Tijani Idbarkach

Thejus Mahajan

Marin Chabot

Karine Béroff
email: karine.beroff@u-psud.fr

Néstor F Aguirre

Sergio Diaz-Tendero

Thibaut Launoy

Arnaud Le Padellec

Luc Perrot

Maëlle A Bonnin

Kim Cuong Le

Florian Geslin

Nicolas De Séréville

Fairouz Hammache

Aurélie Jallat

Anne Meyer

Emeline Charon

Thomas Pino

Thibault Hamelin

Valentine Wakelam
email: valentine.wakelam@u-bordeaux.fr

Semiempirical breakdown curves of C 2 N (+) and C 3 N (+) molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts

Keywords:

n=1-3) . . . . . . . . . . . . 5.1.3 Doubly charged molecules n ``(n=1-3) . . . . . . . . . . . 5.1.4 Highly charged molecules n q`( n=1-3, q>2) . . . . . . . . 5.1.5 Anionic molecules n ´(n=1-3) . . . . . . . . . . . . . . . . 5.2 Interpretation of dissociation of n `molecules using the energy deposit calculation performed within IAE/CTMC model. . . . . . . . .

Synthése

Dans cette thèse nous avons étudié des collisions entre des projectiles C n N `(n =1-3) et des atomes d'Hélium à vitesse intermédiaire (2.25 u.a). A cette vitesse, proche de la vitesse des électrons sur les couches de valence externes des atomes et molécules, de nombreux processus électroniques prennent place avec une forte probabilité: ionisation (simple et multiple), excitation électronique, capture d'électron (simple et double). Nous avons mesuré les sections efficaces absolues de tous ces processus.

Un autre aspect intéressant de la collision concerne la fragmentation des molécules excitées, que nous avons également mesurée précisément grâce au dispositif dédié AGAT. L'utilisation de la cinématique inverse (l'objet d'étude étant l'objet accéléré) permet de récolter tous les fragments (cations, anions et neutres) dans un cône angu- I thank Dr. Clara Illescas, UAM Madrid, for introducing me to the exciting world of CTMC. We had several stimulating discussions and the author had the opportunity to study deeply about CTMC under the guidance of Dr. Clara Illescas. I also acknowledge Alba María Jorge Palacious for helping me during the initial phase of CTMC numerical calculations.

The second phase of the CTMC calculations was done at CELIA, Bordeaux. I thank Dr. Bernard Pons for helping me with the calculations. It was Bernard who watered and manured the seeds of CTMC which were sowed at Madrid. The discussions was stimulating and helped me grow my deep appreciation towards this humble classical method in describing the various processes that takes place during the ion-atom collisions at an intermediate velocity.

Shout out to all the Group-C members of Institut des Sciences Moléculaires d'Orsay (ISMO) and all PhD students of ISMO. I thank Dr. Alain Dubois for an exciting course in "Electronic processes in atomic and molécular collisions" organized in the teaching unit "Ultra" fast dynamics of reactive species" (Master of Chemistry, Sorbonne Université). I thank Dr. Bernard Bourguignon, the present director of ISMO for his valuable and suggestions during the course of my Ph.D. I thank the Informatique team of ISMO headed by Mr. Yves Bergougnoux for helping me with the installation and proper maintenance of the work computer. Special mention to the computer team for their immediate responses to any problems that would hinder the smooth flow of the work. I thank the administrative staff of ISMO and Universié Paris-Sud who helped me with a smile with all the administrative tasks. Special mention to Mme. Marie-Claire Paul who would find a solution to any problem related to the administration. I thank Centre National de la Recherche Scientifique (CNRS), Ecole Doctorale Ondes et Matière (EDOM), Insitut des Sciences moléculaires d'Orsay (ISMO), Université Paris-Sud (Université Paris-Saclay) for financing, providing me with an office and ensuring the smooth conduct of research. I thank the government of France and the people of France for welcoming the author to their country, giving me a taste of the celebrated French culture and professionalism. It is the authors' wish to someday give back something substantial to the French society in return. I thank the Government of India, of which the author is a proud citizen, and its Department of Science and Technology (DST) for all the support throughout the years of my scientific development. I acknowledge my friends and family, I love you all. I thank Nimmi Das A (IISC, Bangalore) for her support during the course of this PhD.

Finally, it is with great respect, I acknowledge once again Dr. Karine Béroff. For whatever difficulty or errors that the reader may find in this thesis is soley attributed to the author missing suggestions or recommendations from Dr. Béroff. They instilled in me deep with love and appreciation for the physics of collisions and the "how to's" of accelerator collisions experiments and data analysis. Special mention to their work culture of which the author tried and failed to copy successfully. It was a substantial task and someday the author wish to be as meticulous and detail eyed as Dr. Béroff.

