Standing at the end of my PhD study and looking at the backward path in last three years, I'm impressed by a lot of important moments when I was stepping further with the help from a lot of individuals. I think no one can obtain his or her PhD degree without other people's help. And I did receive a lot of help from a lot of people. I would like to acknowledge these people from the bottom of my heart.

First and foremost, I'd like to express my deepest gratitude to my supervisor Prof. Laurent TASSAN-GOT who is always giving his endless help to me since the very beginning. Laurent is a very nice person and it's always a pleasure to work with him. I'm extremely impressed by his intelligent mind and his rich knowledge in physics, mathematics and computer science.

I consequently learned a lot of things from him. In Chinese traditional culture we define a teacher as "one who propagates the doctrine, imparts the professional knowledge, and resolves doubts". This is exactly what Laurent has done to me. I'm always proud of having him and feeling lucky to be his student.

Then I would like to thank all the jury members of my defense. Especially I'd like to thank two reviewers, Prof. Olivier Serot and Prof. Maurice Morjean.

They took their holiday time in August to review to my thesis very carefully and gave some good suggestions which finally help me to improve the thesis quality. I'd also like to thank examiner Prof. Jingyu Tang came to my defense from China with a very long trip. I would like to thank Laurent Audouin who's offering his help to me throughout my PhD period, especially his financial support sending me to the international conference, academic meetings and other professional activities. i These experiences are very important because they can expand my vision and help me to build up professional connections.

I would like to thank n_TOF collaboration at CERN. I did all my experiments at n_TOF which is a unique and strong facility for nuclear data measurement. The collaboration is very efficient and close. I learned a lot of things there which I believe will be very important and helpful for my future career.

I am extremely grateful to all the PACS group members at IPN Orsay.

Especially, I thank Claire Le Naour for her outstanding work to make the actinide targets. I thank Marc Ernoult for his good suggestions concerning the manuscript and helpful discussion on physics. I thank Xavier Doligez for his organization for my defense rehearsals and his valuable remarks to the presentation. I thank Alice, Yiman, Coralie and Mingjian for being with me as PhD mates.

I would like to acknowledge all my Chinese friends at Orsay, especially Yaqiong Wang, Zizhao Zong, Yanzhou Wang, Gaoyang Ye, Xing Liu, Yuxiang Song, Zicheng Liu and Yang Wan. Because of your company and help in my personal life, I never felt lonely and helpless and I had a good balance between work and private life in the past three years.

Last but not least, I'd like to give my sincerest appreciation to my family: my parents, my sister and her husband. Thank you very much for your endless love to me. We did not have that much time together since 11 years ago when I entered the university. But I know your hearts were constantly going on with me and you were always on my side to support me. I thank you all more than I can say.

List of Figures

Introduction

In this introduction chapter, we will give the motivation of this thesis work respectively on measurement of neutron-induced fission of 237 Np and measurement of a new neutron beam line at neutron time-of-flight (n_TOF) facility at CERN. Then we will give a overview of this thesis.

Motivation

Brief overview of nuclear energy industry

Since the neutron was discovered by James Chadwick in 1932 [1], scientists realized that it would make a good probe of the atomic nucleus. Subsequently, with a series of research work by Fermi, Hahn, Strassman, Meitner and Frisch [2,[START_REF] Hahn | Über den nachweis und das verhalten der bei der bestrahlung des urans mittels neutronen entstehenden erdalkalimetalle[END_REF][START_REF] Meitner | Disintegration of uranium by neutrons: a new type of nuclear reaction[END_REF] in late 1930s, fission phenomenon accompanied with release of a large amount of energy was discovered when the Uranium was bombarded with neutrons. From the mid of 20th century, attention was given to harnessing this nuclear energy in some peaceful applications, such as for making electricity. Then, the nuclear energy industry came out and has been undergoing a rapid development in past 70 years.

The world first "nuclear power plant", which is an experimental breeder reactor located in Arco, Idaho, generated electricity to light four 200-watt bulbs on December 20th, 1951. This milestone symbolized the beginning of the nuclear power industry.

INTRODUCTION

The world first large-scale commercial nuclear power plant, located in Shippingport, Pennsylvania, began operation on December 2nd, 1957 and reached its full design power three weeks later. Since 1960s, several different types of reactors were built and nuclear power industry grew rapidly worldwide. Until January 2017, there are over 440 commercial nuclear power reactors operating in 31 countries, with over 390,000 MWe of total capacity. About 60 more reactors are under construction. They provide over 11% of the world's electricity without carbon dioxide emissions [5]. The use of nuclear energy will probably keep increasing in the future due to its cleaness with respect to dioxide emission and reliability.

Neutron-induced fission cross section of 237 Np

237 Np is one of the most important minor actinides in spent nuclear fuel since it is a byproduct abundantly produced in present nuclear reactor and it has a long half life (2.14 million years). Therefore it can be considered as a potential target of incineration in fast reactors. This requires a good knowledge of 237 Np's behavior under irradiation and in particular its neutron-induced fission properties. Consequently, its fission cross section received a special attention in the last decade and has been measured at different facilities. The recent measurement at CERN n_TOF facility in 2010 [START_REF] Paradela | Neutron-induced fission cross section of 234 U and 237 Np measured at the cern Neutron Time-of-Flight (n_TOF) facility[END_REF] indicates some discrepancies by comparison to previous measurements and evaluations. Figure 1.1 presents the fission cross section of 237 Np from fission threshold to 1 GeV, where the n_TOF data is shown together with evaluations and some experiment data as a comparison. It can be seen that the cross section shape of the n_TOF data is identical with evaluations. And the data from Garlea [START_REF] Garlea | Integral neutron cross sections measured around 14 MeV[END_REF], Meadows [START_REF] Meadows | The fission cross section of 230 Th, 232 Th, 233 U, 234 U, 236 U, 238 U, 237 Np, 239 Pu and 242 Pu relative to 235 U at 14.74 MeV neutron energy[END_REF], Marla [START_REF] Merla | Absolute measurements of neutron induced fission crosssections of 235 U, 238 U, 237 Np and 239 Pu using the time correlated associated particle method (TCAPM)[END_REF] and Alknazov measured with monoenergetic neutron sources around 14 MeV are also in agreement with n_TOF data within the error bars. Besides, our result is also identical with Jiacoletti's data [START_REF] Jiacoletti | Fission cross sections of Neptunium-237 from 20 eV to 7 MeV determied from a nuclear-explosive experiment[END_REF] up to 5 MeV. However, n_TOF data is higher by about 6% above 1 MeV compared with ENDF/B-VII.0 and JENDL-3.3 evaluations. Even larger differences of 8% are found above 6 MeV respecting to JENDL-3.3 evaluation, which is significantly beyond the 3-4% systematic uncertainty of the present data. This singularity of the n_TOF data could shed some doubt on its validity. surements. However, some of them are arbitrarily renormalize to each other instead of using an absolute renormalization based on targets' quantities. Tovesson's measurement [START_REF] Tovesson | Neutron induced fission cross sections of 237 Np from 100 keV to 200 MeV[END_REF] is normalized by reproducing the ENDF/B-VI ratio at 14.8 MeV since their targets' quantities are not well known, which is finally following the results of Meadows [START_REF] Meadows | The fission cross section of 230 Th, 232 Th, 233 U, 234 U, 236 U, 238 U, 237 Np, 239 Pu and 242 Pu relative to 235 U at 14.74 MeV neutron energy[END_REF]. Shcherbakov's measurement [START_REF] Shcherbakov | Neutron-induced fission cross section of 233 U, 238 U, 232 Th, 239 Pu, 237 Np, nat Pb and 209 Bi relative to 235 U in the energy range range 1-200 MeV[END_REF] is actually also a shape measurement based on the evaluated data below 14 MeV. Therefore the data based on the absolute fission cross section ratio with a good knowledge of target quantity and detection efficiency are scarce.

A simulation was carried out to check the validity of 237 Np fission cross section data measured at n_TOF . A 237 Np criticality benchmark experiment performed at Los Alamos [START_REF] Sanchez | Criticality of a 237 Np sphere[END_REF] was simulated [START_REF] Leong | Criticality experiments for validation of cross sections: The neptunium case[END_REF]. The simulation predicts a multiplication factor k ef f in better agreement with the experiment results when we replace the ENDF/B-VII.0 evaluation of the 237 Np fission cross section by the n_TOF data, thus supporting the validity of the latter.

Moreover, a series of measurements relevant to the fission cross section of 237 Np have been done recently by P. Salvador-Castiñeira et al [START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu up to E n = 3 MeV[END_REF][START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu[END_REF] at the Van de Graaff facility at JRC-IRMM (Joint Research Center Institute for Reference Materials and This is not the case when they use 237 Np evaluation data.

INTRODUCTION

Following their previous study, Salvador-Castiñeira et al [START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu[END_REF] have also measured neutron-induced fission cross section of 237 Np, as shown in figure 1.4, by using 235 U and In the above measurement of Salvador-Castiñeira et al [START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu up to E n = 3 MeV[END_REF][START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu[END_REF], their target quan-

INTRODUCTION

tities and detection efficiencies are well known, which means they achieve the absolute cross section ratio instead of using arbitrary renormalization. Therefore the agreement between their results and our n_TOF data is favoring our validity.

From the above discussion and present status we can conclude that a measurement of the absolute fission cross section of 237 Np is highly desired to give a definite answer.

Therefore we are motivated to measure the absolute fission cross section ratio of 237 Np relative to 235 U with accurate control on the detection efficiency and target quantities.

Commissioning of a new neutron beam line at n_TOF

A new second experimental area (EAR-2) at CERN n_TOF facility, having a flight path of ⇠20 m from the spallation lead target and at 90 degrees with respect to the incoming proton beam, was constructed and under commissioning since 2014. It is offering following advantages compared with the former experimental area 1 (EAR-1):

1) much higher neutron flux (by about a factor of 40) due to its short flight path (EAR-1 has a ⇠185 m flight path) and larger solid angle; 2) for highly radioactive samples an additional factor 10 is obtained for the signal to noise ratio due to shorter time interval resulting from the 10 times shorter flight distance [START_REF] Chiaveri | Proposal for n_TOF experimental area 2[END_REF][START_REF] Gunsing | Nuclear data measurements at the upgraded neutron timeof-flight facility n_TOF at CERN[END_REF], thus fulfilling the demands of the neutron science community for a Time-of-Flight (TOF) facility with a higher flux [START_REF] Bracco | Perspectives of nuclear physics in Europe: NuPECC long range plan[END_REF].

With the successful commissioning of the EAR-2, it is urgent and important to know its beam property (flux and beam profile) since it is essential for the experimental proposal, design and analysis. The neutron flux is even mandatory to be known in some experiments, for example neutron-capture measurement. Therefore, a precise measurement of EAR-2 neutron flux in a large energy range is indispensable. Our parallel plate avalanche counter (PPAC) detectors are good candidates to perform the beam measurement due to their good time resolution, fast signals and position sensitive ability. That's the reason why we've done this beam measurement for this new neutron line.

Overview of the thesis

In chapter 1, we introduce the background and motivation of this thesis work.

Overview of the thesis

In chapter 2, the theories about fission model and the fission fragment angular distribution (FFAD) are presented, since fission theory can help us to understand the design of the experimental setup and analysis method. The typical fission models, liquid drop model (macroscopic approach) and the liquid drop model with shell effect correction (macroscopic-microscopic approach), are discussed concerning the deformation and the fission of the nucleus. GEF (GEneral Fission description) code, a semi-empirical model, is also presented since it is a powerful tool to describe the fission. Then a theory on the FFAD taking into account the quantum effect of the nucleus is discussed qualitatively.

In chapter for measuring the beam properties (integral neutron flux, beam profile). The second one is in EAR-1 to measure the fission cross section and FFAD of 237 Np. Their experimental setups are shown independently.

In chapter 5, the data analysis of beam measurement at EAR-2 is presented in details. The data analysis begins with the raw data treatment. The current programs for treating the raw data are generally depicted. Then, we discuss how we proceed the data analysis specifically as following: i) select the fission events, ii) define the neutron energy, iii) locate the fission fragment and reconstruct the fission trajectory, iv) extract the detection efficiency. Finally we show the results: the integral neutron flux and beam profile of EAR-2.

In chapter 6, we discuss the data analysis of fission of 237 Np. The same analysis approach discussed in chapter 5 is applied here to obtain the fission rate and reconstruct the fission trajectory. Then, we present the characteristics of tilted setup which is different from the perpendicular setup described in chapter 5, based on which we extract the FFAD.

INTRODUCTION

In chapter 7, we introduce the method for deducing the cross section and give the first results of 237 Np's fission cross section from fission threshold to 5 MeV. It is compared to the evaluation and some other experimental data as well.

In chapter 8, we give the conclusion of the two experiments and present the outlooks of this thesis work.

Chapter 2

Fission theory

To begin with this chapter, we will firstly present three nucleus fission model: the liquid drop model, nuclear shell model and GEF model. Then we will introduce and quantitatively discuss the theory about fission fragment angular distribution.

Fission model

Liquid drop model

The liquid drop model, which is also referred as macroscopic model, of nucleus was proposed by G. Gamow [START_REF] Gamow | Mass defect curve and nuclear constitution[END_REF] in 1930 based on the following hypothesis:

• The nuclear fluid is made of nucleons (protons and neutrons), which are held together by the strong nuclear force. Hence it is not compressible.

• Like the liquid drop, the nucleus is compact as a spherical volume due to the surface tension.

• The charge and mass densities of nucleus are homogeneous and constant.

Binding energy

Based on the liquid drop model of nucleus, one of the first theory which could describe very well the behavior of the nuclear binding energy and therefore of nuclear mass is the semi-empirical mass formula (SEMF) proposed by C. F. V. Weizsäcker in 1935 [START_REF] Weizsäcker | Zur theorie der kernmassen[END_REF].

FISSION THEORY

The nuclear binding energy as a function of the mass number A and the number of protons Z can be calculated by SEMF as equation 2.1:

E b (MeV ) = a V A a S A 2/3 a C Z 2 A 1/3 a A (A 2Z) 2 A ± a A 3/4 (2.1)
The physical meaning of this equation can be discussed term by term.

(1) Volume term -a V A. The first positive term a V A is known as the volume term and it is caused by the attracting strong forces between the nucleons. The strong force has a very limited range and a given nucleon may only interact with its direct neighbors.

Therefore this term is proportional to A.

(2) Surface term -a S A 2/3 . The second surface term is also based on the strong force, it is a correction to the volume term. In the volume term, it is suggested that each nucleon interacts with a constant number of nucleons, independent of A. This is true for the nucleons deeply inside the nucleus, but causes an overestimation of the binding energy on the surface since the nucleons on the surface are interacting with less nucleons compared with interior ones. If the volume of the nucleus is proportional to A, then the geometrical radius should be proportional to A 1/3 and therefore the surface term must be proportional to the surface area which is proportional to A 2/3 .

(3) Coulomb term -a C Z 2

A 1/3 . The third term describes the Coulomb repulsion between the uniformly distributed protons and is proportional to the number of proton pairs Z 2 R , whereby R is proportional to A 1/3 . This effect lowers the binding energy because of the repulsion between protons.

(4) Asymmetry term -a

A (A 2Z) 2 A
. The fourth term is a quantum correction that is not based on any of the fundamental forces but only based on the Pauli exclusion principle (two fermions cannot occupy exactly the same quantum state in an atom).

The heavier nuclei contain more neutrons than protons. These extra neutrons are necessary to stabilize the heavier nuclei. They provide some compensation for the repulsion between the protons. On the other hand, if there are significantly more neutrons than protons in a nucleus, some of the neutrons will be in higher energy level in the nucleus. This is the basis for a correction factor, the so-called asymmetry term.

(5) Pairing term -a A 3/4 . The last term is the pairing term who captures the effect of spin-coupling. It is 0 for odd mass nuclei, proportional to +A 3/4 for nuclei with an even number of protons and neutrons, and proportional to A 3/4 for nuclei with an odd number of protons and neutrons. 10

Fission model

The coefficients of the five terms have units of MeV and can be calculated by fitting to experimentally measured masses of nuclei. They usually depend on the fitting methodology. According to J. W. Rohlf [START_REF] Rohlf | Modern Physics from alpha to Z0[END_REF] the coefficients in the equation are following: Bohr and Wheeler studied fission mechanism based on the quadrupole deformation of a liquid drop in 1939 [START_REF] Bohr | The mechanism of nuclear fission[END_REF]. The radius elongation at deformation can be described as a function of polynomial:

E b (MeV ) = 15.76A 17.81A 2/3 0.711 Z 2 A 1/3 23.7 (A 2Z) 2 A ± 34A 3/4 (2.2) 2.1.1.

