for each detector slice. In fact, for example, the number of 344 keV events in the fth slice detector is bigger than the ones of 779 keV and 1408 keV . Another factor that can cause discrepancies is the noise level of the pulses used for the χ 2 selection. For example, the noise amplitude of the 122 keV pulses is, in average, ∼ 5 keV and ∼ 2 keV for the core and segment contacts, respectively (see table 4.2 and gure 7.40). Such high distortion, especially on the core contact, can inuence the χ 2 selection . High levels of noise can also lead the T 10 time alignment to failure as the T 10 value can be incorrectly found on the noise (as shown in gure 7.40) and the χ 2 selection would then be performed on events that are not properly aligned. Finally, such levels of noise can inuence the selection on the transient signals which can be too noisy.

In conclusion, the analysis presented above gives elements that goes into the direction of the hypothesis that the pulse shapes are independent from the energy of the interaction. The databases calculated for energies > 500 keV match, in average, within 5% and the 344 keV database follows the same trend until Z C = 40 mm. Nevertheless, further tests should be lead to improve the χ 2 selection algorithm when operating at low energies. Some propositions, that were already made at the end of chapter 6, include using dierent weights for the main and transient pulses, or use non-euclidean metrics for the calculation of the χ factor. For the low energy pulse shapes, noise could be attenuated using ltering or techniques like the Fourier transform noise canceling (although this could aect the shape of the signals). Moreover, dierent scanning conguration could be tested, for example performing a horizontal-horizontal scan which would enable large statistics for large Z C , keeping reasonable statistics close to the bored hole and which would enable checking the impact on the database of low energy gamma rays.

Conclusions and perspectives

A study of the PSCS technique implemented at IPHC to scan germanium detectors in 2D and 3D was performed and the results were discussed in this thesis. The aim of this work is to characterize the accuracy and the critical points of the scanning procedure in order to estimate whether the PSCS technique is able to provide full crystal volume, experimental, pulse-shape databases. The work has been carried out through the use of simulations and real measurements.

The results of the simulations of the Strasbourg scanning system were presented rst.

A simulation of a full volume scan of a planar 3 × 3 pixelated detector was performed with a gamma-ray beam energy of 662 keV ( 137 Cs source). The simulation was realized with Geant4 and ADL softwares, using SIMION to calculate the electric elds and weighting potentials of the detector. The rst parameter extracted from the analysis was the percentage of the selected pulses generated by a single interaction on the total number of events. The values obtained indicate a percentage of single interactions of about 21% on average, which is lower than expected. To improve the selection of single interaction events, the use of a second algorithm (IPP search algorithm) to lter the data was tested. This technique did not prove its eectiveness to select a larger percentage of single interaction events because the useful information is overwhelmed by the signal noise. Since it was not possible to reject multiple interaction events, their inuence on the average pulse shape at each point of the scan grid was inquired. The analysis showed that the many interaction points of multiple interactions are placed relatively close to each other and that the average value of their distance from the point of the scan grid considered is around 6.2 mm. Moreover it was observed that the multiple interaction pulses selected by the PSCS technique are similar to those of single interactions. For this reason it was concluded that the multiple interaction pulses selected by the PSCS technique do not contaminate the database. Finally, the database obtained by the PSCS technique was compared with the theoretical one calculated with ADL. For the comparison, the maximum amplitude dierence calculated sample-by-sample among two geometrically corresponding supertraces (ensemble of all signals, core and segments, represented in one compact signal) was taken as a quality parameter. The analysis showed that the two databases are mostly in agreement, with an average maximum residual value of 3% of the full energy in the bulk of the segments. Exceptions were found along the segmentation surfaces where edge eects, caused by limitations of the PSCS technique, increase the value up to 16%.

The same analysis was repeated with an AGATA S-type detector which was virtually 143 type of electron trap, with large trap concentration, located in a thin plane of less than 1.5 mm thickness. It extends from the bored-hole to a radius value of about 20 mm.

This analysis shows the sensitivity of the scanning technique used and the interest of full crystal volume, 3D scans. Finally, the 2D scans allowed to measure some structural characteristics of the detector, such as the width of the segmentation lines at the front of the detector, the diameter of the central bored hole, the position of the contacts and the cabling of the detector (still dicult to evidence). These measurements showed the imaging capabilities of the IPHC scanning table.

Subsequently, three-dimensional scans were performed with the 137 Cs and 152 Eu sources. Due to the low activity of the source, the europium scan was restricted to one sector of the detector (sector B). The europium scan allowed to construct four dierent databases of pulses, with dierent energies, in a single measurement. The databases were built for the energies 122keV , 344keV , 779keV , 1408keV (europium) and 662 keV (cesium). A comparison was made within each other, and the maximum residual value between two signals associated to the same point of the database was chosen as comparison parameter. The databases with energy > 500keV proved to be comparable within each other, with dierences varying along the crystal length (front to back) from around 2% to about 3% and up to 6% at the very back, in average. Some discrepancies were instead found with the 344 keV database for Z C values larger than 40 mm. The residual values appeared to diverge by a factor 2 towards the back of the detector. Finally the 122 keV database proved to be strongly divergent from the other databases. It was supposed that the reasons behind these divergent behaviors are to be attributed to the PSCS technique that somehow is not ecient at low energies, since the small amplitude of induced signals is strongly aected by the signal noise.

The analysis, above summarized, opens for new perspectives and research opportunities, both for simulations and measurements. The PSCS limitations shown in the analysis can be overcome by proposing improvements for the PSA. Taking inspiration from the work presented in [START_REF] Lewandowski | Pulse-Shape Analysis and position resolution in highly segmented HPGe AGATA detectors[END_REF], dierent metrics may be taken into account for the pulse selection algorithm. The χ-like formula (4.1) would then became χ α where α is a value that can be optimized in order to maximize the fraction of selected single interactions and minimize the average distance of the interaction points from the respective database position. Another way to improve the χ 2 selection could be the use of weights for the transient signals to give them more or less impact on the database construction.

This option was preliminarily tested in [START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF] and a more systematic study with extensive simulations could be done. Moreover the use of noise ltering techniques, such as the Fourier transform noise canceling, could be evaluated, especially for low energy pulses where the PSCS appears to be more aected. If these techniques lead to improvements on the PSCS technique, then they can be applied to real measurements to verify if the discrepancies found between the dierent energy databases are reduced. In order to enable measurements with low energies in a full sector volume using the 152 Eu source, a horizontal-horizontal conguration could be tested. It would reduce statistics issues for low energy gamma-ray beams towards the back of the detector. Finally, it would be interesting to compare the databases obtained by the IPHC scanning table with the ones from other scanning tables exploited by the AGATA collaboration by using the same capsule mounted in a given test cryostat moved from one place to the others. The measurements performed with the 152 Eu source have evidenced the need to buy sources of smaller diameter (1 mm or less to be compared to 3 mm for the actual ones) more compatible with the diameter of the new collimators. Keeping the same source activities would speed up the scans by a factor around 10 making europium measurements as fast as the present cesium scans.

Using these more ecient gamma-ray sources, other tests could be performed making use of the new conguration of the scanning table. In particular, the 152 Eu source combined with the ne collimation of gamma rays (0.5 mm and 0.2 mm) could be used to determine the possible impact of the charge cloud, produced by an interacting gamma ray, on the shape of the pulses. In addition, it would be possible to extract from specic measurements across a segmentation line, the size of the charge cloud which is supposed to vary with the gamma-ray energy release. This study may be performed in conjunction with dedicated COMSOL [74] calculations. Also, ner collimators could be used to perform a deep analysis on the charge carriers behavior in a large HPGe detector (as the S001 anomalous zone for further exploration).

To be complete, the IPHC scanning table could certainly be used to carry out R&D work on position-sensitive detectors. For example, the impact of more exotic geometries and segmentations on the spatial sensitivity of the detector (such as the point-like, well detector [START_REF] Cooper | A novel HPGe detector for gamma-ray tracking and imaging[END_REF]), surface and crystal volume eects of new surface treatments (impact of new passivation treatments, Sb n+ contact, crystal coating as presently developed in LNL, Italy), spatial identication or even characterization of degraded charge collection areas in a defective crystal could be performed with high resolution and precision and in short times. 241 Am, E γ = 60 keV ), de césium ( 137 Cs, E γ = 662 keV ) et d'europium ( 152 Eu, source de nombreux gamma en cascade) sont à disposition pour les scans. Depuis la modication du collimateur, trois parties centrales du collimateur sont interchangeables. Elle sont constituées de cylindres de tungstène perforés de façon coaxiale par des trous de 1 mm, 0.5 mm et 0.2 mm de diamètre. L'emploi des trous de collimation dépend de l'objectif de la mesure. Le trou de 1 mm permet de réaliser des scans 2D et 3D. Celui de 0.5 mm permet des scans 2D pour une imagerie de précision. Celui de 0.2 mm devrait servir à déterminer la taille du nuage de porteurs électrons et trous. Les données obtenues des simulations sont analysées avec un code spécialement écrit qui eectue la sélection par χ 2 pour la technique PSCS. Le fonctionnement du code peut être résumé comme ci-dessous. Les ensemble de jeux de données V et H sont ltrés et nettoyés des signaux générés par les événements dans lesquels les rayons gamma ne sont pas absorbés par un seul segment du détecteur. Les diérents chiers des deux jeux de données sont ensuite comparés par couple en utilisant la sélection de type χ 2 à la n de laquelle les 400 meilleurs signaux sont sélectionnés pour chaque point de la grille de scan. Ces signaux sont ltrés encore une fois (procédure de ranement) et moyennés pour obtenir le signal au point (x,y,z) qui fera partie de la base de données.

Pour chacun des signaux, les informations sur les positions des interactions qui les ont générées (positions et énergies déposées) sont enregistrées.

Les simulations de la technique PSCS ont été eectuées sur un détecteur HPGe planaire segmenté et une unité AGATA de type S. Le premier détecteur mentionné est modelé sur une copie réelle du détecteur propriété de l'IPHC. La simplicité de sa géométrie a été utile lors de la phase de conception des simulations et de l'analyse ultérieure des données. La même approche a ensuite été utilisée avec des simulations du détecteur de type S plus complexe.

Le détecteur planaire a une forme rectangulaire avec un volume actif de 51 × 51 × 19.9 mm 3 . Le contact au bore est pixelisé en 3 × 3 générant neuf électrodes de 17 × 17mm 2 . Le contact opposé est diusé au lithium et mesure l'énergie totale déposée dans le cristal. C'est le contact "core". Le scan complet de ce détecteur est simulé au pas de Comme indiqué précédemment, la même analyse a été répétée avec le détecteur AGATA de type S. Le scan est également eectué au pas de 2 mm et l'énergie des rayons gamma utilisée est de 662 keV (source de césium). Les résultats obtenus ont prouvé, une fois encore, l'ecacité de la technique PSCS appliquée à un détecteur sensible à la position. En général, les valeurs des paramètres obtenus pour le détecteur de type S indiquent que la technique PSCS est plus performante que pour le détecteur planaire segmenté. En particulier, le taux d'événements single sélectionné est en moyenne de ∼ 50% (55% à l'avant du détecteur et 45% à l'arrière) à comparer à 21% pour le détecteur planaire. La cause peut être attribuée à la complexité accrue de la géométrie de segmentation du détecteur, qui ore par conséquent une meilleure résolution spatiale.

En prévision de la modication du collimateur (trous de collimation de 1.0 mm, 0.5 mm et 0.2 mm) et de l'utilisation d'une source de 152 Eu, des simulations supplémentaires sur le détecteur de type S ont permis d'étendre l'analyse de l'ecacité de la technique PSCS. En particulier, l'impact de l'énergie des rayons gamma et du nombre d'événements utilisés pour la sélection de type χ 2 sur le résultat nal de la technique PSCS a été examiné à 122 keV , 344 keV , 779 keV et 1408 keV . L'analyse a montré que l'énergie du rayonnement gamma a un impact non négligeable sur la sélection des interaction single et a peu d'eet sur la distance des interactions du point de la base de données considéré, mais il n'a pratiquement aucun impact sur la comparaison des bases de données. L'impact de la statistique d'entrée a également été analysée en utilisant 1000, 6000 et 60000 événements, pour chaque jeu de données V et H, pour la procédure de χ 2 . Le nombre d'événements utilisés a, en eet, un impact sur la sélection. La technique PSCS est généralement plus performante lorsque la statistique d'entrée est plus élevée. Cependant, la comparaison entre la base de données calculée par PSCS et la base théorique calculée via ADL, eectuée en extrayant le maximum de résidus entre les signaux des deux bases des données, ne semble pas dépendre de ce paramètre.

Parallèlement aux simulations, de vrais scans ont été réalisés avec le détecteur AGATA de type S, S001. Ce détecteur est un cristal quasi-coaxial de grande taille

Figure 1 . 1 :

 11 Figure 1.1:Photon absorption cross section for germanium with the various contributions to the total cross section. Data from[START_REF]NIST XCOM photon cross sections database[END_REF].

Figure 1 . 2 :

 12 Figure 1.2: Simple photoelectric eect scheme.

Figure 1 . 3 :

 13 Figure 1.3: Simple Compton scattering eect scheme.

Figure 1 . 4 :

 14 Figure 1.4: Compton scattering spectrum. A continuum of energies can be transferred to the electron within the interval [0, π]. The Compton edge corresponds to θ = π. Ec is the energy dierence between the actual incident gamma-ray energy and the Compton edge. From [27].

1. 4 .Figure 1 . 8 :

 418 Figure 1.8: Possible gamma-ray interactions outcomes in a medium sized detector and respective predicted response function for low and medium-high energies.

Figure 2 . 1 :

 21 Figure 2.1: Band structure schemes for insulator, semiconductor and conductor materials.

Figure 2 . 2 :

 22 Figure 2.2: (a) Germanium (silicon) covalent bonding. On the left all the electrons participate to the bonding, on the right one bond due to thermal energy is freeing an electron and leaving a hole. (b) Germanium cubic diamond structure with the crystallographic axes.

2. 4 .Figure 2 . 3 :

 423 Figure 2.3: (a)Drift velocity in germanium along axis < 111 > as a function of the electrical eld. From [27]. (b)Drift velocity in germanium along the three main crystallographic axes as a function of the electrical eld. From [29] and references therein.

Figure 2 . 4 :

 24 Figure 2.4: Scheme of donor and acceptor impurity levels induced in the energy bands by doping agents.

Figure 2 . 5 :

 25 Figure 2.5: pn junction principle scheme. The charges drift from their original doped region creating a charge gradient Q which generates the electric eld E and its respective contact potential V . From [24].

23 Figure 2 . 6 :

 2326 Figure 2.6: pn junction scheme with an applied reverse-bias voltage.

CHAPTER 2 .Figure 2 . 7 :

 227 Figure 2.7: Common geometrical congurations for germanium detectors: (a) planar conguration; (b) coaxial congurations.

Figure 2 . 8 :

 28 Figure 2.8: Variation of the electric-eld strength, along the depth of a 2 cm thick planar detector.In (a) the impurity density VD is set at 10 10 cm -3 and the variation is shown for dierent values of the applied bias V . In (b) the applied bias V is xed at 4000 V and the variation is shown for dierent impurity densities VD.

12 )

 12 Plots of the electric-eld intensity along the crystal radius are shown in gure 2.9 for

  symmetric detector geometries, such as planar or true coaxial congurations, have analytical solutions. The solution to the Poisson equation for more complex geometries is obtained numerically by nite dierencing techniques on a point grid.

  (or image charge) and the signals obtained from it are called transient signals (or image signals).

Figure 2 .

 2 Figure 2.11: Pulse-shape examples in a coaxial detector.

Figure 2 . 12 :

 212 Figure 2.12: Pulse shapes for interactions in a planar detector at one extreme of the active volume. (a)Absence of trapping, (b) permanent trapping and (c) trapping with de-trapping. The fast and the slow components of signal (c) are indicated by the arrows. Adapted from [33].

Figure 2 . 13 :

 213 Figure 2.13: Photopeaks at 1332 keV measured with a planar, ∼ 6 mm thick, GeLi detector. The detector is irradiated laterally at dierent positions x in the crystal depth (listed at the top right of the gure, with d the crystal thickness of the active volume) by the collimated60 Co source. The dashed line represents the sum of all the photopeaks and is compared with a photopeak obtained with a free60 Co source (uniform irradiation). From[START_REF] Gutknecht | Phénoménes de capture des porteurs de charge dans les détecteurs au germanium compensé au lithium[END_REF].

Figure 3 . 1 :

 31 Figure 3.1: (a) Simple schematics of EUROBALL detectors. The germanium detectors are shielded by BGO detectors that suppress the events in which a gamma ray doesn't release all its energy in a single detector (cases B and C). (b) Spectrum of a 60 Co source measured with Eurogam array detector. For the spectrum labeled with the letter A the Compton escaping events are not suppressed. The spectrum labeled with the letter B shows the sizable background reduction due to the Compton suppression. From [10].

Figure 3 . 2 :

 32 Figure 3.2: Spectra obtained with AGATA (in a limited, nine detectors, conguration) and EXOGAM coupled with VAMOS in two dierent experimental runs. Gamma-ray energies are gated on 98 Zr produced in the 238 U (6.5 M eV /A) + 9 Be fusion-ssion reaction. The two spectra are obtained in the same experimental conditions, although the two runs had dierent durations, with the AGATA one being shorter. AGATA spectrum shows clearly a better resolution and the potentiality of the complete array. (J. Dudouet, IP2I, Private Communication).

  (a) Rendered gures of the AGATA detector array. The full array composed by 180 hexagonal shaped detectors is visible on the left; the yellow line highlights 3 detectors grouped in the same cluster. On the right a realistic 1π assembly of the array is shown. (b) Picture of a triplet mounted in a triple cryostat. The triplet cover is shown in semi transparency for greater clarity. (c) Picture of the AGATA array composed of 11 triple clusters during the GANIL physics campaign.

Figure 3 .

 3 Figure 3.3

3

 3 Figure 3.3

Figure 3 . 4 :

 34 Figure 3.4: (a) Dimensions (in mm) of the three shapes of the detectors forming the AGATA array (A, B and C), and the prototype S. (b) The six slices of the detector are shown with their respective labeling. The hexagonal shaped slice are toward the front of the detector. The segment labeling corresponds to the detector seen from its back side. (Adapted from [22])

Figure 3 . 5 :

 35 Figure 3.5: Scheme of the AGATA preampliers. The cold (warm) stage of the preamplier is highlighted in blue (orange). The circuit highlighted in green allows the TOT technique (see text for more details). From [40].

Figure 3 . 6 :

 36 Figure 3.6: (a)Example of supertrace coming from a S-type AGATA detector plotted as a (see text for detail). The signals are normalized with respect to the amplitude of the core signal. In panel (b)the core signal is shown isolated. T 10 and T 90 mark the time at which the signal reach the 10% and 90%, respectively, of its maximum amplitude. The dierence between T 10 and T 90 , quoted as T90 10 , corresponds to the rise time of the preamplier pulse. (c) Simple scheme of the MWD algorithm. The input signal is re-shaped into a trapezoid which characteristics are labeled in the scheme. The energy reading corresponds to the energy average for the samples in the peaking area window, highlighted in red. The sum τ of the rise time, the at top shift and the peaking area is called shaping time.

Figure 3 .

 3 6a shows an example of signals generated by a 662 keV gamma ray interacting in a S-type AGATA detector. The signals are shown as a supertrace, a compact representation of the leading edges of each channel of the detector. The signals coming from AGATA detectors have rise times that range

Figure 3 . 7 :

 37 Figure 3.7: Simple representation of the PSA and tracking procedure. The outcome shows three dierent types of event. In event (A) the gamma ray gets absorbed by photoelectric eect; in event (B) the gamma ray interacts through Compton scatterings in two dierent detectors of the array and then gets absorbed by photoelectric eect; in event (C) the gamma ray interacts through Compton scatterings in the same detector and then gets absorbed by photoelectric eect.

Figure 3 . 9 :

 39 Figure 3.9: Experimental sensitivity of the gamma-ray arrays of the past decades as a function of the nuclear spin of the studied system. (J. Simpson, UKRI STFC, Private Communication.)

  lators) are placed around it forming a circle. A perforated tungsten mask is placed in front of each TOHR detector. The mask act as many small oriented collimators giving each detector a focal point. The TOHR detectors are installed so that their focal points coincide. By translating vertically the structure holding the TOHR detectors and rotating the scanned detector and translating the collimated source along one axis, it is possible to change the focal point relatively to the scanned crystal and thus perform a full volume scan. The Orsay table scans 2000 points in about one month.

Figure 4 . 1 :

 41 Figure 4.1: Simple scheme representing the operations needed to perform the PSCS technique. On the left the detector is in vertical conguration while on right the detector is in horizontal conguration. In this example the scan has a 2 mm pitch.

Figure 4 . 2 :

 42 Figure 4.2: Picture of the scanning table:(1) LN2 pipes, (2) test-cryostat Dewar, (3) adjustment frame, (4) holding plate for vertical positioning, (5) holding plate for horizontal positioning, (6) xing studs,[START_REF] Diamond | Proposal for a high resolution ball[END_REF] end cap of the detector, (8) collimator, (9) scanning table motorized axes, (10) alignment laser. The reference frame of the table [XT , YT ] and the reference frame of the detector (crystal) [XC , YC , ZC ] are shown in green.[START_REF] Sigward | Pulse-Shape Comparison Scan of germanium detectors using the IPHC scanning table[END_REF]

3 .

 3 The base of the collimator holds a cylindrical capsule containing the gamma-ray source. The base can slide down in order to open the collimator, allowing the swap of the source capsule. The capsule and the overall collimator are coaxial. Along the central axis of the capsule a channel with 1.6 mm diameter is pierced. This channel runs from the top of the capsule to its center where the source is actually placed. Another channel, 165 mm long, is pierced through the central axis of the collimator and is jointed with the capsules one. There is one capsule per gamma-ray source. Two congurations exist for the central part of the detector. The two will be referred as original conguration and upgraded conguration.In the original conguration, the central part is made by 5 short pierced cylinders with an internal diameter of 2.5 mm and a length of 23 mm. On top of these, 4 lead cylinders lead to the exit of the collimator. Finally, a T a tube with an external diameter of 2.5 mm and an internal diameter of 1.5 mm runs through the cylinders. The upgraded conguration 1 allows to mechanically swap the central part of the collimator. It is possible to choose between three central parts which have diameters of 1.0 mm, 0.5 mm and 0.2 mm.1 The upgrade of the collimator took place during the course of this work.

Figure 4 . 3 :

 43 Figure 4.3: Rendered section of the collimator. The materials that compose the collimator are reported in the legend. A red circle highlights the capsule containing the gamma-ray source.

  cards cover both the digitizing and pre-processing of the signals done by the standard AGATA electronics (see section3.3.1). Each card has 4 channels, so 10 cards are used during the scan of an AGATA detector unit, 9 for the 36 segments and one for the core signal used as trigger. Each channel samples the incoming signal with 14 bit resolution and 100 M Hz rate, subsequently the energy is read applying the MWD algorithm (see section 3.3.1). For the measurements shown in this work, the signals were sampled in a time window of 1.2 µs (120 samples) and a 5.95 µs shaping time (k = 4 µs , m = 2 µs, s = 1.75 µs, w = 0.2 µs, see gure 3.6c) was used for the MWD procedure. The acquisition chain is structured as follows. The dierential signals coming from the detector preampliers are carried to the DAQ via MDR cables and converted to single-ended signals by dedicated modules before entering the TNT2 cards. The 10 TNT2 cards are linked in a daisy chain, with the core card being the master. The DAQ is triggered each time the master card receives a signal from the core. The DAQ is managed through a workstation linked to the cards via USB. Finally, during the data acquisition, all the data are transferred and stored on a dedicated workstation.