Nucleus deformation

R(✓) = R 0 [a 0 + a 2 P 2 (cos✓)] (2.3)
where ✓ is the angle of the radius vector, R 0 is the original radius of the spherical nucleus, a 2 is a parameter quantifying the deformation (a 2 = 0 for a sphere) and P 2 is a Legendre second order polynomial.

The overall variation of the energy brought by this deformation is:

E def = E LDM (a 2 ) E LDM (0) (2.4)
where E LDM (0) is the energy of the undistorted sphere, E LDM (a 2 ) is the energy at deformation status.

According to the liquid drop model the nucleus is incompressible, therefore its volume is not changing at deformation. So the volume term is conserved. Besides, the 2. FISSION THEORY asymmetry term and the pairing term are not affected by the deformation neither, because they only depend on the number of the nucleons which are also conserved during deformation. Therefore only surface and Coulomb terms need to be taken into account.

The surface and Coulomb energies for small distortion are [START_REF] Bohr | The mechanism of nuclear fission[END_REF]:

E S (a 2 ) = E S (0)(1 + 2 5 a 2 2 ) E C (a 2 ) = E C (0)(1 1 5 a 2 2 ) (2.5)
where E S (0) and E C (0) are the surface and Coulomb energies of the undistorted sphere. Based on equation 2.4 and equation 2.5, the deformation energy is:

E def (a 2 ) = E S (a 2 ) + E C (a 2 ) E S (0) E C (0) = 2 5 a 2 2 E S (0)
1 5

a 2 2 E C (0) (2.6)
With the deformation of the nucleus, the surface energy is increasing because any deformation results in a larger surface, whereas the Coulomb energy is decreasing since the average distance between protons is increasing. Therefore these two terms compete along the deformation. The deformed nucleus is able to return to the undistorted shape when the potential energy of a spherical nucleus is lower than the deformed one, i.e.

E

def > 0, since the nucleus always tends to have the lowest potential energy. Otherwise, the nucleus will stay at this deformation or even go to further deformation and undergo fission. Therefore the stability of a spherical nucleus is given by E def > 0 which is equal to E C (0) < 2E S (0). This leads to the definition of the fissility parameter: [START_REF] Vandenbosch | Nuclear Fission[END_REF] and corresponds to the saddle point of the nucleus. From this point, the decrease in the Coulomb energy begins to overwhelm the increase in the surface energy. As a consequence, the potential energy of the nucleus starts to decrease. Then the nucleus is not able to recover from the deformation and it will continue deforming and will finally fission. This maximum of the deformation energy is the fission barrier, indicating that fission may occur if the excitation energy of the nucleus is beyond this value.

x = E C (0) 2E S (0) ' 1 50
Z 2 A (2.
The liquid drop model gives a theoretical interpretation for the fission process and provides a satisfactory order of magnitude of fission barrier. However it cannot explain some important fission properties such as the asymmetric fission and "magic numbers".

FISSION THEORY

They can be explained by the Nuclear Shell Model which takes into account the quantum nature of the nucleus.

Nuclear shell model

Nuclear shell structure

The observation [START_REF] Mayer | On closed shells in nuclei[END_REF] of the enhanced stability of nuclei due to "magic numbers" of protons and neutrons pushed forward the development of the shell model of nucleus [START_REF] Haxel | On the "magic numbers" in nuclear structure[END_REF][START_REF] Mayer | Nuclear configurations in the spin-orbit coupling model. i. empirical evidence[END_REF]. In this model, nucleons are assumed to be independent, freely moving in a potential well generated by other nucleons and obeying the Schrödinger equation.

Strutinsky's method

Nilsson extended the shell model to deformed nuclei [START_REF] Nilsson | Binding states of individual nucleons in strongly deformed nuclei[END_REF]. He developed diagrams to show single-particle energy levels as a function of the nuclear deformation.

However, the calculation of the total energy and mass of the nucleus based purely on the shell model was not precise. Then Strutinsky applied shell correction into the liquid drop model to take advantage of both models which is named as the macroscopic (liquid drop model)-microscopic (shell effect) method. In this method, the total energy of the nucleus is taken as the liquid drop model energy E LDM with the shell ( U ) and pairing ( P ) correction, This hybrid macroscopic-microscopic approach overcame the main weakness of liquid drop model and nuclear shell model and gave a good description of the fission.

E = E LDM + U + P (2.

Semi-empirical model GEF (GEneral Fission description)

The GEF model code has been developed in recent years by K. H. Schmidt et al [START_REF] Schmidt | General description of fission observables: GEF model code[END_REF] with the aim to provide dedicated nuclear data for application in nuclear technology and engineering. This model has a high degree of generality. Firstly, it treats spontaneous fission and fission up to an excitation energy of about 100 MeV for a wide range of heavy nuclei from polonium to seaborgium, secondly it calculates the majority of all possible fission quantities, thirdly, it is based on general properties of microscopic systems and general properties of a function in multidimensional space. More details about its theoretical ideas and physical models can be find in references [START_REF] Schmidt | General description of fission observables: GEF model code[END_REF][START_REF] Schmidt | General description of fission observables-JEFF Report 24[END_REF].

Fission Fragment Angular distribution (FFAD)

A theory about FFAD is presented here since we also measured FFAD of 237 Np in our experiment.

Description of the deformed rotating nucleus

The anisotropy of FFAD was observed for the first time in 1952 when studying the photonfission of 232 Th [START_REF] Brolley | Angular dependence of the neutron-induced fission process[END_REF]. In later experiments, anisotropic angular distributions of fission fragments were also found in neutron-induced fission [START_REF] Brolley | Angular dependence of the neutron-induced fission process[END_REF][START_REF] Henkel | Angular distribution of fragments from neutron-induced fission of U 238 and Th 232[END_REF].

R. Vandenbosch and J. R. Huizenga [START_REF] Vandenbosch | Nuclear Fission[END_REF] developed a theory to describe the FFAD based on the model of axially symmetric transition states at the saddle point of the fissioning nucleus. As figure 2.6 shows, when a nucleus is deformed with an axial

Fission Fragment Angular distribution (FFAD)

symmetry (fission direction), its total angular momentum is J. M is the projection of J on an arbitrary fixed axis, which is usually taken as the neutron beam direction in neutron-induced fission, K is the projection on the symmetric axis and R is the projection on any axis perpendicular to K. J is conserved in the entire fission process because of the conservation of the total angular momentum. K is the projection of the angular momentum of the nucleons in the frame of the deformed nucleus which is also rotating like a rigid body with an angular momentum R. Therefore

J = K + R (2.9)
In figure 2.6, ✓ is the angle between the nuclear symmetry axis and the space fixed axis, is the azimuthal angle around it, is the azimuthal angle around the symmetry axis. The angular wave function of the rotating deformed nucleus obeys the equation 2. 10 [36]:

~2 2J ? [ 1 sin✓ @ @✓ (sin✓ @ @✓ ) + (cos✓ @ @ @ @ ) 2 sin 2 ✓ ] + ~2 2J k @ 2 @ 2 + E = 0 (2.10)
where J k is the moment of inertia of the rotation around the symmetry axis, J ? is the moment of inertia around an axis perpendicular to it.

The solution of the equation is:

= r 2J + 1 8⇡ 2 • e iM • e iK • d J M,K (✓) (2.11)

FISSION THEORY

where d J M,K (✓) is the rotation matrix, independent of and and introduced by Wigner [START_REF] Wigner | Group Theory and its application to the quantum mechanics of atomic spectra[END_REF]:

d J M,K (✓) = p (J + M )!(J M )!(J + K)!(J K)!⇥ X n ( 1) n [sin(✓/2)] M K+2n [cos(✓/2)] 2J+K M 2n (J M n)!(J + K n)!(M K + n)!n! (2.12)
Therefore the angular distribution for the fission fragments

W J M,K (✓) at angle ✓ is W J M,K (✓) = 2J + 1 2 | d J M,K (✓) | 2 (2.13)
and the rotational energy levels of the fissioning system is:

E rot = ~2 2J ? [J(J + 1) K 2 ] + 2 J k K 2 (2.14)

Angular distribution in neutron-induced fission

As has been mentioned, the fission direction is the symmetry axis and the FFAD is given by equation 2.13. Here we assume that the projection of J on symmetry axis, K, remains constant along the fission process from the saddle point, where the fission is decided, to the scission point when the fragments are separated. This hypothesis is true if the nucleons stay on their individual orbits along the fission, since K is the projection of the angular momentum of the nucleons in the frame of the deformed nucleus.

In the case of neutron-induced fission, we need to take into account both the neutron's spin s (1/2) and the target's spin Ĩ0 . Hence the channel spin (total spin of the compound nucleus) is:

S = Ĩ0 + s (2.15)
and the total angular momentum J of the compound nucleus is given by the sum of S and its orbital angular momentum L:

J = S + L (2.16)

Case of even-even targets

The spin of even-event targets, for example 238 U, is equal to 0 ( Ĩ0 = 0). According to equation 2.15 and 2.16, the relations of the corresponding quantum numbers are :

S = s = 1/2 J = l ± 1/2 M = ±1/2
(2.17)

Fission Fragment Angular distribution (FFAD)

From equation 2.13, we can obtain the FFAD for a given J and K by:

W J ±1/2,K (✓) = 2J + 1 4 (| d J 1/2,K (✓) | 2 + | d J 1/2,K (✓) | 2 ) (2.18)
Figure 2.7 shows the FFAD calculated by equation 2.18 for even-even target with different couples of (K, J), from which we can deduce following arguments. • If only s-waves (l = 0) are involved, J = K = 1 2 , the FFAD is flat because J is fully de-oriented and the probability of the different emission angle is the same.

The theoretical FFAD curve is shown in figure 2.7 labeled with W ( 1 2 , 1 2 ).

• When K ⌧ J, the emission is forward-backforward peaked. In this case, the direction of J is very close to l which is orthogonal to the beam axis, which means fragments are emitted orthogonally to J. Beam axis is the only direction that all the contributions from all directions of J add up, therefore the angular 2. FISSION THEORY distribution, as the curves with W ( 1 2 , 7 2 ) and W ( 1 2 , 5 2 ) in figure 2.7, is peaked at 0 degree.

• When K ⇡ J, the fission axis is along J. As J is orthogonal to the beam axis, so is the fission direction and the FFAD is sideward peaked as the curve of

W ( 3 2 , 3 2 ) in figure 2.7.

Case of even-odd targets

The spins of the even-odd targets, such as 235 U and 237 Np, are not 0:

I ⇡ 0 = 7 2 for 235 U, I ⇡ 0 = 5 2 +
for 237 Np. The corresponding channel spin is S = 3 or S = 4 for 235 U, S = 2

or S = 3 for 237 Np. Since the channel spin is unpolarized here and larger than the case of even-even targets, S contributes significantly to the de-orientation of the J.

An even-odd target becomes a compound even-even target after capturing a neutron.

Due to the pairing effect, the neutron binding energy is larger. As a consequence, the excitation energy of the compound nucleus is much larger than the fission barrier for the even-even target. At high excitation energy the distribution of K becomes statistical and the probability is proportional to the number of intrinsic single particle states contributing to this K at the saddle point. So statistical method is needed to describe the states.

The distribution of K probability has a Gaussian form like:

⇢(K) / exp( K 2 2K 2 0 ), K  J (2.19)
where

K 2 0 = J ef f T ~2 , J
ef f and T are, respectively, the effective moment of inertia and the thermodynamic temperature of the fissioning nucleus. J ef f can be calculated by:

J ef f = J ? J k J ? J k (2.20)
where J ? and J k are respectively the parallel and perpendicular moment of inertia as have been introduced in section 2.2.1.

From equation 2.19 we can see that K distribution extends to higher values when the temperature is increasing or the mass is increasing which can cause the increase of the moment of inertia. At high incident energy l increases more rapidly than K 0 so that K is generally lower than J. According to the above discussion, the FFAD is often forward-backward peaked. Anisotropy also shows a multiple chance structure similar to the fission cross section as shown in figure 2.8. A structure occurs at an excitation energy where second-chance (n, nf), third-chance (n, 2nf), ..., become energetically possible. When a new fission chance is open, the total angular momentum J is slightly affected whereas K 0 drops significantly due to the drastic decrease of the temperature due to the emission of the neutron. Therefore anisotropy is enhanced.

Chapter 3 n_TOF facility at CERN

The experiments in this thesis work have been performed at the n_TOF facility at CERN. In this chapter, we will briefly present the structure of n_TOF facility and its features for measuring nuclear data.

The idea of n_TOF was proposed by C. Rubbia et al [START_REF] Rubbia | FACIL-ITY AT THE CERN-PS TO MEASURE NEUTRON CROSS SECTIONS IN THE INTERVAL FROM 1 eV TO 250 MeV: A RELATIVE PERFORMANCE ASSESSMENT[END_REF]

Proton beam

The 20 GeV/c proton beam is from CERN's Proton Synchrotron (PS) accelerator, which is capable of accelerating ⇡3⇥10 13 protons per cycle. This extraordinarily prolific beam is concentrated in a very short pulse to serve a tremendous precise time-of-flight (TOF) determination for neutron energy. The proton beam line allows to vary the beam spot size at the lead target level [START_REF] Berthoumieux | The neutron Time-Of-Flight facility nTOF at CERN (I)[END_REF].

The proton beam can be delivered on spallation target in two different operational modes: dedicated (primary) mode and parasitic mode. In primary mode a typical 7 ⇥ 10 12 protons bunch with 20 GeV/c momentum is sent to the target with a 1.2 s PS cycle fully dedicated to n_TOF . The bunch time distribution has a Gaussian shape with 7 ns RMS. In parasitic mode, ⇠ 3.5 ⇥ 10 12 protons bunch is extracted from PS and sent to n_TOF . The pulse shape and beam profile at the spallation target are almost the same as the one in dedicated mode.

The number of protons per pulse is determined pulse by pulse by using a Beam Current Transformer (BCT) located in proton beam about 6 m upstream from spallation target. A resistive Wall Current Monitor (WCM) is mounted immediately after the BCT which provides a signal proportional to the proton beam current and could be used either for timing reference or to monitor directly the proton beam intensity [START_REF] Abbondanno | CERN nTOF facility: performance report[END_REF].

Spallation target

The spallation target, figure 3.2, is a cylindrical lead block of 60 cm in diameter and 40 cm in length with a high purity of 99.99%. It is surrounded by a 1 cm layer of demineralized water dedicated for cooling and in the forward direction is attached an additional 5 cm moderator layer filled with 10 B-loaded water. The water in the moderator layer can moderate the initially fast neutrons into the desired energy spectrum, which ranges down to thermal energies. 10 B is used for absorbing the 2.23 MeV rays emitted from the neutron capture in water to reduce the background.

N_TOF FACILITY AT CERN

Neutrons beam lines

Horizontal beam line to EAR-1

The neutrons emitted from the spallation target are traveling in a vacuum tube kept at 10 2 mbar to avoid the scattering by nitrogen and oxygen in the air. The angle on the horizontal plane between the proton beam axis and neutron beam is 10 in order to minimize the collection of unwanted secondary particles in the EAR-1. A sweeping magnet at a distance of ⇠150 m is used to remove all the remaining charged particles.

Neutrons fly toward to EAR-1 at ⇠185 m downstream from the target through two collimators as shown in figure 3.3.

The first collimator located at ⇠135 m has a 11 cm aperture in diameter and consists of iron and concrete with a total thickness of 2 m. The second collimator close to experimental area located at ⇠175 m defines the beam spot which is changeable. For the neutron capture measurement a collimator with a small aperture, 1.9 cm in diameter, is used to reduce the neutron halo around beam. In the case of neutron-induced fission measurement, when samples with large size are used, we can enlarge the collimator Filter station can hold some filters inserted in the beam line to measure the background in the resonance region. Filters are typically made of thick materials having strong resonances: neutrons having an energy corresponding to the resonance are totally absorbed by filters so that those which are still seen at this energy come from a background or from neutrons outside the expected time-energy dependence. Silver, tungsten, cobalt, molybdenum and aluminum filters have been used as filters at n_TOF for neutron energies at 5.1, 18.8, 45, 132, 3.5⇥10 4 and 8.7⇥10 4 eV respectively.