Figure 4 . 4 :

 44 Figure 4.4: Geant4 render of the S001 detector and collimator geometry used for the Monte Carlo simulation.

Figure 4 . 5 :

 45 Figure 4.5: Simple schematics of the planar 3 × 3 pixelated HP Ge detector. The sizes of the segments and the guard ring are shown in the top panels along with the distances of the center of the detector, placed both in vertical and horizontal conguration, to the front face of the collimator. The picture on the bottom shows the cold electronics of the segments which is facing the pixelated contact and is highlighted by the blue outline.

(4. 2 )

 2 where I(t) is the input current. It is possible to extract the response function from the preamplier output signal if the input current is known, by deconvolving equation 4.2. For the simulations presented later in this work, the response functions for both the S001 detector and 3 × 3 segmented detector were convoluted with the corresponding calculated signals.The response function used of the S001 detector was extracted from the AGAPRO software source code. AGAPRO [66] is a software used by the AGATA collaboration that contains routines and algorithms to process the data ow coming from the AGATA acquisition system. The response function, shown in gure 4.6, is derived from data taken during the LNL (Laboratori Nazionali di Legnaro) experimental campaign using a pulser. Both the core and segments response functions were sampled, in fact these two possess dierent characteristics due to the fact that the core contact has dierent (bigger) intrinsic capacitance with respect to the segment contacts. Due to this, generally core signals have slower leading edges than the segments ones.

Figure 4 . 6 :

 46 Figure 4.6: (a) Response functions for the AGATA detector. (b) Response functions for the 3x3 segmented detector.

59 Figure 4 . 7 :

 5947 Figure 4.7: Pictures of the test box used to measure the response function of the 3 × 3 pixelated detector. On the left, a plugged preamplier can be seen.

Figure 4

 4 Figure 4.8: (a) Input signal used to measure the response function of the 3 × 3 pixelated detector. (b) Inverted output signal measured from the core preamplier. (c) Output signal measured from one of the segments preamplier.

4. 4 .

 4 BEAM SIMULATIONS AND MEASUREMENTS 61 S001 detector and ∼ 50000 for the 3×3 pixelated detector. The histograms show that, as expected, the noise has a Gaussian prole. Also, it is assumed that the amplitude of the noise is independent of the amplitude of the considered signal. A Gaussian t allowed the extraction of the noise amplitude as the σ of the curve. The extracted values are reported in table

Figure 4 . 9 :

 49 Figure 4.9: Scheme of noise extraction procedure.

CHAPTER 4 .

 4 Figure 4.10: Beam prole projection on the ZX plan for both the americium (a) and cesium (b) sources. The collimator is in the original conguration.

Figure 4 . 11 :

 411 Figure 4.11: Beam prole sections at dierent heights above the collimator Z = z -zp for both americium (a) and cesium (b) sources. The prole sections are obtained by considering the events in a 50 µm thick slice at the center of the beam spot.

Figure 4 . 12 :

 412 Figure 4.12: Pictures of the experimental setup for the beam-prole measurement with the IPIX detector. (a)The IPIX detector is placed on a lifting platform (b) perpendicular to the beam direction.

Figure 4 . 13 :

 413 Figure 4.13: Beam spot distribution of the americium source measured at Z = 3 mm for the 1.5 mm collimator. (a) 2D distribution and (b) beam prole tted with equation 4.4.

Figure 4 .

 4 Figure 4.14: (a) Vertical section of a S-type AGATA detector (cut at YC = 0 mm) implemented in ADL. The black lines roughly show the separations between segments. The white line indicates the beam path used for this simulation. The numbers show the name of the respective segments. The D and A sectors are highlighted in shades of red and blue, respectively. (b) Horizontal top section of the same detector. The white dot indicates the xC , yC coordinates from which the beam is propagated. The 6 slices are highlighted in dierent colors.

Figure 5 . 1 : 70 CHAPTER 5 .

 51705 Figure 5.1: Simple work-ow scheme.

Figure 5 . 2 :

 52 Figure 5.2: ADL I/O scheme (adapted from[START_REF] Bruyneel | Pulse shape analysis and position determination in segmented HPGe detectors: The AGATA detector library[END_REF]). In blue and red are represented the parameters or inputs to be set in the code while in green are represented the dierent routines that form the code.

5. 1 .

 1 THE AGATA DETECTOR LIBRARY (ADL) 71 image charges at the electrodes of the detector are created instantaneously in response to the charges created in the bulk of the detector. Furthermore it is assumed that the extra eld generated by the charges created by the gamma radiation is negligible compared to the external applied collection eld.

Figure 5 . 3 :

 53 Figure 5.3: (a) Type-S AGATA detector geometry as it appears in the SIMION visualizer. (b),(c) Weighting elds of segment A3 calculated with SIMION. The values are relative to Z = 32 mm for (b) and Y = 0 mm for (c).

2 .

 2 ADL allows to regulate some parameters of the pulse shapes such as the time alignment of the signal (trigger time), the number of time steps (samples) and the step size (time resolution or sampling rate). For this work, the pulses are 100 samples long and are calculated with a step size of 10 ns (sampling rate of 100 M Hz). The paths of the charges along the electric eld are calculated with the 5th-order Runge Kutta integration method with adaptive step size control. The induced signals for every electrode of the detector are calculated depending on the drift of the electrons and holes to the electrodes. For every time step and for each interaction the weighting eld evaluated at the position of the electrons is subtracted from the weighting eld evaluated at the position of the holes. These dierences are multiplied by the charge produced at the individual interaction. The sum of all interactions result in the signal set for the given event. In order to have a realistic output, the resulting signal can be convoluted with the response function of the preampliers and the crosstalk function. The used response functions were discussed in section 4.3.1. The crosstalk, instead, was not considered for this work mainly because the selected events are single segment hits, but also because crosstalk don't have an inuence on the nal shape of the signal. Finally, realistic noise (see section 4.3.2) was added to the nal signals though a Gaussian random generator which was initialized with the measured values. Examples of calculated signals can be seen in gures 5.4 and 5.5. In the former, a signal generated by a single interaction in the simulated S001 AGATA detector is compared with the corresponding signal extracted from a measured database of the detector S001 (see chapter 7). In the latter, dierent signals are generated with ADL by single interactions in the S001 AGATA detector at dierent positions. The top gure shows the signals for dierent interaction radii: the graph in the center shows the main signal generated by the hit segment, while the four graphs around show the transient signals of the neighboring segments. The graphs also show the dierence in the maximum amplitude between the main signal (normalized to 1) and the transient signals. The gure on the bottom shows the signals for dierent interactions along a xed radius. As the radius is xed, the rise-time of the main pulse remains constant (there is a slight change due to the fact that charges speed depends on the germanium crystal orientation). On the other hand the amplitude of the transient signals changes with the interaction position: as the interaction approaches a neighboring segment, the respective transient signal (left or right) grows in amplitude.

Figure 5 . 4 :

 54 Figure 5.4: Comparison between a signal extracted from a measured database of the detector S001 (in red) and the corresponding signal calculated with ADL (in black). The rst two panels show the core and hit segment (B5) signals. A5 and C5 are the right and left neighbor segments, respectively. B6 and B4 are the top and bottom neighbor segments, respectively.

5. 2 .

 2 TREATMENT OF SIMULATED DATA AND χ 2 ALGORITHM 75 at which the beam should be shot are given to Geant4 via a script and for each position an individual output le is generated. The les contain information on the position and energy released by each interaction of each gamma ray that interacts in the detector (event).

Figure 5 . 6 :

 56 Figure 5.6: Renement procedure scheme.

Figure 6 . 1 : 3 × 3

 6133 Figure 6.1: 3 × 3 pixelated detector: numbering of the segments and reference frame used to present the results of the simulation. More details on the 3 × 3 pixelated detector are in section 4.3.

Figure 6 . 2 :

 62 Figure 6.2: (a) Number of interactions for 662 keV gamma rays that are fully absorbed in segment 5.

Figure 6 . 4 :

 64 Figure 6.4: Figures from[START_REF] Crespi | A pulse shape analysis algorithm for HPGe detectors[END_REF] reporting a study performed on a coaxial, multi-segmented MARS detector[START_REF] Th | A genetic algorithm for the decomposition of multiple hit events in the gamma-ray tracking detector MARS[END_REF]. Numerically calculated pulse generated from gamma rays interacting in a segmented true coaxial detector (schematized on the left) and its respective current signal. The signal is originated by a 2-fold interacting gamma ray, depositing 60% of its energy at R = 11.0 mm, θ = 22 • in the rst interaction and the remaining 40% at R = 31.0 mm, θ = 26 • in the second interaction. The signal on top shows the ideal case while the electrical noise, the transfer function of the preamplier and a digital ltering where added to the calculation of the bottom signal.

6. 1 .

 1 SIMULATIONS OF THE PSCS TECHNIQUE ON THE 3 × 3 DETECTOR 81

Figure 6 . 5 :

 65 Figure 6.5: Pulse, simulated using ADL, generated by a single-interacting gamma ray in the 3 × 3 pixelated detector at position XC = 25.5, YC = 5.0 , ZC = 25.5 and its respective current pulse. The signals on the left show the ideal case while a realistic electrical noise, the transfer function of the preamplier and a digital ltering where added to the calculated signals on the right. The time shifts of the signals in the right panels is due to the introduction of the transfer function.

Figure 6 . 6 :

 66 Figure 6.6: Pulse, simulated using ADL, generated by a two-fold interacting gamma ray in the 3 × 3 pixelated detector at positions X = 25.5, YC = 11.0 , ZC = 25.5, releasing 60% of the total energy, and XC = 25.5, YC = 3.0 , ZC = 25.5, releasing the remaining 40%. On the bottom the respective current signal is shown. The signals on the left show the ideal case while a realistic electrical noise, the transfer function of the preamplier and a digital ltering where added to the calculated signals on the right. The time shifts of the signals in the right panels is due to the introduction of the transfer function.

Figure 6 . 7 :

 67 Figure 6.7: Comparison between two current pulses selected by the PSCS technique for the same grid point. The signal on the left is generated by a gamma ray interacting twice, while the signal on the right is generated by a single-interacting gamma ray.

6. 1 .Figure 6 . 8 :

 168 Figure 6.8: Comparison between the simulated signals generated by single-interacting and multiinteracting gamma rays, selected by the PSCS technique at a given point of the database. The trace in black is obtained by averaging the signals generated by single-interacting gamma rays, while the trace in green is obtained by averaging the signals generated by multi-interacting gamma rays. The signal in red shows the residual between the two traces. The trace shown in (a) and (b) are from the database points X = 24.0 mm, YC = 10.0 mm, ZC = 24.0 mm and X = 32.0 mm, YC = 10.0 mm, ZC = 22.0 mm, respectively. In the rst case the maximum residual is obtained by the dierence of the main signals, while in the second case the maximum dierence lies between two corresponding transient pulses (see inserts).

Figure 6 .

 6 Figure 6.9 shows the maximum residual value for each point of a slice with a thickness of 1 grid unit (2 mm) at a given depth position (Y C ) in the detector. It can be seen that the values are quite homogeneous across the slice, with an average value of around 3%. The gure also shows that the maximum residual value tends to be higher along the segmentation lines of the boron contact. These are border eects which are mostly due to the fact that, as previously mentioned, signals at the borders, vary very rapidly meaning that a small dierence in the interaction position can lead to large dierence in the pulse shape of the transient signals. If these anomalous points are ignored, the value is constant across the volume of the detector and this shows that even if conceptually pulses formed by multiple interacting gamma rays should be rejected they don't pollute the database in a sizable way.

Figure 6 . 9 :

 69 Figure 6.9: Maximum residual value, in percent with respect to the maximum amplitude of the main signal, between the averaged signals of single-interaction events and the averaged signals of multi-fold events (see also gure 6.8). The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for YC =4 mm, 10 mm and 16 mm from left to right.

6. 1 .

 1 SIMULATIONS OF THE PSCS TECHNIQUE ON THE 3 × 3 DETECTOR 85 with a thickness of 1 grid unit (2 mm) at dierent depths (Y C ) in the detector. The values are once again quite homogeneous in the volume of the detector, oscillating in a range between 3.6 mm and 11.6 mm with an average of 6.2 mm, except in the proximity of the segmentation lines where the average values raise due to the reasons previously explained.

Figure 6 . 10 :

 610 Figure 6.10: Average distance (color scale in cm) of the interactions of the PSCS selected events from the position of their database point. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for YC =4 mm, 10 mm and 16 mm from left to right.

6. 1 .

 1 Figure 6.12: Comparison between a simulated PSCS signal and the corresponding ADL signal at XC = 24.0, YC = 10.0 , ZC = 24.0.

Figure 6 . 13 :

 613 Figure 6.13: Maximum residuals between simulated PSCS signals and their corresponding ADL signals. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for YC =4 mm, 10 mm and 16 mm from left to right.

Figure 6 . 14 :

 614 Figure 6.14: Comparison between a simulated PSCS signal and the corresponding ADL signal at XC = 36.0, YC = 6.0 , ZC = 34.0. It can be seen that for the PSCS track (in black) the main signal is generated in segment 8 while the theoretical track (in green) has the main signal in segment 9. The maximum of the residual track (in red) is then 100% of the maximum amplitude.

Figure 6 . 15 :

 615 Figure 6.15: Reference frame used to present the results of the PSCS technique analysis.

Figure 6 . 16 :

 616 Figure 6.16: Percentage of single-interaction events selected by the PSCS technique over the total number of events. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm. In the top-left panel, the segment labeling is shown while in the top-center panel the red arrow shows the horizontal beam direction.

Figure 6

 6 Figure 6.17: Percentage (pct.) of selected single-interaction events along the ZC direction. The bars show the standard deviation for slices at the front, center and back of the detector.

Figure 6 .

 6 Figure 6.18: Maximum residual value, in percent with respect to the maximum amplitude of the main signal, between the averaged signals of single-interaction events and the averaged signals of multipleinteraction events. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm. In the top-left panel, the segment labeling is shown while in the top-center panel the red arrow shows the horizontal beam direction.

6. 23 .Figure 6 . 19 :

 23619 Figure 6.19: Average distance (in cm) of the interactions of the PSCS selected events from the position of their database point. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm. In the top-left panel, the segment labeling is shown while in the top-center panel the red arrow shows the horizontal beam direction.

Figure 6 . 20 :

 620 Figure 6.20: Average distance (averaged in each 2 mm slice) of the interactions of PSCS selected events from the position of their database point along the ZC direction. The bars show the standard deviation for slices at the front, center and back of the detector.

6. 2 .Figure 6 .

 26 Figure 6.21: Furthest interaction distance of a multiple-interaction event from its rst interaction position versus its respective released energy. Each graph gathers the interactions of all the points for a slice of the database with a thickness of 1 grid unit (2 mm). The slices considered are at ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm.

Figure 6 . 22 :

 622 Figure 6.22: Maximum residuals between simulated PSCS signals and their corresponding ADL signals. The graphs are relative to slices with a thickness of 1 grid unit (2 mm) for ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm. In the top-left panel, the segment labeling is shown while in the top-center panel the red arrow shows the horizontal beam direction.

Figure 6 . 23 :

 623 Figure 6.23: Maximum residuals, averaged for each 2 mm slice, between simulated PSCS signals and their corresponding ADL signals along the ZC direction. The bars show the standard deviation for slices at the front, center and back of the detector.

Figure 6 . 24 :

 624 Figure 6.24: Scan results for the four considered gamma-ray energies. (a) Percentage (pct.) of selected single interaction events along the ZC direction for dierent gamma-ray energies. (b) Average distance of interactions of the PSCS selected events from the position of their database point along the ZC direction for dierent gamma-ray energies. (c) Maximum residuals between simulated PSCS signals and their corresponding ADL signals along the ZC direction for dierent gamma-ray energies. For all the graphs, the bars show the standard deviation for slices at the front, center and back of the detector.

Figure 6 . 26 :

 626 Figure 6.26: Values of the three considered parameters along the ZC direction for the 779 keV scans. (a) Percentage (pct.) of selected single-interaction events. (b) Average distance of the selected events from the position of their corresponding database point. (c) Maximum value of the residual signal between the simulated PSCS and ADL supertraces. The positions of the scanned points are given in gure 6.25.

Figure 6 . 27 :

 627 Figure 6.27: Values of the three considered parameters along the ZC direction for the 1408 keV scans. (a) Percentage (pct.) of selected single-interaction events. (b) Average distance of the selected events from the position of their corresponding database point. (c) Maximum value of the residual signal between the simulated PSCS and ADL supertraces. The positions of the scanned points are given in gure 6.25.

4 . 2 )Figure 7 . 1 :

 4271 Figure 7.1: Segment E1 local photopeak eciency as a function of the collimator position for a 100 µm pitch, 241 Am source scan. Left panel: schematic drawing showing the 11 scans (green lines) performed across the E1 -F 1 segmentation line (the YT of the lines are reported in table 7.1). The beam irradiates the detector from below (parallel to the ZT axis) and the moves from left to right for each one of the green lines. Right panel: the boundary of the segment corresponds to the abscissa x0 of the point laying on the t curve (solid red line) with an ordinate f (x0) = N/2.

Figure 7 . 3 :

 73 Figure 7.3: Local eciency graph of the linear scans across the E1 -F 1 segmentation line performed at 60 keV (see table7.2) to determine its width. The graph in (a) refers to the scan performed with a 1.0 mm diameter collimator and a 100 µm pitch at YT = 158 mm (see table7.1). The graph in (b) refers to the scan performed with a 0.5 mm diameter collimator and a 50 µm pitch at the same position. For both the graphs the red line refers to the data taken in segment E1, while the blue line refers to the data taken in segment F 1. Note that the measurement duration was 120 s for (a) and 2000 s for (b). In the latter case, background from the detector-laboratory environment lead to a minimum of about 1000 counts in the energy gate.

Figure 7 . 4 :

 74 Figure 7.4: Bored-hole alignment scanning procedure (see table7.2). (a) Cross scan and respective normalized local photopeak eciency histograms for slice 5. The red lines represent the linear ts performed on the edges of the eciency graphs. (b) Tilt of the vertical axes of the crystal after the alignment. Note that in this graph the ordinates refer to the scanning table reference frame (YT ) while the abscissas refer to the crystal reference frame (ZC). In this particular case, slice 6 was not considered for the t. See text for more details.

7. 2 .Figure 7 . 5 :

 275 Figure 7.5: Horizontal alignment procedure. (a) linear scan along the bored-hole of the detector. (b) Eciency graph for slice 3. The red lines represent the linear ts performed on the edges of the eciency graphs. (c)Tilt of the vertical axes of the crystal after the alignment. In this particular case, slices 1, 2 and 6 were not considered for the t. See text for more details.

109 7 . 2 . 1

 721 Local detection eciency: 137 Cs source

Figure 7 . 6 :

 76 Figure 7.6: Local detection-eciency distribution for the core (a) and the segments (b) at 662 keV . See text for more details.

7. 2 .Figure 7 . 7 :

 277 Figure 7.7: Europium core spectrum obtained from the 1 mm diameter collimator. The peaks of interest are marked by their energy and branching ratio.

1. 0

 0 mm, is performed on the S001 detector with an acquisition of 360 s per point which is short regarding the source activity and the branching ratio of the transitions. Gates on 122 keV , 344 keV , 779 keV and 1408 keV events are set and the local eciency (dened in the previous section) distributions are plotted for each considered energy.

Figure 7 . 8 :

 78 Figure 7.8: Local detection-eciency distribution for the segments at 122 keV .

Figure 7 . 9 :

 79 Figure 7.9: Local detection-eciency distribution for the segments at 344 keV .

Figure 7 . 10 :

 710 Figure 7.10: Local detection-eciency distribution for the segments at 779 keV .

Figure 7 . 11 :

 711 Figure 7.11: Local detection-eciency distribution for the segments at 1408 keV .

Figure 7 .

 7 Figure 7.12: T 90 10 distributions for the core (a) and the segment contacts (b) obtained with 662 keV gamma rays. The segment distributions are produced by considering the T 90 10 of the signals generated by the core gated on 1-fold events. Figure (a) shows the orientation of the < 100 > and < 110 > crystallographic axes and the angle θ4 between the crystallographic axis < 100 > and the detector axis XC (see text for more information).

Figure 7 . 13 :

 713 Figure 7.13: Experimental T 90 10 values, for the core (a) and each segment slice (b) obtained for a xed radius (see gure 7.12 and table7.3). The curves are t using equation 7.2 and θ is in radians. See text for more details.

Core - 16 . 8 •

 168 ± 0.7 • r = 23 mm Slice 1 -16.7 • ± 0.5 • r = 25 mm Slice 2 -16.6 • ± 0.8 • r = 27 mm Slice 3

CHAPTER 7 .Figure 7 . 14 :

 7714 Figure 7.14: Example of photopeaks tted with a Crystal Ball function. The Gaussian part of the function is plotted in blue and the tail in red. The spectra refers to segment F 3 and are built with the segment energy gated on 1-fold events.

Figure 7 . 15 :

 715 Figure 7.15: Core contact centroid-position distribution of the 662 keV photopeak.

Figure 7 . 16 :

 716 Figure 7.16: Distribution of the 662 keV photopeak centroid position for the core gated on 1-fold events in the segments contacts. Panel (a) shows that the centroid-position distributions for segments A2, A3 and F 6 are globally shifted versus the ones of the other segments. Panel (b) shows the distributions normalized at 661.7 keV for each segment. See text for more detail.

CHAPTER 7 .

 7 REAL SCAN OF THE S001 DETECTOR

Figure 7 .

 7 Figure 7.17: (a) Distribution of the 662 keV photopeak centroid position for the core gated on 1-fold events in the segments contacts as a function of the radius. The graphs are renormalized so that the nearest point to bored hole has a value of 661.7 keV . (b) Distribution of the 662 keV photopeak FWHM values for the core gated on 1-fold events in the segment contacts as a function of the radius.

Figure 7 .

 7 Figure 7.17b shows the FWHM average value, as a function of the radius, for the core and the slices of the detector. As it can be seen the photopeaks slightly widen

Figure 7 . 18 :

 718 Figure 7.18: Distribution of the 662 keV photopeak centroid position for the segment contacts gated on 1-fold events. The distributions are normalized at 661.7 keV for each segment.

Figure 7 .

 7 Figure 7.19: (a) Distribution of the 662 keV photopeak centroid position for the segment contacts gated on 1-fold events as a function of the radius. The graphs are renormalized so that the nearest point to bored hole has a value of 661.7 keV . (b) Distribution of the 662 keV photopeak FWHM values for the segment contacts gated on 1-fold events as a function of the radius.

Figure 7 .F 2 , F 3 and F 4 .