Neutrons beam lines

After the shielding at the exit of the experimental area, the neutron escape line, a tube with a =400 mm in diameter and ⇠8 m in length ending at 200 m from the spallation target, is used to avoid neutron back-scattering in the experimental area.

After that, neutrons reach the beam dump composed of borated paraffin. Thanks to the above very efficient collimating and shielding system, the background at EAR-1 of n_TOF is very low. The beam dump installed on the roof of the experimental hall consists of three layers to fully absorb the neutron beam. The core of the dump is a block of B-PE to slow down and capture neutrons from the beam and back-scattered neutrons from the consecutive beam dump layers as well. This core part is a block of 400 ⇥ 400 ⇥ 400 mm 3 with a hole, 250 mm in height and 340 mm in diameter, where the last vacuum tube of the beam line is inserted. The B-PE is surrounded by iron blocks to absorb the fast neutrons and photons in the beam with outer dimensions of 1600 ⇥ 1600 ⇥ 1600 mm 3 . The beam dump is finally shielded by concrete with outer dimensions of 3200 ⇥ 3200 ⇥ 2400 mm 3 [START_REF] Weiss | The new vertical neutron beam line at the CERN n_TOF facility design and outlook on the performance[END_REF].

Neutron flux

A permanent dipole magnet is installed at 10.4 m above the spallation target to deflect out all the charged particles originated in the spallation process in the lead target. The magnetic field in the center of the magnet is 0.253 T, over the total dipole length of 1.134 m. The integrated field is 0.287 Tm.

A neutron filter station is placed at 11.4 m above the spallation target. Filters can be used are molybdenum, tungsten, cobalt, silver, aluminum, lead, bismuth and cadmium with a thickness from less than 1 to tens of millimeters to blank out different neutron energies from the beam or to attenuate the in-beam photons.

Neutron flux

N_TOF FACILITY AT CERN

The measured neutron fluxes of EAR-1 [START_REF] Barbagallo | High-accuracy determination of the neutron flux at n_TOF[END_REF] and EAR-2 [START_REF] Sabate-Gilarte | High-accuracy determination of the neutron flux in the nex experiemntal area EAR2-n_TOF at CERN[END_REF] are shown in figure 3.5.

The shapes the EAR-1 and EAR-2 fluxes are similar. The high energy neutrons above 10 MeV are from the high energy processes of spallation. The strong peak around 1 MeV is the evaporation of neutrons from spallation process. The falling tail from 1 MeV to tens of keV is due to the moderation in the lead target. The flat part less than ⇠10 keV is caused by the moderation in the water surrounding the target. The strong absorption at thermal neutron peak in EAR-1 caused by the 10 B-loaded moderator on the target only attached to the forward direction to EAR-1 (see in figure 3.2). The several deeps between 100 eV and hundreds of keV are caused by the absorption of aluminium, manganese and oxygen in the beam.

The flux of EAR-2 is higher than EAR-1 with a factor of about 40 due to its shorter flight path and larger solid angle. This much higher flux makes it possible to measure targets of low mass and/or for reactions with low cross section in a reasonable time.

However this higher flux comes with the price of lower energy resolution compared with EAR-1 since the time-of-flight (TOF) is shorter.

Time-energy correlation

Neutron kinetic energy can be calculated in relativistic framework as:

E n = ( 1)m n c 2 (3.1)
with:

= 1 p 1 2 (3.2) = v c (3.3)
where m n is the neutron rest mass, c is the speed of light, v is the neutron velocity. So the incident neutron energy can be obtained directly from its velocity which is calculated as:

v = L geom T OF (3.4)
in equation 3.4, L geom is the geometric fixed flight length from the outer surface of the moderation layer around the spallation target to the experimental area where the neutron-induced reaction happens. T OF is the neutron time of flight of this path.

Time-energy correlation

When neutrons are generated in the spallation target, to begin with, they are slowed down in the lead target and further moderated in the cooling and moderation layer, then they fly through the geometric flight path L geom with a constant velocity. The experimental measured time of flight T is the difference between the detection of a neutroninduced reaction and the generation of neutrons, which is a sum of the moderation time T mod and T OF .

T = T mod + T OF (3.5) so the neutron velocity is v = L geom T T T OF = L geom T T OF + T mod T OF = L geom T (1 + T mod T OF ) = L geom + vT mod T (3.6)
vT mod can be defined as an equivalent moderation length which can be obtained by simulation, so the velocity can be written as

v = L geom + T (3.7)
where L geom + can be regarded as an effective flight path L. (we use the most probable at each given energy), we can deduce the effective L at different energy. This approach will be discussed in section 5.4.1.

Energy resolution

According to equation 3.1, 3.2 and 3.3, we have

dE E = d 1 = ( + 1) d = ( + 1) dv v (3.8)
from which it can be seen that energy resolution is directly related to the velocity resolution. Therefore the energy resolution is

E E = ( + 1) r ( L L ) 2 + ( T T ) 2 (3.9)
where stands for the standard-deviation. L is from the fluctuation of the moderation distance from the simulation, T is due to the width of proton bunch which is of order of 7 ns. Apparently the longer the flight path, the better the resolution. At high energy T dominates the energy resolution and at low energy L is dominant. The simulated energy resolution as function of neutron energy in EAR-1 [START_REF] Guerrero | Performance of the neutron time-of-flight facility n_TOF at CERN[END_REF] and EAR-2 [START_REF] Lerendegui-Marco | Geant4 simulation of the n_TOF -EAR2 neutron beam: Characteristics and prospects[END_REF] are shown in table 3.1, through which it can be seen that the energy resolution in EAR-2 is limited compared with EAR-1.

Energy resolution

E n E n /E n (eV) EAR-1 EAR-2 1
Chapter 4

Experimental setup at n_TOF

In this PhD work, two experiments have been done at n_TOF facility at CERN, one in each of the experimental areas. Their setups will be discussed in this chapter. In the last section, other detection systems at n_TOF that are not used in our experiments will be briefly introduced.

Parallel Plate Avalanche Counter

The high energy neutrons generated at n_TOF , up to GeV, make it possible to study neutron-induced fission in spallation region. In this domain, on one hand, other reaction channels are opened to compete with fission; on the other hand, the instantaneous counting rate is very high. These constraints lead us to select fission event by the detection of two fission fragments in coincidence and to use PPAC due to its excellent time resolution.

Principle of the fission detection by PPAC

The principle of the fission event detection by PPACs is sketched in figure 4 Concerning the detection method and n_TOF facility characteristics, the detection system is designed as following to fit them well:

1) detector is close to target to cover a large solid angle.

2) target and its backing are very thin so that more fission fragments can go through and come out from it.

3) target size is large to suit the large beam spot size and accumulate as much statistics as possible.

When two fission fragments are localized on the detectors, as figure 4.1 shows, the emitting point on the target can be reconstructed out based on the assumption that two fission fragments are emitted in a back to back direction in laboratory system. This is true for the fission induced by the low energy neutrons because the momentum transferred to the fission nucleus is very small. However it's not the case for high energy neutrons where large momentum is transferred which can distort the back to back emission of the fission fragments.

A simulation based on 1 GeV neutrons and 235 U target is done to evaluate this effect. According to the simulation result, 4.2b, most of the events are concentrated on the diagonal of cos✓ m = cos✓ cm , some differences are present only at large emission angles about cos✓ cm less than 0.3. However, in the real case these large emission angles can not be detected due to the detection efficiency which will be described in latter chapter, so the emission of fission fragments could be treated as back to back in our case.

PPAC description

Each PPAC consists of a central anode for timing measurement and two cathodes with Electrodes are made of 1.7 µm thick mylar on which an aluminium or gold layer is deposited to make it conductive. The deposition is done by evaporating the melted aluminium or gold under vacuum so that atoms travel straightly and deposit uniformly on the mylar foil. For the anode an uniform layer of 30 nm is deposited on both sides of the mylar foil since it's the central electrode facing gaps on each side. Cathode is coated with an layer of 60 nm only on the side facing the gap. It is divided into 2 mm The distance between electrodes is 3.2 mm since the gap between them must be limited to a few millimeter to keep a high electric field, which is typically around 550 V 4. EXPERIMENTAL SETUP AT N_TOF over 3.2 mm. This high electric filed combined with a low gas pressure at about 4 mbar create a condition of proportional regime and a good time resolution.

The filling gas is C 3 F 8 (octafluoropropane) at a pressure of 4 mbar. It is preferred to isobutane which is used more generally because octafluoropropane gives more stable working conditions and overall for safety reasons since it is not flammable. A gas flow is mandatory to evacuate degassed molecules absorbed in the electrodes to keep a stable pressure. In this regulation a sensor measuring the pressure is connected to an automaton which gives orders to control valves insuring the constant pressure with 1% precision. A monitor program allows to control the regulation remotely at the n_TOF control room.

PPAC signal readout

When a charged particle is going through the gap, the gas is ionized and primary electron-ion pairs are generated along the trajectory. The electrons and positive ions drift towards the anode and cathode respectively. During this drift, electrons create an avalanche to the anode plane. Electrons drift so fast that their collection time is only around several nanoseconds. This anode signal is fed to a current preamplifier and finally output a signal with typical full width of 20 ns and rise time of 5 ns whose typical time resolution is 0.3 ns. This fast and high resolution anode signal helps avoiding pileup when the counting rate is high. In the meanwhile, negative charges induce positive charges in the cathode with the position centered on the avalanche position, thanks to the strips and delay line the accurate position can be obtained.

The delay line as shown in figure 4.5 built at Institut Physique Nucléaire d'Orsay (IPNO) is a plastic rod of 7 mm in diameter holding a cell of 1.4 mm in length in every 2 mm. Each strip on the cathode is connected to a delay line cell where there is a coil composed by 6 windings copper wire of 0.3 mm in diameter. A capacitor of 6.8 pF joints adjacent strips and a 10 pF capacitor connects each strip to ground.

With such a setup, the delay line has a typical impedance of about 300 ⌦ and its propagation velocity for signals is about 3.2 ns/strip. These delay lines have a better rise time and less amplitude attenuation than commercial ones. Both ends of one delay line are connected to a charge preamplifier which is matching its resistive impedance to minimize the reflection. When a signal is delivered out from a strip, it is split into two and transmitted oppositely to the ends of the delay line. The time for a signal to

Isotopes targets

Isotopes targets

A good compromise between a small energy loss of fission fragments in a thin target for good detection efficiency and a reasonable statistical counting rate can be obtained with a target thickness from tens to hundreds of µg/cm 2 . All the targets were made by electrodeposition of hydroxides in an organic solvent made conductive by adding some nitric acid. The deposition was done on a very thin aluminium backing (a few micrometers in thickness) placed as cathode in an electrolytic cell. The dimension of the target deposit is a circle of 8 cm in diameter. The yield of electrolysis was found to be better than 90% from the measured amount of deposit.

237 Np target material was from IPNO, 235 U and 238 U material were from CSNSM Orsay. All of the targets were made at IPNO. Some of them are shown in figure 4.6.

The purity of isotope targets is important to know. The purity of 235 U targets was measured by mass spectrometry with following results: 92.71% of 235 U, 6.28% of 238 U, 0.74% of 234 U and 0.27% of 236 U. The 238 U targets have a high purity since they are

EXPERIMENTAL SETUP AT N_TOF

prepared from natural uranium by a mass separator with a factor of separation better than 10,000.

The total mass of targets were measured by ↵-counting with a silicon detector in a well defined geometrical system. The solid angle of the silicon detector to the target was determined precisely with less than 1% uncertainty. The time duration of the measurement was determined by taking more than 10,000 counts in the silicon detector for the target isotopes. Consequently, the uncertainty of the target mass is lower than 1%.

PPAC experimental setup

We did one experiment at each experimental area. First one is the beam measurement of the EAR-2, second one is the measurement of the 237 Np(n, f) cross section and fission fragment angular distribution at EAR-1. Their setups are described in following sections.

PPACmon setup at EAR-2

A PPAC monitor chamber, which is called PPACmon, was designed and constructed by IPNO, jointly with the University of Santiago de Compostela (Spain) and CERN for monitoring the EAR-2 neutron beam. Its experimental setup is shown in figure 4.7a.

Neutrons coming from the underneath tube traverse the chamber and enter the above escape line which is connected to the dump at the end. There is a kapton foil with a thickness of 80 µm at both entrance and exit of the chamber. Inside chamber (5.

Detection systems at n_TOF

Several kinds of neutron-induced reaction measurements have been commissioned at n_TOF facility, among which the most significant ones are neutron-induced fission (n, f), capture and charged particle (n, cp) measurements. These systems have not been used in our experiments, but here we give a brief introduction to them.

Fission measurement

Apart from PPACs, a multi-stack Fission Ionization Chamber (FIC) and MicroMegas detector can be used for fission measurements. tor can also be used to detect neutron beam with a neutron/charged particle converter on the entry face [START_REF] Pancin | Measurement of the n_TOF beam profile with a micromegas detector[END_REF].

Capture measurement

Two different detection systems have been set up for capture measurement: a segmented array of 40 B a F 2 Total Absorption Calorimeter (TAC) [START_REF] Guerrero | The n_TOF Total Absorption Calorimeter for neutron capture measurements at CERN[END_REF] and an array of deuterated liquid scintillation detectors (C 6 D 6 ).

Chapter 5

Flux and beam profile measurement at EAR-2

In this chapter, the experiment at EAR-2 for measuring the beam will be discussed in details. We shall present how we proceed the data analysis step by step. At the end, we shall give the results we are interested in: the integral neutron flux and beam profile.

Steps of the analysis

The Data Acqusition system (DAQ) of n_TOF consists of tens of 12 bits and 14 bits digitizers with sampling rates of 1 GS/s and 500 MS/s. The signals delivered from the detectors' preamplifiers are sent to these digitizers directly. DAQ system is triggered by the signal given by the proton beam. Once a proton bunch is delivered to the n_TOF spallation target, the DAQ is activated and digitize all of the present channels in a given time window. This DAQ system is very powerful because it records the full detector response, so that we can recover the full experiment offline and do some corrections (such as dead time, pile-up) if necessary. As a consequence, huge raw data are generated and stored in CASTOR at CERN [51]. For example, the total raw data generated at n_TOF in 2016 including both EAR-1 and EAR-2 is 1400 TB.

The analysis of the data starts from the raw data treatment. At this step, we directly access the raw data on CASTOR to extract the characteristic information of signals, such as time and amplitude, and write them into new DST (Data Summary Tape) files or ROOT [52] files which are much more reduced than raw data for further

FLUX AND BEAM PROFILE MEASUREMENT AT EAR-2

analysis. With these new DST files or ROOT files, we can search the coincidences to identify fission events, reconstruct the trajectories of fission fragments and do other further analysis that we are interested in.

Raw data treatment

The main purpose of raw data treatment is to extract the relevant useful information from raw data for further analysis. Generally speaking, it is to scan the signal frames, to recognize the interesting pulses and pick out their characteristics, then write them into new files.

Dedicated PPAC routine

The dedicated PPAC routine recognizes the signals by applying derivative to signals above a setting threshold, since the waving of the baseline (especially close to the -flash region) could be removed and the signals of interest are still retained after derivative. However, the high frequency noise with low amplitude will be enhanced by direct derivative. So a low-pass filter is applied to smoothen the signals before derivative. files. Peak-to-peak amplitude of derivative signal is enough for PPAC since we are only interested in ratios of amplitudes in latter analysis.

n_TOF lib

The n_TOF lib package has the same philosophy as the PPAC routine to recognize the signals: first smoothen the original signals by filtering the high frequency noise, then calculate the derivative, finally recognize the signals by crossing the 2 thresholds with a lower-lower-upper-upper sequence. However, n_TOF lib can extract more signal information than PPAC routine since it is a general treatment that is applicable to a wide range of signals and detectors. For example, the output ROOT file generated by

FLUX AND BEAM PROFILE MEASUREMENT AT EAR-2

n_TOF lib contains the following information of each signal:

• Amplitude and area of each signal (PPAC routine outputs the peak-to-peak amplitude of derivative signal instead). Since it fits the baseline of the signal frame, it can find the absolute amplitude and area. The red curve in figure 5. [START_REF] Hahn | Über den nachweis und das verhalten der bei der bestrahlung des urans mittels neutronen entstehenden erdalkalimetalle[END_REF] shows the fitted baseline.