 724 [START_REF] Simpson | The EXOGAM array: A radioactive beam gamma-ray spectrometer[END_REF] shows the distribution of F oM for the core contact and for the six segment slices of the detector. The plots show that the F oM value is globally homogeneous except in some well dened areas. A trail of anomalous values is visible in segments These anomalous points can be seen as well in the distributions of the centroids (gure 7.18). Some of the spectra extracted from the trail are shown in gure 7.14. The trail seems to follow the charge-carrier trajectory (gure 7.21) suggesting 7.2. TWO-DIMENSIONAL SCANS 123 that the trapping center is actually concentrated in a narrow area inuencing the charge carriers on the path. Since, normally, trapping centers are homogeneously distributed in the crystal, the nature of this anomalous zone is not clear.

Figure 7 . 20 :

 720 Figure 7.20: Distribution of the factor of merit F oM for the core (a) and segment contacts (b) gated on 1-fold 662 keV events.

Figure 7 . 21 :Figure 7 . 22 :

 721722 Figure 7.21: Plot of the charge-carrier trajectories in the middle of segment F 3 thickness projected on the XY plane (red lines). The trajectories are superposed to the F oM distribution of slice 3 (see gure 7.20). The black circular markers highlight the points of the trail.

7. 2 .Figure 7 . 23 :

 2723 Figure 7.23: Characteristics of the two Gaussian components of the photopeak as a function of the radius. (a) Centroid positions. (b) relative distance between the two Gaussians. (c) FWHM values. (d) Ratio of the low end Gaussian area to the total peak area.

  lost and thus a second peak should appear in the lower end of the peak. The spectra have been successfully tted with a double Gaussian as shown in gure 7.[START_REF] Akkoyun | AGATA-Advanced GAmma Tracking Array[END_REF]. In gure 7.23a the centroid position of the two peaks is plotted as a function of the radius together 126 CHAPTER 7. REAL SCAN OF THE S001 DETECTOR with the average centroid value of slice 3. It can be seen that the high-energy peak follows quite nicely the values and the general trend of the slice, while the low-energy peak is shifted by, in average, ∼ 1.6 keV . The values are somehow at for R > 20 mm.The distance between the two Gaussian peaks is plotted in gure 7.23b and shows a growing trend which then saturates towards radii larger than 20 mm. The FWHM of the peaks, in gure 7.23c, also shows that the resolution of the high-energy peak follows the average of the segment (∼ 2 keV ) while the lower energy peak has a much larger FWHM (3.5 to 4 keV ). Finally the ratio of the low end Gaussian area versus the full peak area, shown in gure 7.23d, indicates that the low-energy component grows from the bored hole towards R 20 mm and saturates for larger radii.

Figure 7 .

 7 Figure 7.24 shows an example of one transversal slice of the database (2 mm thick), on the tapered section of the detector, before and after the ltering.

Figure 7 .Figure 7 . 25 :Figure 7 . 26 :Figure 7 . 27 :

 7725726727 Figure 7.24: A database slice at ZC = 14 mm (2 mm thick) before and after the ltering.

Figure 7 .Figure 7 . 28 :

 7728 Figure 7.28: Pulses along a circumference of the detector with R = 32 mm in segment A5.

Figure 7 . 29 :

 729 Figure 7.29: Pulses at the xed position XC = 20 mm and YC = 0 mm and along ZC of the detector in segment A5.

Finally gure 7 .Figure 7 .

 77 Figure 7.30: (a)Pulses along the irregular trail in segment F 3 discussed in section 7.2.5. (b) Pulses along the symmetrical trail in segment C3 (see gure 7.26d). All the pulses are taken from the database slice at ZC = 30 mm.

Figure 7 . 31 :

 731 Figure 7.31: Spectra for each of the six segments of sector B of a beam irradiating the center of the sector (XC = 10 mm YC = 20 mm). The red arrows indicates the photopeaks of interest (122 keV , 344 keV , 779 keV and 1408 keV ).

Figure 7 . 32 :

 732 Figure 7.32: Distributions of the T 90 10 in 6 slices of the 662 keV database (the histograms include part of sector A and sector B) (a) and the 779 keV database (sector B) (b). The slices considered are at ZC = 6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm.

Figure 7 . 33 :

 733 Figure 7.33: Distribution of the ICA lef t/right in 6 slices of the 662 keV database (the histograms include part of sector A and sector B) (a) and the 779 keV database (sector B) (b). The slices considered are at ZC = 6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm.

Figure 7 . 34 :

 734 Figure 7.34: Distribution of the ICA top/down in 6 slices of the 662 keV database (the histograms include part of sector A and sector B) (a) and the 779 keV database (sector B) (b). The slices considered are at ZC = 6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm.

Figure 7 . 35 :

 735 Figure 7.35: Comparison of two pulse shapes taken at the same point (XC = 10 mm, YC = 20 mm, ZC = 30 mm) of the 662 keV database (black line) and 779 keV database (red line). The green line shows the residual value between the two pulses.

Figure 7 . 36 :Figure 7 . 37 :

 736737 Figure 7.36: Distributions of the maximum residuals between the pulses of the 662 keV and 779 keV databases. The data are relative to the database slices at ZC =6 mm, 20 mm, 30 mm, 48 mm, 64 mm and 80 mm. The color scale indicates the percentages of the residual amplitude relative to the full energies normalized to 1.

Figure 7 . 39 :

 739 Figure 7.39: Distributions of the maximum residuals between the pulses of the 344 keV and 662 keV databases. The data are relative to the database slices at ZC = 58 mm, 60 mm, 62 mm, 64 mm, 66 mm and 68 mm.

Figure 7 . 40 :

 740 Figure 7.40: Examples of pulses used for the χ 2 selection interacting in segment B1. The pulse shown in (a) and (b) are relative to the 122 keV and 1408 keV datasets respectively. The noise in the 122 keV signal is non-negligible, while it has no inuence on the 1408 keV signal.

  Le faisceau des rayons gamma qui sortent du collimateur a fait l'objet d'une étude préliminaire réalisée par simulations à l'aide de GEANT4 et par des mesures réelles. La géométrie et les matériaux du collimateur, mais aussi les dimensions et la position des sources sont reproduits dèlement dans la simulation qui a permis d'obtenir les prols des faisceaux de rayons gamma pour les trois sources ( 241 Am, 137 Cs, 152 Eu) et d'estimer leur diamètre à diérentes distances du trou de sortie. Ces résultats ont ensuite été comparés aux mesures réelles eectuées avec un capteur IPIX pixelisé (fourni par la société MIRION Technologies Canberra). Il s'agit d'un capteur CdTe de 256 × 256 pixels chacun ayant une taille de 55x55µm 2 et de 1 mm d'épaisseur. Les résultats expérimentaux trouvés sont en bon accord avec les résultats des simulations. Cette étude a permis de vérier le bien-fondé de l'application GEANT4, qui a ensuite été utilisée pour réaliser d'autres simulations. L'étude a également permis d'obtenir des informations sur le diamètre de la tache du faisceau à n'importe quelle profondeur dans le détecteur. Des informations sur le rendement du collimateur pour les diérentes sources et leur taux d'émission ont également été extraites de la simulation. Enn, le calcul du taux d'absorption des rayons gamma par les segments d'un détecteur de type AGATA a été mené. Les résultats de ces simulations et mesures préliminaires ont été utilisés pour concevoir les simulations complètes de la technique PSCS et les mesures réelles. La simulation complète de la technique PSCS est réalisée à l'aide de GEANT4 et ADL. Le rôle de GEANT4 dans la simulation est de déterminer pour chaque absorption complète du rayon gamma dans un segment, les positions des point d'interaction et l'énergie déposée en chaque point. Une fois que les interactions sont simulées avec GEANT4, les signaux générés par le détecteur sont calculés grâce à ADL qui nécessite les éléments suivants: la description des champs électriques et des potentiels "de pondération" du détecteur, les paramètres de mobilité des électrons et des trous, l'orientation du cristal et la densité des impuretés. Les champs électriques et les potentiels "de pondération" peuvent être calculés par un solveur d'équation de Poisson. Dans ce travail de thèse, j'ai utilisé SIMION qui calcule les champs électriques et les potentiels à partir de la description de la géométrie du détecteur à simuler. Les autres paramètres ont été repris de la littérature. Enn, chaque signal calculé avec ADL est convolué avec un bruit réaliste et la fonction de réponse des préamplicateurs. Le bruit réaliste a été mesuré pour les deux détecteurs étudiés dans cette thèse, un détecteur planaire et un cristal AGATA symétrique S001 (voir ci-dessous). La fonction de réponse a été mesurée pour le détecteur planaire et extraite d'AGAPRO pour S001 (voir ci-dessous).

2

  mm et pour une énergie des rayons gamma de 662 keV (source de césium). Le premier paramètre extrait de l'analyse est la fraction des signaux sélectionnés générés par une interaction single sur le nombre total d'événements. Les valeurs obtenues indiquent une sélection d'interactions individuelles d'environ 21% en moyenne, une valeur bien inférieure à celle de 90% obtenue par la table de scan utilisée à Liverpool (qui est la table de scan de référence pour la collaboration AGATA). Pour essayer d'améliorer la sélection d'événements d'interactions singles, l'utilisation d'un second algorithme pour ltrer les données a été testée. Cet algorithme est en principe capable d'identier des événements à plusieurs interactions à partir de la première dérivée des signaux, c'est à dire à partir des signaux de courant. Ces derniers présentent des sous-structures dont le nombre est proportionnel au nombre d'interactions réalisées dans un segment par le rayon gamma qui l'a produit. Toutefois cette méthode n'a pas prouvé son ecacité, car les sous-structures individuelles ne peuvent être distinguées que quand les interactions des rayons gamma sont bien espacées les unes des autres (∼ 10mm). De plus, le bruit du signal de courant est important. Il est donc nécessaire que les dépôts d'énergie en chaque point d'interaction soit élevé pour pouvoir les identier. Puisqu'il n'est pas possible de rejeter les événements d'interactions multiples, l'étude suivante a consisté à caractériser ces événements et à déterminer leur possible inuence sur la forme d'impulsion moyenne en chaque point de la grille de scan. Pour les événements de diusion multiple sélectionnés par χ 2 , l'analyse montre que les interactions sont relativement proches et que la valeur moyenne de leur distance au point de la grille de scan considérée est comparable à la résolution spatiale du détecteur après analyse des formes d'impulsion et tracking gamma. Pour cette raison, les signaux d'interactions multiples sélectionnés par la technique PSCS sont similaires à ceux d'interactions single. S'il n'est pas possible de nettoyer la base de données des signaux d'interactions multi-ples, ces derniers ne la contaminent pas. De plus, les simulations indiquent que, pour un événement de diusion multiple, le dépôt d'énergie du point d'interaction le plus éloigné de la première interaction diminue quand la distance entre ces deux points augmente. Généralement, la plus grande libération d'énergie se produit au voisinage de la première interaction où la majeure partie du signal est générée. Ainsi, un événement de diusion multiple dont la forme d'impulsion correspond à la somme des impulsions générées en chacun de ses points, pondérée par l'énergie partielle déposée en chaque point, présente une réponse très voisine de celle d'une interaction unique. Enn, la base de données obtenue par la technique PSCS est comparée à la base de données théorique calculée avec ADL aux mêmes points de la grille de scan. La comparaison porte sur la diérence maximale d'amplitude calculée échantillon par échantillon entre un signal obtenu avec la technique PSCS et le signal correspondant de la base de données théorique. L'analyse a montré que les deux bases de données sont pour la plupart en accord, sauf le long des lignes et surfaces de segmentation où des eets de bord sont causés par la technique PSCS. En conclusion, on peut considérer que la technique PSCS appliquée au détecteur planaire est able.

table 2

 2

.1). At moderate electric eld values, the drift velocities v e and v h vary linearly with E (equation 2.2). At higher electric eld values, v e and v h increase slower with E. A saturation velocity may be reached at very high electric eld (see gure 2.3a).

Table 2 .