• Rise time. The time interval for the leading edge to rise from 10% to 90% of the amplitude.

• FWHM (full width at half maximum of amplitude) and FWTM (full width at tenth maximum of amplitude) time.

Fission event identification by coincidence method

As mentioned in section 4. There is an extra bump around 5 ns with amplitudes around 200. These events

FLUX AND BEAM PROFILE MEASUREMENT AT EAR-2

are actually from fissions in target0 which have to be removed since they are not from the fissionning target1 that we are tagging. These fission fragments from target0, after crossing PPAC1, continue flying through target1 and are detected by PPAC2. In this case, one fission fragment crosses two detectors, the other oppositely emitted fragment is detected by the third detector, so that to the end there is a triple coincidence. We can use the time difference between PPAC2 and PPAC0 to identify the triple coincidences and determine the corresponding fissionning target. For fissions from target0, T2 is definitely larger than T0 because the travel distance from target0 to PPAC2 is three times to the path from target0 to PPAC0. Fission from the target1 is the reverse case. (T2-T0) versus the amplitude of PPAC2 (A2). It can be seen that two bumps are well separated, the left bump are the fissions from target1 since T2-T0 is less than 0 and the right part is from target0. We can apply a cut to count the left part from target1. Besides, we also need to reject the coincident events due to the spallation reactions.

Spallation light nuclei coming from the impinging of high energy neutrons onto low Z elements in dead layers (C, O in mylar foil, Al in target backings and electrodes) can emit light particles (such as ↵ particle), thus there is a coincidence between it and spallation residual. However, their amplitudes are so much lower compared with fission fragment that they can be rejected. The sum of the amplitude of the coincident events as a function of neutron energy is shown in figure 5.7. We'll explain how to determine

Fission event identification by coincidence method

incident neutron energy in next section. Here we just show that there is a region for neutrons above 10 MeV with much lower amplitudes, these events are from spallation reactions instead of real fissions that has to be cut.

FLUX AND BEAM PROFILE MEASUREMENT AT EAR-2

Neutron energy determination

The incident neutron energy is determined by its velocity

v = L T T 0 (5.1)
where L is the flight path, T is the time recorded by the detector and T 0 is the starting flight time. So T T 0 is the time-of-flight (TOF). Among these 3 parameters, only T is precisely known because it is directly given by the anode of the PPAC. L and T 0 need to be determined. L is determined by the resonance peaks of 235 U at low energy (a few eV) where T 0 has a negligible impact because T is huge enough. And then T 0 is defined at high energy region where T is comparable to T 0 . The details of defining the L and T 0 are discussed in following subsections. enough to neglect T 0 so that we can use T instead of TOF. We compare the measured fission rate to the cross section in the database and use the sharp peaks to calibrate L. We know the flight path to EAR-2 is roughly around 20 m, so first we assume a

Flight path L

Neutron energy determination

flight path around 20 m to calculate the fission rate as a function of neutron energy and compare it with 235 U (n, f ) cross section in database. Then we adjust L until the best match is obtained. The comparison of fission rate with the cross section in database from 1 ev to 10 eV is shown in figure 5.9. The L determined here, 19.37 m, is the flight path including the moderation distance at this energy region. However we know from section 3.5 that the moderation distance varies with the energy. Therefore we can include the varying moderation distance (the most probable one) in the L determination which makes L depending on the neutron energy.

Starting flight time

T 0 T
0 is usually determined by the prompt -flash signal which is a sharp narrow peak at the beginning of the signal frame in case of the measurement at EAR-1. But this method is not applicable here since the sharp peak is not visible at EAR-2. Instead, we use the pickup (P K) signal of proton beam as the time reference to determine T 0 . Because the P K signal is delayed compared with the true T 0 , an offset has to be added to determine TOF:

T OF = T P K + of f set (5.2)
The offset is determined from both the the first fission event and simulation.

Localization method

The signal propagation in the delay is exemplified in figure 5.14. The cathode signal injected in the delay line at point x splits up into two signals that propagate oppositely until they reach the end.

The propagation time t X is defined as

t X = t SX t anode (5.
t SL t anode = t + L 2 + x v t SR t anode = t + L 2 x v (5.5)
where v is the propagation velocity, L is the length of the delay line, t is an additional delay taking into account the signal process in electronics. The position x can be obtained by making a subtraction of equation 5.5. The y position can be obtained in

Fission fragment localization

same way based on Top and Bottom signal.

x = v(t SR t SL ) 2 y = v(t SB t ST ) 2
(5.6)

The propagation velocity was measured with a fast signal generated by an electronic pulser. The signal was injected at different points of delay line, then we measured the time difference between two output signals at the both ends. With the given input position information, we can calculate the propagation velocity. With all the delay lines measured, we obtained an average propagation velocity: 2 mm/3.2 ns.

The equation 5.6 will be used for reconstructing the fission trajectory in following sections. For a given anode signal, we open a time window to search for the corresponding cathode signal couples (Left, Right) and (Top, Bottom). Then x and y position can be extracted by equation 5.6.

Cathode signal selection

From equation 5.4 and equation 5.5 we have the following relations:

t L + t R = (t SL t anode ) + (t SR t anode ) = 2 t + L v t B + t T = (t SB t anode ) + (t ST t anode ) = 2 t + L v
(5.7)

Above relations show that the sum of the propagation time is independent on the position but only depends on the total propagation time in the delay line which is determined by its length. This characteristic can be used as a selection criterion for cathode signals with the following procedure. The slight slope of the distribution is due to the attenuation in the delay line. For example, when it goes to the positive direction, Left signal propagates more distance than Right signal, so the attenuation of Left signal is larger and the a L /a R ratio is decreasing. When there are more than one combination present for one given anode signal, we use the above two criteria to select the proper combination with the following algorithm. For all the events inside the diagonal contour in figure 5.15, figure 5.17a is the distribution of sum of the t L and t R with its mean (M1) and RMS ( 1) value, figure 5.17b shows the distribution of ratio a L /a R with its mean (M2) and RMS ( 2) value. For each combination, we calculate the deviation from the mean value by weighting these two distributions with the following equation:

Beam profile reconstruction

= ( t T + t B M 1 1 ) 2 + ( a B /a T M 2
2 ) 2 (5.8)

Then we chose the combination whose deviation is the smallest.

Beam profile reconstruction

The methods for searching the anode coincidences and for selecting the proper cathode signals for a given anode signal have been presented respectively. With coincidence and localization information, we can reconstruct the position distribution of fission fragments hitting the detectors and then obtain the beam profile. The algorithm proceeds as follows:

1) Scan the anode signals of two adjacent PPACs to find coincident events within a ±20 ns window.

Beam profile reconstruction

we define the X axis pointing from right to left, Y axis is pointing out perpendicularly to the figure plane. The origin of the coordinate system locates on the target plane.

The first cathode following the beam direction determines the position in X axis (we refer this cathode as X plane), the second cathode determines the Y position (Y plane).

X X 1 X 2 X 1 = Z Z 1X Z 2X Z 1X = d + e 2d Y Y 1 Y 2 Y 1 = Z Z 1Y Z 2Y Z 1Y = d e 2d
(5.9) from which we can reconstruct the position (X, Y) on target by:

X = (d + e)X 1 + (d e)X 2 2d Y = (d e)Y 1 + (d + e)Y 2 2d
(5.10) beam profile is that it's not as uniform as at EAR-1 which will be shown in section 6.3 (figure 6.7). The beam intensity drops lower toward periphery. This is probably caused by the conical collimator setup [START_REF] Weiss | The new vertical neutron beam line at the CERN n_TOF facility design and outlook on the performance[END_REF] that is different with the cylinder collimator design for EAR-1.

Beam profile reconstruction

The fission angle cos ✓ and the azimuth angle can be calculated by equation 5.11.

cos ✓ = 2d p (X 2 X 1 ) 2 + (Y 2 Y 1 ) 2 + (2d) 2 tan = Y 2 Y 1 X 2 X 1 (5.11)
We can use the same reconstruction method (equation 5.12) to project the X, Y positions on the two cathodes on the central anode plane.

X 1anode = (2d + e)X 1 eX 2 2d Y 1anode = (2d e)Y 1 + eY 2 2d X 2anode = eX 1 + (2d e)X 2 2d Y 2anode = eY 1 + (2d + e)Y 2 2d
(5.12)

where (X 1anode , Y 1anode ) and (X 2anode , Y 2anode ) are the coordinates of hitting points on the anode plane of PPAC1 and PPAC2. angles (cos ✓ close to 1) the curve is flat and is not decreasing with the increase of ✓ which implies the efficiency at small angles is 100%. The measured angular dependence at any direction is the multiplication of efficiency and FFAD, so based on one of them we can deduce the other one. Here we use the FFAD of 235 U that we measured in 2012 [START_REF]Fission fragment angular distribution and fission cross section validation[END_REF] with tilted setup to obtain the efficiency.

The FFAD W (✓) in the center-of-mass frame can be represented by equation 5.14 [START_REF] Tutin | An ionization chamber with Frisch grids for studies of highenergy neutron-induced fission[END_REF]:

W (✓) = K norm (1 + (A 1) cos 2 ✓) (5.13)

Integral neutron flux at EAR-2

For the other distributions in figure 5.23 the FFAD is not isotropic any more, so we divide them by the corresponding FFAD to figure out the efficiency.

"(cos ✓) = a 0 (1 + e a 1 a 2 cos ✓ ) a 3
(5.15)

with the 4 parameters a 0 , a 1 , a 2 , a 3 to be fit. Figure 5.25 shows the efficiency curves normalized to 1 at 0 in different energy ranges. Their integrals give the global efficiency: 58.2%, 60.0%, 59.1% and 60.0% for energy range of (0, 100 keV), (100 keV, 1 MeV), (1 MeV, 10 MeV) and ( 10

Flux calculation

The measured fission rate at neutron energy E n in direction ✓ is:

dR(E n , cos ✓) = (E n ) • (E n ) • N • "(E n , cos ✓) • W (E n , cos ✓) • d⌦ cos ✓ (5.16)
where 65

FLUX AND BEAM PROFILE MEASUREMENT AT EAR-2

• E n is the neutron energy,

• R is the fission rate,

• is the neutron number integrated on the target surface which is called integrated neutron flux here,

• is the neutron-induced fission cross section of 235 U (JENDL/HE-2007 evaluation is used here for calculating the flux)

• " is the efficiency,

• N is the target thickness that can be measured by ↵ counting in a well-defined geometric system,

• d⌦ cos ✓ is the solid angle at direction ✓ Since the azimuth angle is isotropic and ranges uniformly from ⇡ to ⇡, we have d⌦ cos ✓ = 2⇡d cos ✓ (5.17 interesting feature is that the intensity of beam profile decreases toward the periphery area instead of a uniform distribution as in EAR-1. This is probably caused by the conical design of the collimator at the entrance of the EAR-2. We also obtained the unnormalized integral neutron flux of EAR-2. PPACmon is the only detection system at n_TOF able to provide the data for high energy region (from 5 MeV to 100 MeV) thanks to its good time resolution and fast signal.

Chapter 6

237 Np(n, f) experiment at EAR-1

In this chapter, we will present the analysis of the measurement on neutron-induced fission of 237 Np at EAR-1. The analysis method we are using for extracting the cross section and FFAD will be described. Then we will show some results. The discussion on the results of 237 Np will be presented in next chapter.

Target and detector sequence

The setup of 237 Np(n, f) measurement at EAR-1 has been introduced in section 4.3.2, here we show the target and detector sequence again as a reminder. As depicted in figure 6.1, we refer the detectors and targets from left to right as PPAC0, PPAC1, ..., PPAC9 and target1, target2, ..., target8. In the later part of this chapter, we take the cases of target6 (cell consisting of PPAC6, 237 Np target, PPAC7) and target8 (cell consisting of PPAC8, 235 U target, PPAC9) to exemplify the analysis.

Fission trajectory reconstruction

amplitude of PPAC8 and PPAC9 for the events inside the central graphical cut in figure 6.2. The two separated bumps corresponding to the asymmetric division of the 235 U target. It can be seen that the low amplitude events are so far away from the fission events that we can put a threshold for the sum of A8 and A9 to reject them.

These low amplitude events are mainly the random coincidences from spallation in high energy region that has been described in section 5.3.

Fission trajectory reconstruction

To reconstruct the fission trajectory, first we need to choose the corresponding proper cathode signals for each anode signal. Here we follow the same procedure as described in section 5.5.2, which is based on the sum of the propagation time of each delay line and on the ratio of amplitude, to find the right cathode signals. We select the events in the diagonal contour in figure 6.4a since the their sum should be a constant. Figure 6.4b is the distribution of the events inside the diagonal region which could be used as a supplementary selection criterion when more than one With the determined corresponding cathode signals for each anode signal, we can obtain the coordinates of the hitting points (X d , Y d ) on each cathode plane (with the cathode center as the origin) by equation 6.1

X d = v(t SL t SR ) 2 Y d = v(t SB t ST ) 2 (6.1)
where t SL , t SR , t ST and t SB are the peak time of Left, Right, Top and Bottom signal as has been defined in equation 5.4.

The top view of a basic cell of the tilted setup is shown in figure 6.5. The neutron beam enters each detector by X plane and exits from Y plane. The detectors are always centered on the beam axis. d is the distance from the target to the anode, e is the distance between anode and cathode. We define the point where the beam axis intersects the target plane as the origin of the frame (there could be an offset from target center to the origin). The reconstruction of fission trajectory is carried out in a perpendicular frame ( X0 , Ỹ 0 , Z0 ) (see in figure 6.5) where we define the X 0 axis as horizontal pointing from right to left, the Y 0 axis as vertical pointing upward and Z 0 axis as perpendicular to the detectors and target orienting at 45 from the beam direction.

✓ 0 and 0 are the polar angle and azimuth angle of the fission trajectory against and around Z 0 axis. ✓ and are the physical angles which are directly related to the beam axis. The relation between (✓ 0 , 0 ) and (✓, ) will be discussed later. From equations 6.2, 6.3 and based on the straight line equation 5.9, the emitting points on the target (X 0 T , Y 0 T ) in the perpendicular frame can be calculated by equation 6.4. The distribution of the emitting points on target8 ( 235 U) and target6 ( 237 Np) reconstructed by equation 6.4 are shown in figure 6.7. We see clearly that the emitting points are concentrated in a circle with a diameter of 8 cm, this is exactly the size of the target. However, there are some reconstructed points beyond the target circle. They are due to the wrong localization in the high energy region where the counting rate is high.

X 0 T = X 0 1 (d e) + X 0 2 (d + e) 2d Y 0 T = Y 0 1 (d + e) + Y 0 2 (d e) 2d
The cosine of the polar angle ✓ 0 and the tangent of the azimuth angle 0 around Z0 in the perpendicular frame can be calculated by equation 6.5:

cos ✓0 = Z 0 2X Z 0 1X p (X 0 2 X 0 1 ) 2 + (Y 0 2 Y 0 1 ) 2 + (Z 0 2X Z 0 1X ) 2 tan 0 = Y 0 2 Y 0 1 X 0 2 X 0 1 (6.5)
We are interested to know the fission angle ✓ and azimuth angle around the neutron beam axis since they are the relevant angles of FFAD. So we define a tilted frame ( X,

Angular distribution

Ỹ , Z) which is a 45 clockwise rotation about the Y 0 -axis of the perpendicular frame ( X0 , Ỹ 0 , Z0 ). In this tilted frame, the Z axis is the neutron beam axis. For a point with a coordinate (X 0 , Y 0 , Z 0 ) in the perpendicular frame, its coordinate (X, Y , Z) in 45 tilted frame can be transformed by the rotation matrix (equation 6.

X 0 Y 0 Z 0 3 5 (6.6)
from which we can obtain the coordinates of the hitting points in the tilted frame and calculate the physics angle cos ✓ and by equation 6.7.

cos ✓ = 1 p 2 ( sin ✓ 0 cos 0 + cos ✓ 0 ) = arctan ✓ p 2 sin ✓ 0 sin 0 sin ✓ 0 cos 0 + cos ✓ 0 ◆ (6.7)
and the reciprocal from (✓, ) to (✓ 0 , 0 ) is:

cos ✓ 0 = 1 p 2 (sin ✓ cos + cos ✓) 0 = arctan ✓ p 2 sin ✓ sin sin ✓ cos cos ✓ ◆ (6.8)
Equation 6.7 and 6.8 will be used in latter analysis for determining the efficiency and FFAD in next section.