 2

1: Physical properties of silicon and germanium. From

[START_REF] Leo | Techniques for nuclear and particle physics experiments[END_REF]

.

  The induced charge starts at zero when electrons and holes are formed and CHAPTER 2. SEMICONDUCTORS AND HPGE DETECTORS reaches it's maximum of q 0 when the two clouds of charge carriers are collected. If it is assumed that the charges are formed at a distance x from the n + contact of the detector

	2.8. SIGNAL FORMATION						31
	2.8.2 Pulse-shapes for coaxial detectors
	(see gure 2.10) and the following denitions are used
	t e = x/v e electron collection time t h = d-x v h hole collection time	(2.23)
	(with v e and v h electrons and holes saturation velocity, respectively) then four possible
	time domain can be dened (see gure 2.10).
	If both electrons and holes are drifting (t < t h and t < t e )
	Q(t) = q 0		v e d	t +	v h d	t	(2.24)
	If electrons have been collected and holes are still drifting (t e < t < t h )
	Q(t) = q 0	x d	+	v h d	t	(2.25)
	If holes have been collected and electrons are still drifting (t h < t < t e )
	Q(t) = q 0	v e d	t +	(d -x) d
	Q(t) = q 0		(2.27)
	Figure 2.10: Pulse shapes examples in a planar detector.

(2.26)

Finally, if both holes and electrons have been collected (t > t h and t > t e )

Table 3 .

 3

1:

  • around the scanned detector. The same eect is obtained for the Salamanca scanning table by rotating the scanned detector by 90 • around its axis. The scanning operation is then repeated and the position of the interactions can be reconstructed by nding intersects between the two obtained datasets of directions. The recorded pulse shapes in the two perpendicular measurements are compared by a χ 2 test (see next section) and identi-

cal pulses are selected and associated to the intersect. Intersects are grouped in voxels which size can be modied. Both Salamanca and Darmstadt scanning tables can scan the full volume (∼ 48500 voxels of 2 × 2 × 2 mm 3 for AGATA crystals) in few days, with a spacial resolution of ∼ 1 -2 mm.

Table 4 .

 4 1: Geometrical and physical information for the dierent sources. All the sources are cylindrical except where noted. The sources are encapsulated in stainless steel and the window thickness is indicated in the fourth column of the table. The source activities are the ones calculated by fall 2018.

	Source	Active / O Active h Wdw. thk. Activity
	241 Am (OLD) Spherical, / O = 1 mm	0.2 mm	0.07 GBq
	137 Cs (OLD)	2 mm	2 mm	0.2 mm	0.37 GBq
	241 Am (NEW)	3 mm	3 mm	0.23 mm	1.5 GBq
	137 Cs (NEW)	3 mm	3 mm	0.38 mm	1.85 GBq
	152 Eu	3.18 mm	2.2 mm	1 mm	0.74 GBq

The geometrical and physical parameters of the sources are summarized in table 4.1. Both the geometrical and physical properties have an important role in the estimation of the output rate which will be discussed in the following section.

Table 4 .

 4 2: Measured standard deviation of the signal noise. For the segments the average of all the values is reported together with the minimum and maximum value measured for a single segment.

		Core	Seg. avg.	Seg. min.	Seg. Max.
	S001	5.9 keV	2.1 keV	1.7 keV	2.6 keV
	3x3 segmented	4.8 keV	2.1 keV	1.7 keV	2.6 keV

Table 4 .

 4 This becomes more evident by looking at the histograms shown in gure 4.11 and by looking at tables 4.3 and 4.4 where the FWHM of the distributions are reported for the original conguration and for the the new conguration respectively.

				Simulated 1.5 mm collimator
			Z		Am		Cs
			3	1.6128 ± 0.0002 1.6443 ± 0.0003
			80	2.2879 ± 0.0004 2.4005 ± 0.0006
			160	3.009 ± 0.001	3.130 ± 0.001
				Measured 1.5 mm collimator
			3	1.60 ± 0.01	1.69 ± 0.01
			80	2.29 ± 0.01	2.41 ± 0.03
			160	3.04 ± 0.04	3.46 ± 0.04
						Simulated
			0.5 mm collimator				1.0 mm collimator
	Z	Am	Cs		Eu (1408 keV )	Am	Cs	Eu (1408 keV )
	3	0.5349 ± 0.0004 0.5525 ± 0.0005 0.5711 ± 0.0007 1.0795 ± 0.0006 1.1133 ± 0.0009	1.147 ± 0.001
	54	0.689 ± 0.001	0.728 ± 0.001	0.753 ± 0.002	1.408 ± 0.002	1.453 ± 0.002	1.504 ± 0.003
	95	0.804 ± 0.002	0.862 ± 0.002	0.887 ± 0.003	1.658 ± 0.003	1.718 ± 0.004	1.774 ± 0.005
						Measured
	Z	Am	Cs		Eu		Am	Cs	Eu
	3	0.531 ± 0.008	0.52 ± 0.02	0.52 ± 0.01	1.074 ± 0.008	1.13 ± 0.01	1.09 ± 0.02
	54	0.68 ± 0.01	0.75 ± 0.02	0.76 ± 0.02	1.43 ± 0.01	1.47 ± 0.03	1.39 ± 0.02
	95	0.81 ± 0.02	0.89 ± 0.02	0.86 ± 0.02	1.65 ± 0.02	1.81 ± 0.03	1.63 ± 0.03

3: FWHM in mm of the beam prole distributions at dierent distances from the exit of the original collimator. All units are in mm.

Table 4 .

 4 4: FWHM in mm of the beam prole distributions at dierent distances from the exit of the upgraded collimator. All units are in mm.

CHAPTER 4. IPHC SCANNING

TABLE

  The values are reported in tables 4.4 and 4.3. The values of the measurements and simulations are in good agreement except for the 152 Eu source. This is due to the fact that the IPIX

sensor is not thick enough to eciently detect high energy gamma rays (i.e. 1408 keV ) and moreover the branching ratio of low energy gamma rays in europium (i.e. 122 keV and 344 keV ) is quite large compared to the one of high energy gamma rays (see table

Table 4 .

 4 GBq 0.36 107 137 Cs (OLD) 1.5 mm 4.32 • 10 -6 0.37 GBq 0.851 1446 137 Cs (NEW) 1.0 mm 8.62 • 10 -7 1.85 GBq 0.851 1357 152 Eu 1.0 mm 8.93 • 10 -7 0.74 GBq 1.393 921 5: Yield and count per second for the simulated sources. Branching ratios are found in [68].

	Source	Coll. / O	R yield	Activity	BR	c.p.s.

.1) as well as the absorption of the stainless-steel window of the source encapsulation. If R Y ield is multiplied by the activity of the source and the branching ratio (BR) of the gamma ray of interest, it is possible to calculate how many gamma rays per second (c.p.s.) are emitted by the collimator. Results are reported in tables 4.5 and 4.6.

241 Am (OLD) 1.5 mm 4.08 • 10 -6 0.07

Table 4 .

 4 6: c.p.s. for the relevant energies of Eu. Branching ratios are found in[START_REF]The Lund/LBNL table of isotopes[END_REF].

Table 4 .

 4 7: Percentage of gamma rays fully absorbed in a single segment when shooting a gamma-ray beam at xc = -20 mm and yc = 0 mm. The second column refers to the percentage of gamma rays absorbed in the full volume of the detector.

	E (keV ) Full det. Seg D1 Seg D2 Seg D3 Seg D4 Seg D5 Seg D6
	122	136	112	7	1	0.1	0.0	0.0
	245	18	7	2	1	1	0.2	0.1
	344	46	11	4	3	2	1	0.3
	662	235	28	10	12	10	5	2
	779	14	1.4	0.5	0.7	0.5	0.3	0.1
	867	4	0.4	0.2	0.2	0.2	0.1	0.0
	964	14	1	0.5	0.7	1	0.3	0.2
	1086	9	1	0.3	0.4	0.4	0.2	0.1
	1112	12	1	0.4	0.5	0.5	0.3	0.2
	1408	17	1	0.5	0.7	1	0.4	0.3

Table 4 .

 4 8: Counts per second (c.p.s.) of gamma rays fully absorbed in a single segment. The second column refers to the c.p.s. of gamma rays absorbed in the full volume of the detector.

	E (keV ) Full det. Seg D1 Seg D2 Seg D3 Seg D4 Seg D5 Seg D6
	122	7572	6704	438	88	8	0	0
	245	1072	419	108	79	37	10	4
	344	2772	681	215	194	117	42	17
	662	14130	1701	600	741	570	276	134
	779	823	85	31	40	33	16	9
	867	257	25	9	12	10	5	3
	964	843	75	28	39	32	18	9
	1086	560	45	18	23	21	12	7
	1112	741	59	24	30	28	16	9
	1408	1033	72	29	41	38	24	15

Table 4 .

 4 Eu source. This is due to the fact that the 152 Eu source is ∼ 3 times less active than the 137 Cs source and moreover its activity is divided among dierent decay branches which leads to rates that are ∼ 20 times smaller for gamma rays with energies of 779 keV and 1408 keV . Never the less the 152 Eu source will be used for advanced testing and 3D scans on limited volumes (e.g. one sector).

9: Counts per minutes (c.p.m.) of gamma rays fully absorbed in a single segment. The second column refers to the c.p.m. of gamma rays absorbed in the full volume of the detector. scans in a reasonable time with the actual 152

Table 6 .

 6 6.1. SIMULATIONS OF THE PSCS TECHNIQUE ON THE 3 × 3 DETECTOR 79γ emitted γ detected γ f ull abs γ single 1: Total number of gamma rays: emitted from the collimator (rst column), interacting in segment 5 (second column), fully absorbed in segment 5 (third column), absorbed in one interaction

	γ single	γ single
	γ detected	γ f ull abs

Table 7 .

 7 Vertical rotation alignment performed at 60 keV (see table7.2). The blue and red marks indicate the left and right delimitations of the segmentation line. The black marks in the middle indicate the barycenter of the two series and are used to determine the misalignment of the E1 -F 1 segmentation line on the YT axis. The dierence of the X coordinates on the blue and red marks gives the segmentation width. Error bars are smaller than the symbol size. 1: Measured values of the E1 -F 1 segmentation line width at dierent YT positions and for the two collimator diameters ( coll ) used. The average (AVG) of the eleven width values is given at the bottom line.

	7.1. DETECTOR ALIGNMENT PROCEDURE	103

Table 7 .

 7 7.2, are realized with the three dierent new sources available: 241 Am, 137 Cs and 152 Eu (see table 4.1). The dierent energy regions, in which the scans are performed, allow

	Type	Source	Coll	Pitch	points	time per point	Tot time
	Vert. rotation alignment	241 Am	1 mm	0.1 mm	583	120 s	22 h
	Vert. across seg. line.	241 Am 0.5 mm	0.05 mm	61	2000 s	1.4 d
	Vert. partial	241 Am	1 mm	1 × 1 mm 2	2769	60 s	2.5 d
	Vert. sector B	241 Am	1 mm	1 × 1 mm 2	1000	60 s	20 h
	Hori. Total Area	241 Am	1 mm	1 × 1 mm 2	7448	100 s	9.9 d
	Vert. axis alignment (1)	137 Cs	1 mm	0.1 mm	806	240 s	2.5 d
	Vert. axis alignment (2)	137 Cs	1 mm	0.1 mm	506	240 s	1.4 d
	Vert. axis alignment (3)	137 Cs	1 mm	0.1 mm	506	240 s	1.4 d
	Hori. alignment (1)	137 Cs	1 mm	0.1 mm	804	240 s	2.5 d
	Hori. alignment (2)	137 Cs	1 mm	0.1 mm	804	240 s	2.5 d
	Vert.Total Area	137 Cs	1 mm	2 × 2 mm 2	1351	150 s	2.5 d
	Hori.Total Area	137 Cs	1 mm	2 × 2 mm 2	2195	150 s	4.2 d
	Vert.Total Area	152 Eu	1 mm	2 × 2 mm 2	1355	360 s	6 d
	Vert. sector B	152 Eu	1 mm	2 × 2 mm 2	271	1 h	12 d
	Hori. sector B	152 Eu	1 mm	2 × 2 mm 2	960	1 h	40 d

2: List of performed scans presented in this work. Times include the pauses for the automatized nitrogen rell (25 minutes every 8 hours).