Angular distribution

As discussed in section 5.7.1, the measured angular dependence in a given direction is the coupling of efficiency and FFAD. So based on the knowledge of one of them, we can deduce the other one. Tilted setup of PPACs is dedicated to decouple these two elements. Any given direction of fission can be defined by the couples (cos ✓ 0 , 0 ) or (cos ✓,

Characteristics of the tilted setup

). It may also be defined with an interesting couple (cos ✓, cos ✓ 0 ) which is directly linked with the characteristics of tilted setup. Equations 6. The features of the (cos ✓, cos ✓ 0 ) plane in figure 6.9 are the following:

1) Any horizontal slice of height cos ✓ 0 corresponds to a constant solid angle ⌦ = 2⇡ cos ✓ 0 since it covers all the 0 in range [ ⇡, ⇡].

2) For the same reason as 1) any vertical slice of width cos ✓ corresponds to constant solid angle of ⌦ = 2⇡ cos ✓.

3) Along a horizontal slice the efficiency is constant and the spectrum of counts in cos ✓, for a given solid angle, reflects the angular distribution 4) Along a vertical slice the angular dependence is constant and the spectrum of counts in cos ✓ 0 reflects the efficiency information

The number of fission events detected in any direction in (cos ✓, cos ✓ 0 ) map can be below 100 keV where fission is isotropic. The elliptic shape is obvious but more counts are accumulated at the elliptic edge. For example, if we take a horizontal slice in figure 6.11a (figure 6.11a and figure 6.10 are exactly the same figure) and project it to cos ✓ axis (figure 6.11b), we can see that more counts are present in the peripheral bins. This is because the peripheral bins take larger solid angles. The reason is the following:

According to equation 6.11, the counts in each bin is

N = CW (cos ✓)"(cos ✓ 0 ) ⌦ cos ✓,cos ✓ 0 (6.12)
Since this is a horizontal slice, the efficiency is constant. And also as fission is isotropic in this energy region (E n <100 keV), the W (cos ✓) = 1. So the different bin counts are only from the solid angle.

We can directly calculate the solid angle of each bin by numerical integration using Gauss-Legendre method. Several points are taken in cos ✓ 0 and for each of them the limits in 0 are computed for the horizontal limits in cos ✓ by using equation 6.7. This gives for each cos ✓ 0 an interval 0 which is integrated over cos ✓ 0 . Figure 6.12 shows solid angle's variation of several horizontal slices. We can see that the solid angle increases quickly close to the lower and upper edge, which explains the shape in figure 6.11b. 100 keV where the counts in each bin have been divided by its solid angle. Figure 6.13b is the projection of hatched horizontal slice in Figure 6.13b. Now it's flat as expected since the solid angle of each bin has been taken into account and the angular distribution is isotropic in this energy region.

Correction of the geometric cut

Until now we assumed that the stopping of the fragments at large angles is the only constraint limiting the detection efficiency. However, there could be another constraint reducing the efficiency at some given direction (cos ✓ 0 , 0 ): the geometrical cut due to the limited size of the active area of detectors. That is to say, some fission fragments are emitted out from the target successfully but land outside the active region of the detector.

This could happen for emission points at the edge of the target when the emission angles ✓ 0 regarding to Z 0 exceed a given threshold. Figure 6.14 illustrates the geometric cut effect on a top view of a basic cell. The detectors are always centered on the beam axis. is the shift of the target from the origin in X 0 axis. L is half length of the square active area, R is the radius of the circular target, d is the target-anode distance. ✓ 0 m1 and ✓ 0 m2 are the threshold angles for the emitting points at the edge of the target. The efficiency loss caused by the geometric cut can be interpreted as a reduction of the visible target area in direction (cos ✓ 0 , 0 ) and it can be computed analytically. For We need to calculate the red area in figure 6.15 and obtain its fraction of the total area which will be the coefficient of the geometric limitation. The fraction is: broad energy range, the average angular distribution is rather smooth and can be well approximated by a polynomial in cos ✓ with terms of order 4:

Angular distribution

F (x 1 , x 2 ) = g(x 1 ) + g(x 2 ) ⇡ (6.14)
W (cos ✓) = (1 + ↵ 2 cos 2 ✓ + ↵ 4 cos 4 ✓) (6.20)
Based on equation 6.19 and 6.20 we can extract the efficiency " i in each horizontal line by a fit with the chi-square minimization method, where we define the chi-square

as 2 = X i,j [C(1 + ↵ 2 cos 2 ✓ j + ↵ 4 cos 4 ✓ j )" i ⌦ 0 ij N ij ] 2 (6.21)
with " 0 = 1. The fitted efficiency for 235 U and 237 Np in different neutron energy regions are shown in figure 6.17. The angular dependence is not very sensitive to the inducing neutron energy except in the high energy region (above 10 MeV), where the difference is obvious, which could come from mislocalization due to the high counting rate.

The fitted efficiencies from minimization of equation 6.21 are separated points, so the efficiency curve is not very smooth and there are some fluctuations. Instead of using them directly we use a Fermi-like function which can well reproduce the efficiency curve:

"(cos ✓ 0 ) = 1 (1 + e a 1 a 2 cos ✓ 0
) a 0 (6.22)

Angular distribution

W (cos ✓ j ) = K P i N ij P i " i ⌦ 0 ij (6.24)
where K is a global normalization factor to fix the W (cos ✓) function.

It can be seen in figure 6.10 that the counts number below cos ✓ 0 = 0.5 are rather limited due to the low efficiency, so in the final results we will discard the events below cos ✓ 0 = 0.5 and extract angular distribution as follows. For a given column j the sum of the counts is:

S 1j = X i,cos ✓ 0 >0.5 N ij (6.25)
The corresponding sum of effective solid angle and efficiency of above bins is:

S 2j = X i,cos ✓ 0 >0.5 ⌦ 0 ⇥ " i (6.26)
where the efficiency " i is calculated by the Fermi-like function 6.22. The angular distribution at this column is:

W (cos ✓ j ) = K S 1j S 2j (6.27)
The normalization factor K is defined based on the definition of W (cos ✓) because it can represent different quantities that are proportional to each other. For example, it can be normalized so that its integral is equal to 1 as in equation 6.11. It can be also normalized to 4⇡ solid angle. Here we normalize the angular distribution at 90 Chapter 7

Results and discussion

In this chapter, we will present the method to deduce the cross section. The first results of 237 Np neutron-induced fission cross section from fission threshold up to 5 MeV will be presented. The comparison between our results, the evaluation and some other experimental data will be shown and discussed.

Integral Efficiency determination

The approaches to extract the efficiency ("(cos ✓ 0 )) and FFAD (W (cos ✓)) have been introduced respectively in details in section 6.4.3 and section 6.4.4. However, the probability to detect a fission at a given angle is the product of efficiency and FFAD, which will be referred as global efficiency in latter part. Here we show again the tilted setup (figure 7.1) to illustrate the following analysis. The efficiency P (cos ✓) corresponds to the integration of "(cos ✓ 0

) on all the possible angles for this given cos ✓,

P (cos ✓) = 1 ⇡ Z ⇡ 0 "(cos ✓ 0 )d (7.1)
where "(cos ✓ 0 ) has a distribution as shown in figure 7.2, and cos ✓ 0 is given by equation 7.2.

cos ✓ 0 = 1 p 2 (sin ✓ cos + cos ✓) (7.2)
According to equation 7.1 and equation 7.2 we can obtain the efficiency as a function of cos ✓ as shown in figure 7.3. We can see that this kind of efficiency distribution permits us to cover all the angles from 0 to 90 degree, thus we can obtain the FFAD over the whole angular distribution. This is a strong advantage of tilted setup compared to perpendicular setup (figure 5.18). In the perpendicular setup, the fission fragments can not be detected in large angles because efficiency drops dramatically with the increase of the fission angle. At 90 , the detectors are physically not present, therefore the detection of fission fragments is simply impossible. As mentioned in section 6.4.3 FFAD can be well approximated by a polynomial in cos ✓ with terms of order 4: The neutron-induced fission cross section is:

Integral Efficiency determination

W (cos ✓) = (1 + ↵ 2 cos 2 ✓ + ↵ 4 cos 4 ✓) (7.3)
(E n ) = R(E n ) (E n )⌘(E n )N (7.5)
where in our case

• E n is neutron energy,

• R is the fission rate,

• is the integral neutron flux on the target, 91

RESULTS AND DISCUSSION

• N is the target thickness (atoms/cm 2 ) that has been measured by ↵ counting,

• ⌘ is the global efficiency including the anisotropy correction for FFAD.

In the experiment, the integral neutron flux for all the targets is the same because the material quantity in the beam is so tiny that the attenuation of the flux is negligible.

Therefore according to equation 7.5 we can obtain the cross section ratio of 237 Np over 235 U by

7 (E n ) 5 (E n ) = R 7 (E n ) R 5 (E n ) ⇥ ⌘ 5 (E n ) ⌘ 7 (E n ) ⇥ N 5 N 7 (7.6)
where 7 stands for the 237 Np and 5 stands for the 235 U.

The analysis method to select the fission event and extract the fission rate have been presented in details in section 5.3, section 5.4 and section 6.

Anode versus localization application

Consistency of the fission rate

In this thesis work, we analyzed 3 237 Np targets (target 5, 6, 7 in figure 6.1) and a 235 U target (target 8 in figure 6.1) as reference. Before using the fission rate to calculate the cross section, it is very important to check the consistency of the fission rates from different targets because it checks the reliability of the data. The consistency can be checked by comparing the normalized fission rates of different targets, which is calculated by

R nor (E n ) = R(E n ) m ⇥ ⌘ (7.7)
where R nor (E n ) is the normalized fission rate, R(E n ) is the measured fission rate, m is the target mass, ⌘ is the global efficiency. However, the pile up does not affect the measured angular dependencies and angular efficiency since pile up is not depending on angle or localization but is only changing with energy. Figure 7.11 shows the efficiency of Np target in different energy range. We can see that the angular dependence is still consistent from 1 to 6 MeV as expected, therefore our method to determine the efficiency and FFAD is still reliable. Based on the above discussion we see the fission rate with the localization requirement is affected by the pile up and is not reliable. Now we have to rely on the fission rate without localization to deduce the cross section. First important thing is still to check their consistency with the normalized fission rates. In our PPAC measurement, we only know the efficiency with the localization, but the efficiency related to the anode signals only is not definitely known since it's impossible to directly reconstruct it without the localization information. Therefore here we assume temporarily that the efficiency without localization is the same for the three 237 Np target and we normalize the fission rate only by the mass:

R nor (E n ) = R(E n ) m (7.9)
and define their average as evaluation. However, it is slightly, about 3-4%, higher than the evaluation above 1 MeV.

< R nor (E n ) >= R 5 (E n ) + R 6 (E n ) + R 7 (E n ) m 5 + m 6 + m 7 ( 7
The two black circle points are the measurement by Diakaki et al [START_REF] Diakaki | Determination of the 237 Np(n, f ) reaction cross section for En = 4.5-5.3 MeV, using a MicroMegas detector assembly[END_REF]. Their result at 4.58 MeV is consistent with our result, whereas their data at 4.85 MeV is identical to the evaluation. Chapter 8

Conclusions and outlook

Conclusions

• EAR-2 beam measurement

We present the first PPACmon experiment, done at n_TOF EAR-2, for characterizing the beam profile and neutron flux at this new facility. The obtained neutron beam profile shows that the beam intensity is much lower in the peripheral region, forming a halo around the central intense part. This is different with the beam profile at EAR-1 which is quasi-uniform. This beam profile feature of EAR-2 is caused by the collimator located before the experimental hall, which has a conical design for the inner hole [START_REF] Weiss | The new vertical neutron beam line at the CERN n_TOF facility design and outlook on the performance[END_REF].

The measured beam profile could be a reference for the future experiment design and analysis.

The TOF, fission rate and unnormalized flux spectra at EAR-2 are obtained by PPACmon, finally contributing to the flux evaluation. From the fission rate we can see that PPACmon is able to monitor the neutrons from thermal energy up to 200 MeV, which makes it the detection system covering the largest energy range at n_TOF .

Especially, PPACmon is the only one that can provide data for the high energy region, from a few MeV to 200 MeV, due to its fast signal and reliable method to identify the fission event.

• 237 Np(n, f) measurement

The experiment at n_TOF EAR-1 for studying the neutron induced fission of 237 Np is presented. The experimental and analysis methods for extracting the FFAD and

Outlook

For the beam measurement at EAR-2, since the prompt -flash sharp peak is not visible for PPACmon, we used the first fission event and a simulated neutron flux to determine the T 0 . Another option is to use the fission threshold of some isotopes to determine the T 0 . We have done another experiment with PPACmon at EAR-2 with one 235 U and one 238 U target, intending to use the fission threshold of 238 U around 1 MeV as a reference to deduce the T 0 . Concerning the 237 Np(n, f) measurement, this thesis gives the first results. There are some analysis left to be done to complete the work.

1. As mentioned in chapter 6 and 7, the pile up of the cathode signal not only brings some mislocalizations, but also generates some difficulties to use the fission rate with localization. Besides, we also found some other issues in the raw data, for example, high frequency oscillation occurs sometimes. Fortunately, these issues can be solved by a more sophisticated routine dedicated to PPAC. It needs a full long reprocessing of the raw data. This is foreseen to be done in the near future.

2. As long as the raw data are treated by the PPAC dedicated routine, with the expected improvement of localization and sufficient statistics, we can extract the FFAD 8.2 Outlook in high energy region. Therefore we expect to obtain the FFAD and neutron-induced fission cross section of 237 Np up to hundreds of MeV.

3. In this thesis, we presented the results of three 237 Np targets (target 5, 6 and 7) and one 235 U target (target 8). The remaining targets will be analyzed in the future, especially the two 237 Np targets (target 2 and 3). They will be compared with the three 237 Np targets and the consistency of the cross section will be checked. La seconde partie de la thèse a pour but l'étude de la fission de 237 Np. Cet isotope est abondamment produit dans les réacteurs nucléaires actuels et est un des constituants des déchets à vie longue. A ce titre on peut le considérer comme une cible potentielle pour l'incinération en réacteur rapide. Ceci a motivé des mesures récentes de sa section efficace de fission. Cependant des déviations importantes sont apparues, en particulier la mesure effectuée à n_TOF en 2010 est 6% supérieure aux évaluations basées sur les mesures antérieures. Ceci a motivé une nouvelle mesure à n_TOF avec une configuration permettant une mesure précise de l'efficacité de détection, pour apporter une réponse au problème. Ce travail a permis de mettre en évidence une dépendance de l'efficacité de détection avec l'élément, résultant des conditions de l'électrodéposition. Après application de cette correction d'efficacité dans la région 1 à 5 MeV la section efficace de fission ainsi extraite est 2 à 3% plus petite par rapport à la mesure de 2010, cependant elle reste 3 à 4% plus forte que les évaluations. The second part of the thesis aims to study the neutron-induced fission of 237 Np. 237 Np is abundantly produced in present nuclear reactor and is one of the major long-lived components of nuclear waste which can be considered as a potential target of incineration in fast neutron reactors. Consequently its neutron-induced fission cross section has been measured at different facilities. However, significant discrepancies exist between different experiments. Especially, the recent one performed at n_TOF in 2010 is about 6% higher by comparison to the evaluation data based on previous experiments. Therefore an experiment has been performed at n_TOF EAR-1 to measure its fission cross section, in a configuration allowing an accurate control of the detection efficiency, aiming to give a definite answer to the puzzle. In this work, we found that the efficiencies for different target elements are different, even though they have similar thickness, reflecting the conditions of electrodeposition. After application of this efficiency correction in the energy range from 1 to 5 MeV, the newly extracted fission cross section is 2-3% lower compared with our previous measurement in 2010, however they are 3-4% higher than the evaluation.