Table 7 .

 7 4: Peak to total ratio (P/T ) values of the photopeaks of interest for each of the six segments of sector B. I lef t , I right , I top and I down are the integrals of the transient signal of the neighboring segments. The +1 is an oset to make the ICA value range in [0, 2]. The ICA parameters give an indication on the location of the interaction relative to the neighboring segments. Of course the ICA top/down signal has no meaning for the rst and last slices of the detector. In these cases, the ICA top/down is considered as the integral of the available transient signal multiplied by a normalization factor. The distributions of the T 90 10 , ICA lef t/right and ICA top/down values in six database slices, one for each segment of sector B, for both databases are shown in gures 7.32, 7.33 and 7.34. The distributions are very similar, hinting that the two scans are comparable.

	the Image Charge Anisotropy (I CA), the last one dened as [24]
	ICA lef t/right =	I lef t -I right I lef t + I right	+ 1	(7.5)
	ICA top/down =	I top -I down I top + I down	+ 1	(7.6)

where

  Figure 7.38: Average maximum residual, as a function of ZC , calculated comparing pair by pair the 122 keV , 344 keV , 662 keV , 779 keV and 1408 keV databases. For the data series relative to the 344 keV database, data from the last slice of the detector was not taken into account as the P/T ratio drops to 67% (see gure 7.31 and table 7.4). For the same reasons, for the data series relative to the 122 keV database only the data in the rst two slices of the detector are considered. In (a) the residuals are calculated with the whole supertrace while in (b) only the transient pulses are used. these values are normalized to the maximum amplitude of the main pulses and since the amplitude of transient pulses is in relation smaller, it may mean that actually the dierence between the transient pulses has a more relevant impact on the database comparison.The above analysis can be repeated for the other databases. The databases are compared in pairs and the average maximum residuals as a function of Z C is plotted in gure 7.38. The cross markers refer to the data series related to the comparison among high energies scans (662 keV , 779 keV and 1408 keV ). They show a similar trend with comparable values. However, some discrepancies are found when comparing the high energies databases with the 344 keV database (circular markers in gure7.38). The data series relative to the 344 keV database are self-consistent and follow the same trend of the high energy ones (cross markers) until Z C = 40 mm. From there on, the 344 keV database and the high energy databases start to diverge. For Z C > 56 mm the average maximum residuals reach values around 7%, which is more than a factor 2 larger than the ones for the high energy data series. Finally, the circular markers in gure 7.[START_REF]AGATA TDR (phase 1)[END_REF]

	140	CHAPTER 7. REAL SCAN OF THE S001 DETECTOR

that

Table 7 . 5 :

 75 344 keV and 662 keV databases. The data are relative to the database slices at ZC = 58 mm, 60 mm, 62 mm, 64 mm, 66 mm and 68 mm. Area of the photopeaks of interest, background subtracted, for each of the six segments of sector B.

	Slice (Seg)	122 keV 344 keV 779 keV 1408 keV
	1(7)	735456	159074	26412	23445
	2 (8)	55235	48437	9374	10119
	3 (9)	12866	50699	13843	15915
	4 (10)	0	31307	11728	15618
	5 (11)	0	11524	5324	8808
	6 (12)	0	4826	2864	5614

Table A .

 A a new AGATA detector unit is delivered from the manufacturer facility, it undergoes a series of tests before getting accepted by the collaboration. In these tests, called costumer acceptance test (CAT), specic parameters are measured for each detector segment, such as the resolution, the current oset in function of the applied voltage and, for the full crystal, its eciency and the FWHM/FWTM ratio. These parameters generally show if a detector presents problems or defects and in the case any is found the detector is sent back to the manufacturer for repairing. CATs are performed in few specic laboratories of the AGATA collaboration, the IPHC of Strasbourg being one of them. In addition, before a detector gets scanned with the Strasbourg scanning table, a CAT-like test is generally performed in order to verify that the detector doesn't present anomalies, or got damaged during transportation. Tables A.1 and A.2 report the FWHM values of each segment, at low and high energies respectively, measured before the scan of the S001 detector. The tests are performed by irradiating the detector with free 241 Am and 60 Co sources. The values show that the FWHM values of segments F 2, F 3 and F 4 are in line with the ones of the other segments despite the fact that, as described in section 7.2.5, anomalous values are found locally through 2D scans. 1: Segments FWHM values at 60 keV measured by irradiating the detector with a free 241 Am source. Units in keV . Courtesy of Marie-Hélène Sigward.

	148		APPENDIX A. S001 COSTUMER ACCEPTANCE TEST
	Appendix A
	S001 Costumer Acceptance Test
		A	B	C	D	E	F	Core
	1	2.06	2.00	2.07	2.14	2.27	2.12
	2	1.89	1.91	1.93	1.95	2.04	1.99
	3 4	2.03 2.11	1.91 2.00	2.00 2.03	1.97 2.19	2.02 2.12	2.12 2.25	2.40
	5	2.11	2.05	2.14	2.16	2.12	2.04
	6	2.14	2.14	2.08	2.16	2.23	2.11
		A	B	C	D	E	F	Core
	1	1.03	0.98	1.04	1.05	1.10	1.01
	2	0.98	0.96	0.96	0.98	1.08	0.98
	3 4	1.00 1.05	0.94 0.97	1.03 1.05	1.00 1.13	1.06 1.18	1.11 1.12	1.24
	5	1.02	1.03	1.05	1.10	1.15	1.11
	6	0.98	0.95	1.07	1.06	1.09	1.02
					147

When

Table A .

 A 2: Segments FWHM values at 1332 keV measured by irradiating the detector with a free60 Co source. Units in keV . Courtesy of Marie-HélèneSigward. ou PSA (Pulse Shape Analysis) détermine la position de chaque interaction qui compose un événement (c'est-à-dire l'interaction simple ou multiple d'un rayon gamma avec un détecteur Ge). L'algorithme compare la forme d'impulsion expérimentale avec une base de données de formes d'impulsion pré-calculées associées à des coordonnées spéciques dans le volume du détecteur. Une fois que les positions de toutes les interactions sont obtenues, un autre algorithme de "clustering" groupe les interactions qui sont liées avec la plus grande probabilité au même rayon gamma. Le dernier pas est fait par un algorithme de tracking qui reconstruit la chronologie des interactions de chaque rayon gamma et, si ce rayon gamma est reconnu comme absorbé par le détecteur, l'événement associé est accepté et stocké dans le pool de données, sinon il est rejeté.Il est clair que le PSA joue un rôle clé pour obtenir de bons résultats avec le tracking. AGATA utilise pour le PSA des algorithmes de "grid search" qui fonctionnent avec des bases de données calculées par ADL. ADL (AGATA Detector Library) est un software, développé à Cologne par la collaboration, qui calcule numériquement les formes d'impulsion générées par un détecteur une fois que les valeurs du champs électrique et des potentiels "de pondération" sont connus. Les performances de l'algorithme de tracking sont bonnes mais il présente des limitations quand les interactions ont lieu dans les parties avant et arrière du détecteur, où les formes d'impulsion sont fortement inuencées par la géométrie locale (partie non-coaxiale du cristal) et par les facteurs de construction comme la surface passivée et la distribution des impuretés. Pour éviter ces problèmes, la collaboration se propose d'utiliser des bases de données de formes d'impulsion expérimentales, mesurées par une caractérisation volumétrique (3D) des détecteurs. La caractérisation 3D des détecteurs est possible avec les "tables de scan". Cinq tables qui exploitent diverses techniques de scan sont utilisées par la collaboration AGATA. Toutefois le principe fondamental de chaque table est toujours le même. Le détecteur est xé à la structure de la table et est irradié par une source de rayons gamma. Par des algorithmes, il est possible d'associer les formes d'impulsion enregistrées avec la position d'interaction correspondante. Les tables de scan utilisées actuellement par la collaboration sont localisées à Liverpool, Orsay, Darmstadt, Salamanca et Strasbourg. Elles sont de deux types, les tables à coïncidences (Liverpool et Orsay) et les tables à mesures directes (Darmstadt, Salamanca et Strasbourg). Celles à coïncidences (Darmstadt et Salamanca) utilisent des détecteurs collimatés installés autour du détecteur à scanner pour déterminer les positions d'interaction des rayons gamma provenant d'un faisceau collimaté. Pour les tables à mesures directes, au contraire, une source de 22 N a (qui émet des rayons gamma dos à dos) est positionnée entre le détecteur à scanner et un détecteur sensible à la position qui permet de reconstruire la direction des rayons gamma émis. Le détecteur est irradié à deux positions diérentes et les interactions peuvent être reconstituées en trouvant des intersections entre les deux ensembles de données de directions obtenus. La table de scan de Strasbourg est conçue pour réaliser des scans complets avec une bonne résolution spatiale en peu de temps. Un scan 3D d'un cristal d'AGATA (∼ 45000 points de scan) peut être réalisé dans un temps de l'ordre de 20 jours. La table exploite la technique PSCS (Pulse Shape Comparison Scanning) qui permet la construction d'une base de données de formes d'impulsion à partir de la comparaison de deux ensembles de données obtenus par irradiation du détecteur avec une source collimatée de rayons gamma. Au début le détecteur est positionné verticalement sur la table et est irradié par la source collimatée qui est déplacée à intervalles réguliers sur un plan perpendiculaire à l'axe central du détecteur. Pour chaque position du collimateur tous les signaux générés par le détecteur de long du faisceau de rayons gamma sont enregistrés et un ensemble de donnée V est obtenu. Le détecteur est ensuite pivoté de 90 • et mis en position horizontale. En répétant la même opération on obtient un ensemble de données H. Les points de scans V et H sont choisis pour que les axes des faisceaux gamma V et H se croisent (virtuellement) et dénissent une "grille de scan" à trois dimensions (3D). Pour un détecteur sensible à la position, deux rayons gamma V et H qui interagissent à la même position, génèrent la même forme d'impulsion. La comparaison deux à deux des formes d'impulsion du jeu de données V avec celles du jeu de données H permet de sélectionner les formes d'impulsion V et H les plus similaires, de les moyenner et d'associer une forme d'impulsion moyenne à chaque coordonnées de la grille. La sélection deux à deux est eectuée par une formule de type χ 2 . Plus cette valeur calculée est basse, plus les deux signaux sont similaires. Malheureusement, il n'existe pas une valeur absolue pour laquelle deux signaux peuvent être considérés identiques. Cette valeur dépend en fait des conditions expérimentales et il n'est possible d'eectuer qu'une comparaison relative des formes d'impulsion. Un autre désavantage de la technique PSCS est qu'elle ne peut pas distinguer entre des signaux générés par des événements d'interactions unique ou single et des événements d'interaction multiples. Les formes d'impulsion générées par des interactions multiples sélectionnées comme des événements d'interaction single peuvent avoir un impact négatif sur la base de données et la polluer. Des procédures ancillaires peuvent aider à améliorer la sélection, mais elles ne susent pas à éliminer le problème. Une partie du travail de thèse consistait à réaliser des simulations Monte Carlo de la table de scan de Strasbourg pour extraire des valeurs de paramètres qui permettent de quantier les performances de la technique PSCS et d'évaluer la solidité des bases de données mesurées ainsi produites. La table de scan de Strasbourg est constituée comme suit. Un collimateur métallique est posé sur deux axes motorisés qui permettent un mouvement planaire sur un intervalle de 300 mm dans chacune des deux directions. Au-dessus du collimateur, deux plateaux xes permettent le placement du détecteur en position verticale et horizontale. Le détecteur est xé dans un cadre de réglage (ou équerre) qui est centré sur les plateaux par des plots de centrage. Lorsque la source est retirée un système laser solidaire du collimateur envoie un faisceau dans le collimateur du point source vers le détecteur en suivant le parcours du faisceau gamma. Il permet d'aligner précisément le détecteur en position verticale et nous assure de la perpendicularité de la position horizontale. Enn, il est possible de replacer précisément le détecteur en position verticale grâce au laser. Le collimateur est un bloc métallique cylindrique de 189 mm de hauteur et de diamètre externe de 220 mm. Les métaux qui le constituent sont des absorbeurs de rayons gamma en tungstène, plomb et acier. Il est possible d'ouvrir le collimateur pour loger à sa base l'un des godets qui contiennent les sources. Des sources d'américium (

This is true if one of the two contribution to the trapping is negligible, ie. holes are less likely to be trapped if the crystal has not sufered from neutron damages.