Title

1. 1 1 . 3 4 . 2 4 . 6 4 . 7 6 . 6 7 . 6 7 . 7 7 . 9

 11342464766767779 figure presents the ratios of each fission rate divided by the average fission rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Detection of fission by PPACs . . . . . . . . . . . . . . . . . . . . . . . . 7.9 Fission rates of 237 Np targets. (a), (b) and (c) are the fission rates of 3 237 Np targets with and without the localization; (d) is the the ratios without localization over with localization. . . . . . . . . . . . . . . . . . 7.10 Fission rates of 235 U targets. (a) presents the fission rates of 235 U target with and without the localization; (d) presents the their ratio without localization over with localization. . . . . . . . . . . . . . . . . . 7.11 Effciency of 237 Np (target6) in 3 different energy range . . . . . . . . . . 7.12 Comparison of normalized fission rate of 3 237 Np targets without localization. The left figure is the comparison of the 3 normalized fission rates without localization. The right figure presents the ratios of each fission rate divided by the average fission rate. . . . . . . . . . . . . . . . 7.13 Dispersion of the fission rate without localization . . . . . . . . . . . . . 7.14 The neutron-induced fission cross section ratio of 237 Np relative to 235 U from 1 to 5 MeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.15 The neutron-induced fission cross section of 237 Np from 1 to 5 MeV . . .

Fermi

  and his group created the first self-sustaining nuclear chain reaction at University of Chicago in 1942. They transformed scientific theory into technological reality successfully.

Figure 1 .

 1 Figure 1.2 shows the fission cross section ratio of 237 Np relative to 235 U where n_TOF data presents discrepancies compared with evaluation data and other mea-

Figure 1 . 1 :

 11 Figure 1.1: The fission cross section of the 237 Np from threshold to 1 GeV. -n_TOF data is compared to the ENDF/B-VII.0 and JEFF-3.1 evaluations and some experiment data. The error bars include the statistical and systematic uncertainties. The figure is extracted from [6].

Figure 1 . 2 :

 12 Figure 1.2: The fission cross section ratio of 237 Np relative to 235 U from threshold to 1 GeV. -n_TOF data is compared to ENDF/B-VII.0 evaluations and some experimental data. The error bars correspond to the statistical uncertainties only. The figure is extracted from [6].

Figure 1 . 3 :

 13 Figure 1.3: Preliminary results on the neutron-induced fission cross section of 240 Pu and 242 Pu

  238 U as references. The red crosses dataset in figure1.4 are weighted average results using the data of 235 U and 238 U in ENDF/B-VII.1 evaluation as references. The green stars dataset are weighted average results obtained by taking the 238 U data measured by themselves as reference. We can see clearly that both of them are higher than the evaluations but have an agreement with n_TOF data (black circles) within the error bars.

Figure 1 . 4 :

 14 Figure 1.4: Neutron-induced fission cross section of 237 Np. -The figure is extracted from[START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu[END_REF]

Figure 2 . 1 :

 21 Figure 2.1: The stages of binary fission in a liquid drop model -Energy input deforms the nucleus into a oval, then a dumbbell, followed by binary fission as the two fragments exceed the short-range nuclear force attraction distance, then are pushed apart and away by the Coulomb force. The penultimate drawing corresponds to the scission point.

Figure 2 . 2 :

 22 Figure 2.2: Nuclear shapes at the saddle point for various values of x -The figure is extracted from[START_REF] Cohen | The deformation energy of a charged drop: Part v: Results of electronic computer studies[END_REF]

Figure 2 . 3 :

 23 Figure 2.3: Correlation of the surface and Coulomb energy and the net deformation energy with the quadrupole deformation (a 2 ). -The indicates the position of the saddle point of the nucleus. The figure is extracted from[START_REF] Vandenbosch | Nuclear Fission[END_REF]

Figure 2 . 4 :

 24 Figure 2.4: Nuclear energy levels -The figure is extracted from [29]

8 )

 8 The shell correction, just like the liquid drop model energy, is a function of the nuclear deformation. It tends to lower the ground state masses of spherical nuclei with magic or near-magic numbers of nucleons. It also tends to lower the ground state mass of midshell nuclei at some finite deformation, thus accounting for deformed nature of the actinides.The deformation energy calculated for a typical actinide nucleus with the Strutinsky's procedure is schematically illustrated in figure2.5 through which we can tell the double-humped fission barrier. The energy is lowest at a deformation corresponding to the known ground state quadrupole moments of actinide nuclei. The second minimum is due to the strong negative shell correction and it corresponds to fission isomers. The second minimum persists for the actinide nuclei up to californium. For heavier nuclei the outer barrier disappears mainly because the liquid drop energy falls off more steeply at a smaller deformation. The dashed line is the potential energy purely calculated by liquid drop model without shell effect correction.

Figure 2 .

 2 Figure 2.5: Schematic illustration of the fission barrier of a typical actinide nucleus -The figure is cited from[START_REF] Wagemans | The nuclear fission process[END_REF]

Figure 2 . 6 :

 26 Figure2.6: Angular momentum of fissioning nucleus -J is the total angular momentum of the deformed nucleus. M , K, R are, respectively, the projections of J on the space fixed axis z, on the symmetry axis of the fission and on an axis perpendicular to K.

Figure 2 . 7 :

 27 Figure 2.7: Theoretical FFAD calculated by equation 2.18 for even-even target.-The figure is cited from[START_REF] Vandenbosch | Nuclear Fission[END_REF]

Figure 2 . 8 :

 28 Figure 2.8: Comparison of total fission cross section and relative differential fission cross sections (anisotropy parameter) for 232 Th -The multiple-chance fission structure is visible both in cross section and FFAD. The figure is cited from[START_REF] Henkel | Angular distribution of fragments from neutron-induced fission of U 238 and Th 232[END_REF]

  in 1998. It is based on a spallation neutron source by impinging 20 GeV/c protons to a thick lead target which can provide neutrons from thermal energy up to GeV. The proton beam has a typical intensity of 7⇥10 12 /pulse and a cycle of 1.2 s or a multiple of it, yielding about 300 neutrons per single incident proton. The layout of n_TOF facility is shown in figure 3.1.

Figure 3 . 1 :

 31 Figure 3.1: Layout of the of n_TOF facility.

Figure 3 . 2 :

 32 Figure 3.2: Schematic of n_TOF spallation target.

Figure 3 . 3 :

 33 Figure 3.3: Layout of the n_TOF horizontal neutron beam line to EAR-1 from the spallation target to the beam dump (distances are given in meters).

3 .

 3 N_TOF FACILITY AT CERN 3.3.2 Vertical beam line to EAR-2 The beam line to EAR-2 stands vertically above the spallation target and is ⇠ 20 m long as shown in figure 3.4.

Figure 3 . 4 :

 34 Figure 3.4: Layout of the n_TOF vertical neutron beam line to EAR-2 from the spallation target to the beam dump.

Figure 3 .

 3 Figure 3.5: Neutron fluxes of EAR-1 and EAR-2.-The number of neutrons per equidistant logarithmic energy bin (dn/dlnE) per 7⇥12 protons integrated over a radius of r= 0.87 cm for EAR-1 and r=2.5 cm for EAR2.

Figure 3 . 6 :

 36 Figure 3.6: Distribution of moderation distance for EAR-1 as a function of neutron energy.

  is a stochastic quantity with a probability density distribution depending on the neutron energy or time-of-flight.The distribution of as a function of the neutron energy at EAR-1 and as a function of neutron time-of-flight at EAR-2 simulated by FLUKA are

Figure 3 . 7 :

 37 Figure 3.7: Distribution of moderation distance for EAR-2 as a function of neutron TOF.

  .1. A target (yellow circle) is closely surrounded by two PPACs to detect two fission fragments, fission fragment 1 (FF1) and fission fragment 2 (FF2) in figure4.1, in coincidence to identify the fission event. Most of the background other than fission event could be rejected by this coincidence method. Since PPAC is position sensitive, the fission angle ✓ and azimuth angle could be measured as well.

Figure 4 . 1 :

 41 Figure 4.1: Principle of fission event detection and fission angle measurement with 2 PPACs

Figure 4 .

 4 2a is the simulation setup simplifying the target to a point at the center between two PPACs. Asymmetric fission is considered in the simulation. The blue trajectories are the back to back emission of fission fragments in the center of mass frame which is slightly distorted by a momentum transfer P n in the laboratory frame. So the real track are the red ones and the emission angle changes to ✓ m from ✓ cm . The momentum transfer for 1 GeV incident neutron is 331 MeV/c[START_REF] Fatyge | Linear momentum transfer in 40-150 MeV proton-induced reationS with 238[END_REF].

Figure 4 . 2 :

 42 Figure 4.2: Simulation on the effect of momentum transfer from high energy neutrons on the emission angle of fission fragments. -(a): simulation setup, (b): Relation between the measured angle cos✓ m and the emission angle in center of mass frame cos✓ cm as given by the simulation for a momentum transfer of 331 MeV/c from 1 GeV incident neutrons

2

  mm separated strips for position measurement in two orthogonal dimensions. PPAC has a square active surface of 200⇥200 mm 2 , and the overall assembled dimensions of a PPAC is a square of 305 mm ⇥ 305 mm with 13 mm in thickness. A global scheme of a PPAC is shown in figure 4.3.

Figure 4 . 3 :

 43 Figure 4.3: Principles of bidimensional, induced charge, read-out from parallel plate avlanche counters. -The figure is extracted from [47].

  Anode frame (b) Cathode frame

Figure 4 . 4 :

 44 Figure 4.4: PPAC electrodes

Figure 4 .

 4 Figure 4.5: Picture of delay line plugged on a cathode frame

(a) 237

 237 Np target (b) 238 U target

Figure 4 . 6 :

 46 Figure 4.6: Actinides targets.

4 ), there are 3

 43 PPACs and 2 235 U targets with 0.7 µm thick aluminium backings perpendicular to neutron beam. Detectors are centered on the beam axis. The distance between each anode to target is 17.1 mm. The results of this experiment is shown in chapter 5.

Figure 4 . 7 :

 47 Figure 4.7: PPACMon setup at EAR-2 -(a) PPACMon located on the vertical beam line (b) Drawing of 3 PPACs and 2 targets inside PPACMon which are orthogonal to the incoming neutron beam

Figure 4 .Figure 4 . 8 :

 448 Figure 4.8 is the setup for measuring the 237 Np(n, f) cross section and FFAD at EAR-1. The horizontal neutron beam enters the chamber and goes through a stack of 10 PPACs interleaved with 9 target, figure 4.8b shows the inside structure of the chamber. The 45 tilted setup of detectors and targets regarding to neutron beam is used for decoupling the efficiency and FFAD and to cover FFAD in entire range. It will be dedicatedly discussed in chapter 6.

Figure 4 . 9 :

 49 Figure 4.9: Detector and target sequence inside chamber -top view of detectors and targets

FIC was used at

  n_TOF during phase-I (2001-2004) for fission cross section measurement. The target inside the chamber does not have to be as thin as for the PPAC since only one fission fragment is detected. It can be also used for monitoring the neutron beam. Micromegas detector was used since n_TOF Phase-II (2009-2012) which is characterized by its good signal-to-noise ratio. It's a double-stage parallel plate chamber, a conversion gap and an amplification gap, separated by a micromesh. Charged particles firstly travel through the conversion gap where electron-ion pairs are produced and electrons drift toward micromesh. Then electrons enter into the amplification gap and they are multiplied due to the high electric field. The subsequent electron avalanche induces signals on the anode strips which can give the position information. Micromegas detec-

Figure 5 . 1 [

 51 Figure5.1[START_REF]Fission fragment angular distribution and fission cross section validation[END_REF] shows the original signals (one anode and two different cathodes) and their derivatives by convoluting the low-pass filter to remove the high frequency noise. It can be seen that the waving of the baseline at the beginning of the frame is completely removed after the derivative. The effect of high frequency noise in derivative is also inhibited since the filter is applied. However the signal peaks become bipolar. Then two thresholds are set to the derivative bipolar signals for selection. In figure 5.2 [54], there is one anode derivative signal (blue) and one cathode derivative signal (red). The two red dash lines are the thresholds set for the derivative cathode signal. Signals crossing two thresholds with a lower-lower-upper-upper sequence are selected out. Their zero-crossing time and peak-to-peak amplitude, which are the peak time and proportional to the amplitude of original signals respectively, are saved in DST

Figure 5 . 3 :

 53 Figure 5.3: nTOFLib -Black line is an anode signal frame, red curve is the fitted baseline of signal frame.

1 . 1 ,

 11 a fission event is identified by the coincidence of two adjacent PPACs surrounding the fissionning target. The diagram of the PPACMon chamber setup is shown again here (figure 5.4). The anode signals are used for searching the coincident events. For each anode signal, we open a time window of 20 ns (from -20 ns to +20 ns) to select the coincident events.

Figure 5 .

 5 Figure5.5 shows all the coincidences between PPAC2 and PPAC1. The horizontal axis is the anode time difference between PPAC2 and PPAC1 (T2-T1), the vertical axis is the anode amplitude of PPAC1 (A1). When a fission comes out from the central target between two adjacent PPACs, the two fission fragments reach each detector almost at the same time because they travel the same distance from target to detector. So they

Figure 5 . 5 :

 55 Figure 5.5: All the coincidences between PPAC2 and PPAC1 -2D distribution of amplitude on PPAC1 versus the time difference between PPAC2 and PPAC1

Figure 5 .

 5 Figure 5.6 is the 2D distribution of anode time difference between PPAC2 and PPAC0

Figure 5 . 6 :

 56 Figure 5.6: Distribution of triple coincidences -2D distribution of the anode time difference between PPAC2 and PPAC0 versus anode amplitude of PPAC2 for all the triple coincidence events

Figure 5 . 7 :Figure 5 . 8 :

 5758 Figure 5.7: Distribution of sum of the anode amplitude of PPAC2 and PPAC1 as a function of neutron energy

Figure 5 . 9 :

 59 Figure 5.9: Comparison of the experimental fission rate and 235 U(n,f ) cross section in the database

2 Figure 5 . 10 :

 2510 figure 5.10 that the 1800 ns offset (red curve) is the good one. There are still several events before 64.6 ns, they are probably due to the width of the proton beam (7 ns RMS) and some background. With this determined 1800 ns offset, we can calculate the incident neutron energy by time-of-flight method and obtain the fission rate as a function of neutron energy.The offset can be also checked by the simulation. The simulated fission rate can be obtained by multiplying 235 U(n, f) cross section[START_REF] Fukahori | [END_REF] by a simulated flux, then we

Figure 5 . 11 :

 511 Figure 5.11: Comparison of fission rate with different offsets and simulation -

  Figure 5.12: TOF and fission rate spectra

4 ) 2 Figure 5 . 13 :

 42513 Figure 5.13: Five output signals of a PPAC

For each anode

  signal, we open a window starting from anode peak time and lasting 400 ns to record all the related Left and Right signals inside it. The 2D distribution of t L versus t R for all the anode signals of PPAC1 is shown in figure 5.15. The highly concentrated events in diagonal region in figure 5.15 prove the relation in equation 5.7 is correct. The other events with some structures are due to the signal reflection and distortion in the delay line. The flat background events beyond the diagonal are from the high counting rate in the high energy region. The time intervals between signals are contracted in high energy region, one anode signal is followed by many cathode signals in a 400 ns window. As a consequence, many combinations show

Figure 5 .

 5 Figure 5.15: 2D plot of t L versus t R -All the combinations consists of one Left and one Right signal inside 400 ns windows for the anode signals of PPAC1 without coincidence requirement.

Figure 5 .

 5 Figure 5.16: 2D plot of t L t R versus a L /a R for events in contour of figure 5.15

d

  is the distance from the 235 U target to anode, e is the distance between each anode and cathode. ✓ is the fission angle between fission fragment trajectory and neutron beam. We can obtain the (X, Y ) position of fission fragments on each detector by equation 5.6. Figure5.[START_REF] Bracco | Perspectives of nuclear physics in Europe: NuPECC long range plan[END_REF] shows the distribution of fission fragment hitting points on PPAC1 and PPAC2.

( a )

 a Figure 5.19: Distribution of fission fragment hitting points on PPAC1 and PPAC2

Figure 5 . 20 :

 520 Figure 5.20: Neutron beam profile at n_TOF EAR-2 with small collimator Figure 5.20 is the distribution of emitting points on the target1. This distribution also stands for the beam profile since the target is uniform. It can be seen that the beam profile is well collimated, circular and well centered. The interesting feature of this

( a )Figure 5 . 21 :

 a521 Figure 5.21: Distribution of fission fragment hitting points on the anode plane

5. 7

 7 Integral neutron flux at EAR-2

( a )Figure 5 . 23 :

 a523 Figure 5.23: Distributions of fission angle dependence in different neutron energy regions

  Figure 5.24b, 5.24c and 5.24d are the distributions of figure 5.23b, 5.23c and 5.23d after the anisotropy correction. They reflect the efficiency distributions as a function of cos ✓ in each energy range. They can be fit (red curves in figure 5.24) by a Fermi-like function (5.15) :

  MeV, 100 MeV) respectively. The similarity of the efficiency distribution and the global efficiency value in different energy ranges indicates that PPAC's efficiency is not very sensitive to neutron energy. The fitted efficiency function will be used for deducing the flux in next section.

Figure 5 . 25 :

 525 Figure 5.25: Efficiency curve of target1 in different energy regions

)Figure 5

 5 Figure 5.26 shows the correlation between cos ✓ and , where (a) is the 2D distribution of cos ✓ versus and (b) is a projection of a vertical slices at cos ✓ = 0.9. It can be seen that at a given cos ✓ we can treat as a uniform distribution and calculate its differential solid angle by equation 5.17.

  .

Figure 5 . 26 :

 526 Figure 5.26: Distribution in angles (cos ✓, )-(a) 2D distribution of cos ✓ versus (b) Projection of a vertical slice, where cos ✓ = 0.9, in (a)

Figure 6 . 1 :

 61 Figure 6.1: Detector and target sequence inside chamber

Figure 6 .

 6 4 shows the distribution of propagation time and the ratio of the amplitude of one cathode of PPAC8. The definition of propagation time is introduced in section 5.5.1 and equation 5.4.

Figure 6 . 4 :

 64 Figure 6.4: Statistics of one cathode of PPAC8-(a) 2D distribution of propagation time, t L8 is the propagation time of the Left signal of PPAC8, t R8 is for the Right signal;(b) 2D distribution of amplitude ratio versus the difference of propagation time, a L8 is the amplitude of the Left signal of PPAC8, a R8 is the amplitude of the Right signal.

6 .

 6 237 NP(N, F) EXPERIMENT AT EAR-1 combinations of Left and Right signal are present. The black curve in figure 6.4b is the profile of 2D distribution.

Figure 6 .

 6 Figure 6.5: top view of a basic cell of tilted setup

Figure 6 . 7 :

 67 Figure 6.7: Reconstructed emitting points on target8 (a) and target6 (b)

Figure 7 .

 7 Figure 7.1 shows the tilted setup. The blue curve stands for a fission trajectory with back-to-back emission. Z 0 axis is perpendicular to the detectors and targets. The angle between the fission trajectory and Z 0 is ✓ 0 which defines the efficiency, because the efficiency is determined by the travel distance of the fission fragment in target and dead

Figure 6 . 8 :

 68 Figure 6.8: top view of a basic cell of tilted setup

p 2 ( 6 . 4

 264 7 and 6.8 show the relation between cos ✓ and cos ✓ 0 . In equation 6.8, it can be seen that for a given cos ✓ the range of possible cos ✓ 0 is covered by varying in its full range [-⇡, ⇡]. By using ±1 instead of cos in equation 6.8, it gives the limits of the cos ✓ 0 as a function of cos ✓:cos ✓ 0 = 1 ± sin ✓ + cos ✓)(6.9) Angular distribution which becomes as: cos 2 ✓ + cos 2 ✓ 0 p 2 cos ✓ cos ✓ 0 10 is an ellipse tilted 45 in the (cos ✓, cos ✓ 0 ) plane as shown in figure 6.9 where the horizontal axis stands for the fission physics (FFAD) and vertical axis stands for the efficiency. All the measured (cos ✓, cos ✓ 0 ) counts should lie inside the curve as the hatched zone in figure.

Figure 6 . 9 :

 69 Figure 6.9: Ellipse curve from equation 6.10

  calculated by dN = CW (cos ✓)"(cos ✓ 0 )d⌦ = CW (cos ✓)"(cos ✓ 0 )d cos ✓d = CW (cos ✓)"(cos ✓ 0 )d cos ✓ 0 d 0 (6.11) where C is a normalization constant factor including the neutron flux, cross section, target thickness and 4⇡ solid angle, W (cos ✓) is the angular distribution which basically stands for the probability of the angular distribution whose integral on cos ✓ is equal to 1, "(cos ✓ 0 ) is the detection efficiency which is only depending on cos ✓ 0 , d⌦ is the differential solid angle which could be calculated either by d cos ✓d or by d cos ✓ 0 d 0 .

Figure 6 . 10 :

 610 Figure 6.10: Distribution of counts in (cos ✓, cos ✓ 0 ) plane of 235 U target (target8) for E n <100 keV

Figure 6 .

 6 Figure 6.10 shows the (cos ✓, cos ✓ 0 ) distribution of 235 U target (target8) for neutrons

Figure 6 .

 6 Figure 6.11: (a)Distribution of counts in (cos ✓, cos ✓ 0 ) plane of 235 U target (target8) for E n < 100 keV ; (b)Projection of the hatched slice in (a)

Figure 6 . 12 :Figure 6 .Figure 6 .

 61266 Figure 6.12: Solid angle of (cos ✓, cos ✓ 0 ) bins with a width cos ✓ = 0.01 and height cos ✓ 0 = 0.05. The numbers above each curve is the central value of cos ✓ 0 of each horizontal slice

Figure 6 . 14 :

 614 Figure 6.14: Illustration of geometric cut at a top view

Figure 6 . 15 :

 615 Figure 6.15: For a given emission direction (cos ✓ 0 , 0 ) limitation of the possible emission points on the target due to limited detection area of the detectors.

Figure 6 .

 6 Figure 6.16: (cos ✓, cos ✓ 0 ) map with partitioned bins. -The bins in the same horizontal line have the same efficiency. The bins in the same column have the same angular dependence for a given energy. The horizontal lines are numbered with i, starting from top, and the columns are numbered with j starting from the right.

Figure 6 .

 6 Figure 6.18: Comparison

6 .Figure 6 . 19 :

 6619 Figure 6.19: FFAD of 235 U and 237 Np-(a) 235 U for neutrons below 100 keV where the fission is isotropic; (b) 237 Np for neutrons between 1 MeV and 2 MeV where the the fission is anisotropic.

to 1 (Figure 6 .

 16 Figure 6.[START_REF] Bracco | Perspectives of nuclear physics in Europe: NuPECC long range plan[END_REF] shows the FFAD obtained by the above procedure for 2 selected cases: 235 U at low energy (less than 100 keV) and 237 Np from 1 MeV to 2 MeV. Figure6.19a is as flat as we expect since the fission of 235 U at low energy (less than 100 keV) is isotropic. For 237 Np above 1 MeV, the anisotropy of fission shows up and the fission fragments are preferentially emitted in forward direction due to the momentum transfer giving by incident neutrons, this is what we can see in figure6.19b.

Figure 7 . 1 :

 71 Figure 7.1: top view of a basic cell of tilted setup

Figure 7 . 2 :

 72 Figure 7.2: Efficiency of 237 Np target (target6) as a function of cos ✓ 0 for neutrons from 1 MeV to 5 MeV

Figure 7 . 3 :

 73 Figure 7.3: Efficiency of the tilted setup as a function of cos ✓ -237 Np target (target6) for neutrons from 1 to 5 MeV

Figure 7 . 4 :

 74 Figure 7.4: Fitted FFAD of 237 Np (target6) for neutrons from 1 to 5 MeV.

Figure 7 . 1 0WFigure 7 . 6 :

 7176 Figure 7.4 is the angular distribution of 237 Np (target6) fitted by equation 6.21 for neutrons from 1 MeV to 5MeV. We apply it to the efficiency curve (figure7.3) and make the integration of their product by equation 7.4, in order to obtain the global efficiency ⌘ which will be used for calculating the cross section.

2 .

 2 The procedures to extract the efficiency and make the anisotropy correction to obtain the global efficiency have been presented respectively in section 6.4.3 and section 7.1. It should be noticed that in our method, the efficiency can only be obtained when the cathode localization signals are present besides the anode signal. Therefore the efficiency we extracted according to the previous description is the efficiency with localization. It is different if the localization signals are not considered and only anode signals are requested. A discussion will be dedicated in next section.

Figure 7 . 9 :

 79 Figure 7.9: Fission rates of 237 Np targets. (a), (b) and (c) are the fission rates of 3 237 Np targets with and without the localization; (d) is the the ratios without localization over with localization.

Figure 7 . 10 :

 710 Figure 7.10: Fission rates of 235 U targets. (a) presents the fission rates of 235 U target with and without the localization; (d) presents the their ratio without localization over with localization.

Figure 7 . 11 :

 711 Figure 7.11: Effciency of 237 Np (target6) in 3 different energy range

. 10 )

 10 The left part of figure7.12 shows the comparison of the normalized fission rate by taking only anode signals. The right figure shows their dispersion. We can see that the

7. 4 Figure 7 . 14 :

 4714 Figure 7.14: The neutron-induced fission cross section ratio of 237 Np relative to 235 U from 1 to 5 MeV. -The results of this work are compared to the ENDF/B-VII.0 evaluation and our previous measurement data [6]. The error bars of the present data in this work only stands for the statistical uncertainties.

Figure 7 .

 7 Figure 7.15 is the comparison of the neutron-induced fission cross sections of 237 Np. Our results are obtained by multiplying the ENDF/B-VII.0 fission cross secion of 235 U to the ratio in figure 7.14. It is compared with the evaluation and some experimental data. It can be seen that our data can well reproduce the shape of the ENDF/B-VII.0

Figure 7 . 15 :

 715 Figure 7.15: The neutron-induced fission cross section of 237 Np from 1 to 5 MeV -The results of this work are compared to the ENDF/B-VII.0 evaluation and some experimental data [6, 57]. The error bars of the present data in this work only stands for the statistical uncertainties.

8 .

 8 CONCLUSIONS AND OUTLOOKdeducing the fission cross section are described. The fission rates of 237 Np and the reference 235 U as a function of neutron energy are obtained. The first results of 237 Np neutron-induced fission cross section until 5 MeV are obtained relative to 235 U, using the ENDF/B-VII.0 evaluation as a reference.In this experiment, the target quantities of 237 Np and 235 U are well-known since they were measured in a well-defined geometric system with an uncertainty less than 1%. The efficiency with cathode localization is obtained and the anisotropy of FFAD are corrected to obtain the global efficiency from 1 MeV and 5 MeV. Based on the hypothesis that the efficiency without localization is proportional to the efficiency with localization, we obtained the cross section ratio of 237 Np over 235 U from the fission rate solely from the anode coincidence and the efficiency ratio with localization. A first results of fission cross section ratio of 237 Np relative to 235 U from threshold up to 5 MeV are presented. The results are about 3-4% higher than the ENDF/B-VII.0 evaluation, and 2-3% lower than our previous measurement in 2010.

  bases de données. The flux absolu résulte de la normalisation de cette dépendance par rapport à d'autres mesures donnant ce flux absolu sur certains domaines en énergie. La position des fragments traversant les PPAC est enregistrée et il est donc possible de reconstruire la trajectoire de fission en supposant une émission à 180 . On peut ainsi remonter au point d'émission sur la surface de cible étendue. La distribution des points d'émission est représentative de la forme géométrique du flux de neutrons car les cibles d'émission ont une bonne homogénéité. • Mesure de 237 Np(n, f ) à EAR-1 Le 237 Np est un isotope abondamment produit dans les réacteurs actuels et est un actinide mineur de longue durée de vie actuellement présent dans les déchets. Il pourrait à ce titre est un candidat à l'incinération dans des réacteurs à neutrons rapides. Une telle perspective réclame une connaissance précise de son interaction avec les neutrons en particulier sa section efficace de fission. Pour cette raison cette section efficace a fait l'objet de plusieurs mesures dans les dix dernières années auprès de diverses installations. La plus récente, réalisée à n_TOF au CERN en 2010, apparaît comme 6% plus élevée que la plupart des mesures et les bases de données. Cette singularité pourrait mettre en doute sa validité, cependant certains points plaident en faveur d'une section efficace plus élevée que celle contenue dans les bases de données : 1) les sections efficaces préalablement mesurées reposent souvent sur des normalisations mutuelles à certaines énergies, 2) les expériences de criticité sont mieux reproduites avec le jeu de données de n_TOF . La situation a donc besoin d'être clarifiée et une mesure absolue et précise de la section efficace de 237 Np(n,f) est souhaitable. La mesure de la section efficace de fission de 237 Np induite par neutrons a été réalisée à EAR-1. Le système utilise dix PPAC et neuf cibles de fission parmi lesquelles cinq cibles de 237 Np, deux cibles de 235 U et de 238 U utilisées comme références de section efficace permettant de déterminer le flux de neutrons. Les quantités d'atomes dans ces cibles ont été mesurées par comptage alpha dans une géométrie bien définie avec une précision inférieure à 1% essentiellement définie par l'angle solide. L'identification des fissions suit la même démarche que pour le PPACmon avec détection en coincidence des fragments et reconstruction de la trajectoire de fission. La différence principale par rapport au PPACmon réside dans le fait que détecteurs et cibles sont inclinés à 45 par rapport au faisceau de neutrons. Au prix d'une plus grande taille la mesure est moins sensible à la distribution angulaire des fragments (FFAD) et elle assure un découplage de l'efficacité de détection et de la distribution angulaire, le nombre de fissions à un angle donné étant proportionnel au produit de l'efficacité et de la distribution angulaire. On peut pour chaque fission définir deux angles polaires, le premier par rapport au neutron incident et noté cos ✓, le second par rapport à la normale aux détecteurs et cibles et noté cos ✓ 0 . Un cos ✓ 0 donné peut être atteint avec toute une gamme de cos ✓, et tous ces évènements ont la même efficacité de détection, leur distribution est donc une représentation fidèle de la distribution angulaire (FFAD). On obtient ainsi la FFAD par morceaux. Réciproquement un même cos ✓ est atteint par une gamme de cos ✓ 0 et leur distribution est proportionnelle à l'efficacité de détection. Ceci rend possible la reconstruction de l'efficacité de détection par morceaux.Le système permet donc le découplage et la mesure séparée de l'efficacité de détection et de la distribution angulaire de fission.Quand l'efficacité de détection est mesurée pour chaque cible, le rapport des sections efficaces 237 Np/ 235 U est extrait. Nous en avons finalement déduit la section efficace 237 Np(n,f) entre 1 et 5 MeV à partir de la section efficace standard de 235 U. Les valeurs ainsi obtenues sont 3-4% plus hautes par rapport à ENDF-BVII.0, mais 2.2% au-dessous de la mesure n_TOF de 2010.

•

  Caractérisation du faisceau à EAR-2 Le profil du faisceau ainsi que le flux de neutrons non normalisé ont été mesurés à EAR-2. Le profil met en évidence un halo autour du pic central. Il diffère du profil à EAR-1 qui est quasiment uniforme. C'est la conséquence des différences de conception du collimateur final et la parallaxe induite par des distances très différentes. Nous avons montré que le PPACmon peut contrôler le faisceau de neutrons depuis l'énergie thermique jusqu'à 200 MeV ce qui en fait le système de détection couvrant la plus grande gamme en énergie à n_TOF . En particulier il est le seul système de détection accédant à la partie haute énergie du spectre des neutrons, depuis quelques MeV jusqu'à 200 MeV. • Mesure de 237 Np(n,f ) à EAR-1 Dans les mesures antérieures notre système ne permettait pas la mesure de l'efficacité de détection cible par cible et nous avions supposé que l'efficacité était la même pour les cibles de même épaisseur, support compris. Dans le présent travail de thèse l'inclinaison à 45 permet de résoudre le problème et apporte un bon contrôle de l'efficacité cible par cible. Nous avons trouvé que des éléments cibles différents donnaient des efficacités différentes malgré une épaisseur similaire. Les causes en sont la rugosité différente du dépôt ainsi que la composition chimique différente, une teneur plus grande en oxygène et hydrogène (eau, radicaux OH) ralentissant plus les fragments de fission. Il s'agit donc d'une amélioration significative du système de détection par rapport à la version antérieure. Les premiers résultats de la section efficace 237 Np(n,f) de 1 à 5 MeV sont obtenus en relatif à 235 U en utilisant ENDF/B-VII.0 comme référence. Les valeurs sont 2-3% plus basses que la mesure précédente obtenue en 2010 à n_TOF avec le système de PPAC, en raison de la correction d'efficacité. Elles restent supérieures de 3-4% par rapport à l'évaluation ENDF/B-VII.0. Le résultat est donc cohérent avec les mesures de criticité qui demandent une section efficace 237 Np(n,f) supérieure à celle des bases de données, bien que légèrement inférieure à celle de la mesure antérieure avec le système de PPAC. Université Paris-Saclay Espace Technologique / Immeuble Discovery Route de l'Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France Titre : Caractérisation de la nouvelle ligne de neutron à n_TOF CERN, et étude de la fission induite par neutrons de 237 Np Mots clés : fission, neutron, détecteur gazeux, n_TOF Résumé : L'installation n_TOF au CERN est une source pulsée de neutrons, unique au monde pour la mesure de données nucléaires sur le spectre en énergie le plus étendu, avec deux lignes actuellement exploitées. Une ligne horizontale alimente l'aire expérimentale 1 (EAR-1) avec une base de vol de ~185 mètres. La seconde ligne est verticale et alimente l'aire 2 (EAR-2) à ~20 mètres de la cible de production La première partie de ce travail de thèse concerne la caractérisation du faisceau de neutrons (flux, profil géométrique, spectre en énergie) de la nouvelle ligne EAR-2, particulièrement importante pour la définition des expériences et leur analyse. Une mesure a été réalisée à EAR-2, basée sur des détecteurs PPAC enregistrant la fission de 235 U, à partir de laquelle nous avons obtenu le profil et le flux sur la gamme en énergie accessible (thermique à 200 MeV).