The FETs of the preampliers work at an optimal temperature of 130 K, where the noise component is minimal.

An event is dened as the interaction history of a gamma ray in the array. It is a time ordered collection of interaction positions and respective energy release.

The cascade between the

keV and 779 keV transitions was simulated with Geant4. All the gamma rays with energies 344 ± 5 keV and 779 ± 5 keV going out of the collimator were counted. The ratio between this number and all the 779 ± 5keV gamma rays out of the collimator gives the 0.06% probability.

The z values correspond to three distances of interest: exit of the collimator and position of the center of the S001 AGATA detector in horizontal and vertical positions.

This is an approximation, as the signal is generated by the ionization caused by the electron involved in the gamma-ray interaction. For an interaction of 1 M eV in germanium, the electron can travel 1 mm away from the gamma-ray interaction.

In fact, the pulse shape is not aected by the process since no energy is released during the interaction. Although, as stated in[START_REF] Lopez-Martens | Gamma-ray tracking algorithms: a comparison[END_REF], the coherent scattering can impact the tracking algorithm performances as it aects the ending parts of the tracks of multi-scattered gamma rays (∼ 17% of 1.332 M eV events undergo coherent scattering).

-210 -205 -200 -195 -190 -185 -

A detailed description of the time alignment is given in section 3.4.3 of[START_REF] Ginsz | Characterization of high-purity, multi-segmented germanium detectors[END_REF].

In fact, at the beginning of this chapter it was remarked that a precise alignment of the detector on the table is essential for the scan.

Acknowledgments

This work has been supported by the MIRION Technologies Canberra Company under the contract N°152521,

the OASIS ANR grant under the contract ANR-17-CE31-0026-02. I'd like to thank Gilbert Duchêne for guiding me through this PhD. Thanks also to Benoit Pirard from MIRION Technologies Canberra for the founding provided for the project.

CONCLUSIONS AND PERSPECTIVES

scanned with a beam energy of 662 keV ( 137 Cs source). In general, the values of the parameters obtained in the analysis indicated that the PSCS technique performs better on the S-type detector than on the 3 × 3 segmented planar detector. The cause of this has been attributed to the much more complex segmentation geometry of the detector, which consequently provides better spatial resolution. In particular it was observed that the single interaction selection reach values that range, in average between the 55% at the front of the detector and 45% at its back. The average distance of the interactions from the scanning point was found to be around 2 mm. Finally the comparison between the PSCS calculated database and the ADL one showed an average maximum dierence of 5% ÷ 10% at the very front of the detector (in the rst segment slice) and then decreases rapidly to ∼ 2% towards the back. Additional simulations of the S-type detector extended the analysis of the eciency of the PSCS technique. In particular, the impact on the nal results of the gamma-ray energy and the number of events used for χ 2 selection was examined at 122keV , 344keV , 779keV and 1408keV ( 152 Eu source energies). The analysis showed that the energy of the gamma-ray beam impacted only the percentage of selected single interaction events, enhancing this value for low energies gamma rays. The rest of the parameters were found comparable within each other and with the results obtained for the 662 keV scan. The impact of the input statistics was also analyzed using dierent numbers of input events to be compared with the χ 2 selection algorithm for both the vertical and the horizontal datasets. The input statistics proved to have a greater impact with respect to the beam energy, as it was shown that the PSCS technique perform better with higher input statistics. However, the nal comparison between the PSCS calculated database and the ADL one didn't seem to depend on this parameter.

Subsequently, the results of real measurements of a S-type detector were presented.

The aim of this analysis was to test the PSCS technique performed with a 152 Eu source and prove, comparing dierent energy databases, that the pulse shapes don't depend from the interaction that generates them.

A rst characterization of the detector was performed through 2D scans with the 241 Am, 137 Cs and 152 Eu sources. Some parameters were retrieved and discussed such as the local eciency distribution, the crystal axis orientation, the centroid and FWHM distributions. The local eciency distribution exhibits the expected behavior. The crystal orientation was determined, the < 100 > axis being at θ 4 = -16.7

The centroid and FWHM distributions measured with the core contact show the known electron trapping which occurs in n-type detectors. Surprisingly, the same distributions obtained from the segment contacts present a similar trend which was not expected. This may be caused by the rather short integration time of the TNT2 digital amplier settings (5.95 µs) used in the scans. In addition, the centroid and FWHM distributions prompted a deeper analysis on the charge collection properties of the detector. In particular a defective zone expanding in segments F 2, F 3 and F 4 was found in the detector. The energy spectra exhibit large tails towards low energy which is not expected in the several macroscopic trapping models. The charge collection properties of this zone were further analyzed and an hypothesis on the nature of the phenomenon was speculated. This unusual peak shape has been interpreted as the consequence of the presence of a second Résumé en français L'étude de la structure des noyaux loin de la vallée de stabilité par spectroscopie gamma joue un rôle très important dans la physique nucléaire moderne. Ces noyaux sont caractérisées par un rapport entre protons et neutrons qui est loin de l'unité et présentent, de ce fait, des structures particulières (eg. noyaux halo, peau de neutrons, structure en amas ou cluster, îlots d'inversion et modication des nombres magiques). De par leurs propriétés, ces noyaux sont appelés noyaux exotiques et l'étude de leur structure peut fournir des données essentielles pour améliorer les modèles de physique nucléaire existants. Il est possible de créer de tels noyaux auprès d'accélérateurs de faisceaux Ces mesures ont montré les capacités d'imagerie de la table de scan de l'IPHC. Par la suite, des scans tridimensionnels ont été eectués avec les sources 137 Cs et 152 Eu. En raison de l'activité limitée de la source en regard des petits diamètre des collimateurs, le scan à l'europium a été limité à un secteur du détecteur (secteur B). Ces données ont permis de construire en une seule mesure quatre bases de données de formes d'impulsions correspondant chacune à une énergie diérente, 122 keV , 344 keV , 779 keV et 1408 keV .

Le scan au césium a permis de construire une base de données de référence à l'énergie de 662 keV . Une comparaison a été faite entre ces bases de données, et la valeur résiduelle maximale entre deux signaux associés au même point de la base de données a été choisie comme paramètre de comparaison. Les bases de données ayant une énergie > 500 keV se sont avérées comparables entre elles, les diérences variant sur la longueur du cristal en moyenne d'environ 2% à l'avant, environ 3% dans le corps du cristal et jusqu'à 6% à l'arrière. Des divergences ont par contre été constatées avec la base de données de 344 keV pour les valeurs le long de l'axe du crystal supérieures à 40 mm. Les valeurs résiduelles semblaient diverger d'un facteur 2 vers l'arrière du détecteur. Enn, la base de données à 122 keV s'est avérée très divergente des autres bases de données. Il a été supposé que les raisons de ces comportements divergeants sont à attribuer à la technique PSCS qui n'est pas ecace aux basses énergies, puisque la petite amplitude des signaux induits est fortement aectée par le bruit du signal. L'analyse, résumée ci-dessus, ouvre de nouvelles perspectives et possibilités de recherche, tant pour les simulations que pour les mesures. Les limites du PSCS indiquées dans ce travail peuvent être surmontées en proposant des améliorations pour le PSA. En s'inspirant de travaux récents, des mesures diérentes peuvent être prises en compte pour l'algorithme de sélection des impulsions. La formule de type χ 2 deviendrait alors χ α où α est une valeur qui peut être optimisée an de maximiser la fraction des interactions individuelles sélectionnées et, dans le cas d'interactions multiples, de minimiser la distance moyenne des points d'interaction par rapport à la position correspondante dans la base de données. Une autre façon d'améliorer la sélection χ 2 pourrait être l'utilisation de poids pour les signaux induits an de leur donner plus ou moins d'impact sur la construction de la base de données. En outre, l'utilisation de techniques de ltrage du bruit, telles que la réduction du bruit par transformée de Fourier, pourrait être évaluée, en particulier pour les impulsions de faible énergie où le PSCS semble être plus aecté. Si ces techniques permettent d'améliorer la technique du PSCS, elles peuvent être appliquées à des mesures réelles pour vérier si les écarts constatés entre les bases de données d'énergies diérentes sont réduits.

An de permettre des mesures à basse énergie dans un volume de secteur complet en utilisant la source d'europium, une conguration horizontale-horizontale pourrait être testée. Elle permettrait de réduire les problèmes de statistique pour les faisceaux de rayons gamma de basse énergie vers l'arrière du détecteur.

Enn, il serait intéressant de comparer les bases de données obtenues par la table de scan de l'IPHC avec celles d'autres tables de scan exploitées par la collaboration AGATA en utilisant la même capsule montée dans un cryostat d'essai donné.

Les mesures eectuées avec la source d'europium ont mis en évidence la nécessité d'acheter des sources de plus petit diamètre (1 mm ou moins à comparer à 3 mm pour les sources actuelles) plus compatibles avec le diamètre des nouveaux collimateurs. En conservant la même activité de source, un scan à l'europium serait accéléré d'un facteur 10 environ, ce qui rendrait les mesures aussi rapides que les scans actuels au césium.

Grâce à ces sources de rayons gamma plus compactes, d'autres tests pourraient être eectués en utilisant la nouvelle conguration de la table de scan. En particulier, la source d'europium combinée à la collimation ne des rayons gamma (0.5 mm et 0.2 mm) pourrait être utilisée pour déterminer l'impact éventuel du nuage de porteurs de charge, produit par un rayon gamma en interaction, sur la forme des impulsions. En outre, il serait possible d'extraire de mesures spéciques à travers une ligne de segmentation, la taille du nuage de porteurs de charge qui est censée varier avec l'énergie des rayons gamma. Cette étude peut être réalisée en conjonction avec des calculs spéciques. De plus, des collimateurs plus ns pourraient être utilisés pour eectuer une analyse approfondie du comportement des porteurs de charge dans un grand détecteur HPGe comme la zone anormale dans S001. Enn, la table de scan peut certainement être utilisée pour réaliser un travail de R&D sur des détecteurs sensibles à la position. Par exemple, l'impact de géométries et de segmentations plus exotiques sur la sensibilité spatiale du détecteur, les eets de surface et dans le volume du cristal de nouveaux traitements de surface, l'identication spatiale et la caractérisation de zones de collection de charges dégradée dans un cristal défectueux. They are applied on a pixelated 3x3 planar detector and a symmetrical S-type AGATA detector. The method is tested with different gamma-ray energies and input statistics. Several real scans are performed as well on both detectors, which are fully characterized. In particular a scan with a gamma-ray source of 152 Eu, the first ever done, prove some assumptions on which the tracking technique is based.

Bartolomeo DE CANDITIIS

Keywords: gamma-ray spectroscopy, high purity germanium detectors, scanning table, pulse-shape analysis, AGATA array, detector characterization, PSCS technique.