:

  Characterization of the new neutron line at CERN-n_TOF and study of the neutron-induced fission of 237 Np Keywords : fission, neutron, gaseous detector, n_TOF Abstract : The neutron time-of-flight (n_TOF) facility at CERN is a unique worldwide pulsed neutron source to measure the nuclear data over the widest energy range with two beam lines currently exploited. One is horizontal with a ~185 meters flight path, sending neutrons to experimental area-1 (EAR-1). The second one is a new line sending neutrons vertically to experimental area-2 (EAR-2) with a ~20 meters flight path. The first part of this PhD work is dedicated to the characterization of the beam (flux, geometrical profile, energy spectrum) of the new EAR-2 neutron beam, of the utmost importance for the experimental proposals and analyses. An experiment was carried out at EAR-2, based on PPAC detectors looking at fission of 235 U, and the beam profile and neutron flux have been obtained for the entire available energy range (from thermal to 200 MeV).

Table 3 .

 3

	10 10 2 10 3 10 4 10 5 10 6	3.2 ⇥ 10 4 3.2 ⇥ 10 4 4.3 ⇥ 10 4 5.4 ⇥ 10 4 1.1 ⇥ 10 3 2.9 ⇥ 10 3 5.3 ⇥ 10 3	4.8 ⇥ 10 3 5.7 ⇥ 10 3 8.1 ⇥ 10 3 1.4 ⇥ 10 2 2.3 ⇥ 10 2 4.6 ⇥ 10 2 5.6 ⇥ 10 2

1:

The energy resolution as function of neutron energy for EAR-1 and EAR-2

Table 7 . 1 :

 71 The global efficiency in case of isotropic and anisotropic FFAD of different targets

	7.2 Neutron-induced fission cross section of 237 Np from 1 MeV
	to 5 MeV

Acknowledgements

2 crystals for detecting the ray cascade emitted in neutron capture reactions form a spherical shell, which covers 95% of 4⇡ solid angle. The neutron sensitivity of the TAC is inhibited by combining the spherical neutron moderator/absorber made of C

12 H 20 O 4 ( 6 Li) 2 surrounding the sample with the 10 B loaded carbon fiber capsules of the crystals. Capture events can be identified from competing reactions by reconstructing the total energy of the -ray cascade. TAC performs a high quality way for neutron capture measurements of small mass and/or radioactive samples at EAR-1.

The feature of C 6 D 6 liquid scintillator is its low sensitivity to background signals induced by scattered neutrons thanks to the use of a thin-wall carbon fiber cell to cover the scintillator [START_REF] Lederer | 197 Au(n, ) cross section in the unresolved resonance region[END_REF]. It's suitable for measuring light isotopes whose elastic scattering cross section is much higher than for capture.

(n, cp) measurement

(n, cp) reactions can be measured by Micromegas or Silicon-based detectors. Particularly, the setup of n_TOF EAR-2 facilitates the (n, cp) measurements with very low cross section thanks to its high neutron flux. For example, Micromegas has been used for 33 S(n, ↵) and 7 Be(n, ↵) measurements [START_REF] Gunsing | Nuclear data measurements at the upgraded neutron timeof-flight facility n_TOF at CERN[END_REF]. Recently, a new concept of Si-based detector has been developed with the sample sandwiched between two silicon detectors for detecting the back-to-back emission products in coincidence to reject the background. 3) If more than one cathode combinations are present, we use the method described in section 5.5.2 to select out the most proper one. We save these coincident events with complete localization information for latter analysis.

Several cuts as shown in figure 5.6, figure 5.7 and figure 5.8 have also to be applied to identify the fissioning target and reject the low amplitude background events before reconstruction. we define the neutron beam direction as the Z axis. To follow the right-hand system,

Integral neutron flux at EAR-2

To obtain the neutron flux, we need to determine the efficiency " and take into account the anisotropy of FFAD for neutrons above 1 MeV.

Efficiency determination

The coincidence method limits the detection efficiency of PPACs because it requires both fission fragments emerge out from the target, traverse the electrodes and reach the second gap. This is illustrated in figure 5. [START_REF] Rohlf | Modern Physics from alpha to Z0[END_REF] where the fissile target is red and the dead layers (aluminium target backing and mylar electrodes) are pink. It's easy for both fission fragments to be detected at small fission angle (✓1), whereas it's more difficult at large angle (✓2) because the travel path is increasing with the increase of fission angle, especially difficult for the fission fragment that has to additionally cross the target backing. So the stopping of the fission fragments before reaching the second gap at large angle limits the efficiency of PPAC. On the contrary, we can take the efficiency at fission angle ✓ = 0 as 100% since the fission fragments are traversing the minimum distance. to the low incident neutron energy, so it is directly reflecting the efficiency distribution.

Summary

From equation 5. [START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu[END_REF] we can calculate the unnormalized integral neutron flux at E n by:

Summary

We give the results of beam profile and integral neutron flux for the new neutron beam line EAR-2 at n_TOF . The beam is well centered and well collimated to circular. The

Fission event identification

The selection of the fission events follows the same procedure as in the case of PPACmon as described in section 5. [START_REF] Hahn | Über den nachweis und das verhalten der bei der bestrahlung des urans mittels neutronen entstehenden erdalkalimetalle[END_REF]. We open a window from -20 ns to +20 ns as the coincidence time to select the fission events. As shown in figure 6.2, we can simply use a graphical cut to select the central spot where the events are from target8 ( 235 U). After the coincidence selection, we also need to reject the events with low amplitude that are not true fission events. Figure 6.3 shows the correlation between the anode

Fission trajectory reconstruction

The coordinates of the hitting points on PPAC1 in the perpendicular frame are

where (X 0 1 , Z 0 1X ) is the coordinates of the hitting points on the X plane, (Y 0 1 , Z 0 1Y ) is the coordinates on the Y plane. X 1d and Y 1d are the coordinates obtained by equation 6.1 taking the cathode geometric center as the reference origin. The coordinates of the hitting points on PPAC2 in perpendicular frame can be obtained by equation 6.3.

3)

The distribution of the hitting points on PPAC8 and PPAC9 reconstructed by equation 6.2 and 6.3 are shown in figure 6.6. The cut line around X=10 in figure 6.6b is apparently caused by a strip at this position which was probably not working (no output signal from this strip) during the experiment. where

From figure 6.14 we can obtain

and for a given fission direction (cos ✓ 0 , 0 ), we can obtain its x 1 and x 2 by equation 6.17:

The geometric cut coefficient can be calculated by combining equation 6.14, 6.15 and 6.17. This coefficient is computed at the same time as the solid angle of each bin in the (cos ✓, cos ✓ 0 ) plane, so that the calculation returns the effective solid angle ⌦ 0 of each bin:

where F is defined by equation 6.14.

Determination of efficiency

In this section we present how we extract the efficiency based on the (cos ✓, cos ✓ 0 ) map as shown in figure 6. [START_REF] Nira | Neutron-induced fission cross section of 240,242 Pu[END_REF]. As already mentioned, the counts in each bin of the (cos ✓, cos ✓ 0 ) plane can be calculated by:

where N ij is the counts in bin (i, j) for a broad energy range where we assume that the efficiency is constant, C is a normalization factor including the neutron flux, cross section, target quantity and 4⇡ solid angle, W (cos ✓ j ) is the angular distribution at j th column averaged over the broad energy interval, " i is the efficiency at i th horizontal line, ⌦ 0 ij is the effective solid angle of bin (i, j). Since the counts in each bin cover a with 3 parameters a 0 , a 1 and a 2 to be fitted. Figure 6.18 shows the efficiency curves fitted by equation 6.22 where the black dots are the efficiency points and the red line is the fit. We can see that function 6.22 is able to accurately reproduce the efficiency distribution. Therefore in the further analysis, we shall directly use this function to fit the efficiency curve to facilitate the analysis instead of fitting them slices by slices. That is to say, we define the chi-square as follow instead of equation 6.21.

) to be fitted.

Construction of FFAD

Once the efficiency has been determined, it is used to extract the angular distribution for any energy interval based on the characteristics of (cos ✓, cos ✓ 0 ) map. In figure 6.16, we know that horizontal slices are all proportional to the angular distribution: they are only scaled between each other by the product of the efficiency and solid angles corresponding to the bins. Therefore a point of the angular distribution can be obtained by summing up the counts on a column and summing up their respective weights (efficiency⇥solid

RESULTS AND DISCUSSION

The efficiencies as a function of cos ✓ 0 of 3 237 Np targets and reference 235 U target (target8) from 1 MeV to 5 MeV are shown in figure 7.5. In this energy range, the effect of the anisotropy of FFAD on the global efficiency is rather small, because the FFAD is quite flat before the second chance fission. It can be simply checked by taking different anisotropy parameters and FFAD functions. We take 2 different FFAD functions, polynomial with order 2 and order 4, to calculate the global efficiency of 237 Np (target6) and 235 U (target8) with different anisotropy parameters. It can be seen from figure 7.6 that the global efficiency is increasing with the increase of the anisotropy, and the increasing slope depends on the form of FFAD. However the anisotropy correction on the global efficiency is rather tiny. The maximum anisotropy of 235 U is expected to be around 1.3 at the level of second chance fission, which induces a variation of global efficiency of less than 2%. We will only take into account energy range from 1 MeV to 5 MeV which is even before the second chance fission, so the effect is even less than 1%. If we consider the FFAD is isotropic, then the global efficiency is simply the integral of the curves in figure 7.5. Table 7.1 lists the global efficiency of targets in case of isotropic and anisotropic respectively. For anisotropy correction we use the average FFAD between 1 to 5 MeV fitted from our data. The global efficiencies in table 7.1 will be used to calculate the cross section in later part.

Anode versus localization application

The normalized fission rates should be identical, since they take into account all the factors involved in the relative fission rate. Due to the unavoidable systematic uncertainty, there should be some dispersion between different normalized fission rate, but the dispersion is expected to be very small, around 2-3%. The dispersion can be calculated by dividing each normalized fission rate by the average of them which is defined as:

where 5, 6, 7 stand for the target 5, 6, 7 respectively. A PPAC consists of a central anode and 2 surrounding cathodes. The anode is used to measure the time and to perform the coincidence to identify fission, the 2 cathodes are used to locate the fission fragment in X and Y direction. It can be seen from figure 7.8 that an anode signal will appear as soon as a fission fragment traverses the first cathode facing the target. This anode signal can be immediately used to perform the coincidence requirement to identify the fission. However, the localization of this fission fragment requires the fission fragment to go through the anode, otherwise the second cathode signal will be missing and the reconstruction of the fission trajectory cannot be achieved. It means when we need the localization information, we need both cathodes deliver signals. Therefore the efficiency for events detected in the anode is higher than those whose localization signals are present, because some fission fragments may stop in the anode. In this case the anode signal is present and could be counted as a fission event, but if the localization is requested this event has to be discarded due to the lack of the localization information.

Now let's look at the relation between fission rate with localization requirement and

without localization (only anode coincidence is applied regardless of cathode signal).

The (a), (b), (c) in figure 7.9 and (a) in figure 7.10 shows the fission rate of 3 237 Np targets and the 235 U target. The red curves are the fission events determined only by anode coincidence without localization, the black ones are the fission events acquired by anode coincidence with supplementary localization requirement. We can see that

Anode versus localization application

anode coincidences without localization lead to distributions more consistent between each other. They are dispersed within ±3% discrepancy, resulting from the systematic uncertainty. This indicates that these fission rates without localization are more reliable and can be used to deduce the cross section.

Efficiency of the fission rate without localization

The reliability of the fission rate without localization has been checked. Apart from it, to deduce the cross section we also need to know the efficiency ratio of 235 U and 237 Np target. However, we don't know the efficiency of anode coincidence, we only know the angular dependence when the localization is involved. Here we assume that the efficiency without the localization is defined by the same angular dependence as the one with localization. This hypothesis can be checked if we use the efficiency from localization to normalize the fission rate without localization. We use equation 7.7 and 7.8 to normalize the anode fission rate. Figure 7.13 shows the consistency of the fission rate treated in this way, it can bee seen that they are dispersed within ±3%, which is favoring our assumption. Therefore, we will use the efficiency ratio with localization to estimate the efficiency ratio without localization to calculate the cross section.

RESULTS AND DISCUSSION

Cross section and discussion

We use the normalized fission rate to deduce the fission cross section ratio of 237 Np relative to 235 U by

where < R nor7 (E n ) > is the average of the normalized fission rates of 3 237 Np targets, which is calculated by equation 7.8 with the efficiency listed in table 7.1, R nor5 (E n ) is the normalized fission rates of 235 U calculated by equation 7.7 with its efficiency, C is a correction constant taking into account the different mass number of 237 Np and 235 U, namely 237/235. Figure 7.14 is the comparison of the neutron-induced fission cross section ratio of 237 Np relative to 235 U. We can see that our result is about 3-4% higher than the ENDF-B/VII.0 evaluation above 1 MeV. We also find that our data are about 2.2% lower compared with our previous measurement in 2010 [START_REF] Paradela | Neutron-induced fission cross section of 234 U and 237 Np measured at the cern Neutron Time-of-Flight (n_TOF) facility[END_REF]. This difference is mainly from the efficiency. In our previous measurement, since PPAC is perpendicular to the beam, we can not extract its efficiency as we've done in this work. Therefore it was assumed that the efficiency is the same for all the targets. In this work, we obtained the efficiency for different targets thanks to the tilted setup. We find that the efficiency of same targets (same original source, same backing, same thickness) is quite similar, for example target 5 and 7, as we expected before. However, differences exist for different actinide targets.

Mesures

Dans ce travail de thèse un expérience sur chacune des lignes de faisceau a été réalisée. La première a été réalisée à EAR-2 pour la mesure des propriétés du faisceau de neutron (flux de neutrons, forme du profil). La seconde, réalisée à EAR-1, était dédiée à la mesure de la section efficace de fission de 237 Np et à la distribution angulaire des fragments de fission (FFAD). Le PPACmon contient trois détecteurs PPAC et deux cibles de 235 U perpendiculaires au faisceau de neutrons, chaque cible étant située entre deux PPAC. Quand un neutron incident induit une fission dans une des deux cibles les deux fragments sont émis à 180 l'un de l'autre. Cette fission est identifiée par la détection simultanée des deux fragments. Cette méthode est particulièrement sélective des fissions, rejetant la plupart des évènements de bruit de fond provenant des réactions autres que la fission, abondantes à haute énergie dans le domaine de la spallation.

Après sélection d'un évènement de fission l'énergie du neutron l'ayant produit est déterminé par temps de vol (TOF) et on obtient le nombre de fissions en fonction de l'énergie des neutrons. Comme l'efficacité de détection des PPAC ne dépend pas de l'énergie des neutrons, elle a été considérée comme constante sur la gamme en énergie traitée. La dépendance en énergie du flux est alors obtenue en divisant le nombre de fissions en fonction de l'énergie par la section efficace de fission de 235 U extraite des