3.2.2.2

Overview of process probabilities (1 ´calculations) . 3.2.2.3 Comparison between 1 ´and 2 ´calculations (target ionization and excitation) . . . . . . . . . . . . . . . 3.2.2.4 Comparison between 1 ´and 2 ´calculations (projectile ionization and excitation) . . . . . . . . . . . 3.2.2.4.1 The electron-He model potential for 1 ´calculations . . . . . . . . . . . . . . . . . . . . 3.2.2.4.2 Comparison between 1 ´and 2 ´calculations 3.2.2.5 p, q classical cross sections . . . . . . . . . . . . . . 3.2.2.5.1 The classical p, q to quantum p, q correspondence . . . . . . . . . . . . . . . . . . 3.2.2.5.2 The 2 ´2 excitation process; use of quantum results . . . . . . . . . . . . . . . . . . 3.2.2.5.3 CTMC predictions for p, q cross sections . 3.2.2.6 Comparison between CTMC and experiment for total cross sections (, `, `´ collisions) . . . . Significant progresses have been made in the past in the understanding of ion-atom collisions [START_REF] Bransden | Charge Exchange and the Theory of Ion-Atom Collisions[END_REF]. It is usual to distinct three velocity regimes, depending on the ratio between the projectile velocity p and the velocity of the active electron e , from which different theoretical approaches result. The intermediate velocity regime ( p " e ) is considered as the most difficult to apprehend because all basic electronic processes (electron excitation, ionization, electron capture) have the same order of magnitude and multi-electron processes are large.

Results on cross sections

The same applies to ion-molecule collisions, with some additional difficulty arising from the multi-center nature of the target. Experimentally, pioneering works in the intermediate and high velocity range were performed in the 1990s on small molecules [START_REF] Watson | Time-of-flight analysis of dissociation products from collisions of 40 MeV Ar 13`w ith molecular oxygen[END_REF][START_REF] Sampoll | Two-fragment coincidence studies of molecular coulomb explosions induced by heavy ion impact[END_REF][START_REF] Sampoll | Dissociation of multicharged CO molecular ions produced in collisions with 97-MeV Ar 14`: Total-kinetic-energy distributions[END_REF]. They were pursued in other groups, notably in France, on carbon clusters [START_REF] Wohrer | Swift cluster-atom collisions: experiment and model calculations[END_REF], diatomics [START_REF] Adoui | Fast ion-induced CO molecule fragmentation in the strong interaction regime[END_REF] and triatomics [START_REF] Moretto-Capelle | Fragmentation of CO 2 into C ``O ``O, in collisions with protons[END_REF]. A large interest was also drawn on collisions with 60 [START_REF] Lebrun | Ionization and multifragmentation of C 60 by high-energy, highly charged Xe ions[END_REF][START_REF] Tsuchida | Cross sections for ionization C 60 and fragmentation of by fast H `impact[END_REF][START_REF] Reinköster | Experimental and theoretical study of ionization and fragmentation of C 60 by fast-proton impact[END_REF][START_REF] Bordenave-Montesquieu | Scaling of C 60 ionization and fragmentation with the energy deposited in collisions with H `, H 2 , H 3 and He `ions (2-130 keV)[END_REF]. Presently the ion-molecule collision studies remain an active area, as observed for instance at ICPEAC (International Conference on Photonic, Electronic and Atomic Collisions) conferences.

From the theoretical side, collision studies involving molecular targets strongly developed in recent years. One of the reason is the radiobiological motivation since understanding the damage to biological tissues requires to know collisional cross sections. In that context, numerous works have been devoted to the 2 molecule [START_REF] Lüdde | Nonperturbative, quantum-mechanical approach to ion collisions from molecular targets[END_REF][START_REF] Illescas | Classical treatment of ion-H 2 O collisions with a three-center model potential[END_REF]Murakami et al., 2012b,a) and references therein. In the theoretical treatments, approximations have to be done. In the works of [START_REF] Lüdde | Nonperturbative, quantum-mechanical approach to ion collisions from molecular targets[END_REF] and Murakami et al. (2012b), a quantum-mechanical approach is used but the dynamics of the collision is performed by developing 2 molecular orbitals (MOs) on a single center basis (oxygen atom). In [START_REF] Illescas | Classical treatment of ion-H 2 O collisions with a three-center model potential[END_REF], the molecular structure of 2 is preserved, in the frame of a classical treatment of the collision (Classical Trajectory Monte Carlo or CTMC approach).

Another approach lies in the Independent Atom and Electron (IAE) model [START_REF] Wohrer | Model calculations of multielectron ionization of O 2 molecules by fast-heavy-ion impact[END_REF][START_REF] Wohrer | Model calculations of multi-ionization cross sections in high velocity ion-cluster collisions[END_REF]. In the IAE model, the molecule is supposed to be made of n independent atoms positioned at the equilibrium geometry of the molecule. In that context, the dynamics of the ion-molecule collision is truly reducible to n ion-atom collisions. In an impact parameter formalism and within the independent electron approximation, multi-electron processes may be derived which is a major interest of the method since these are far from being easily "guessable". We recently tested the IAE model in collision of ǹ carbon clusters with He, Ar targets at intermediate velocity using either CTMC or SCAOCC (semiclassical atomic orbital close coupling) calculations for impact parameter probabilities in ion-atom collisions [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF]. In this thesis the IAE/CTMC approach will be further tested for the n `(n=1-3) -He collisions at intermediate velocity (v=2.25 a.u).

Another aspect of ion-molecule collisions resides in the opening of a new relaxation path for excited molecules by fragmentation. A large part of ion-molecule studies refers to the fragmentation analysis that comprises also fundamental and applied aspects. From the fundamental point of view, some questions addressed are: what is the stability of the molecule in regard of its charge and internal energy? How will the molecule dissociate under such specific conditions? How predictable is the result? To answer those questions we used a dedicated setup, able to record the entire fragmentation as will be shown. Although not presented in this thesis but underway, the large set of fragmentation data may be used to test the statistical fragmentation theories such as the Microcanonical Metropolis Monte Carlo method (M3C) recently generalized to polyatomic systems [START_REF] Aguirre | M3C: A computational approach to describe statistical fragmentation of excited molecules and clusters[END_REF]. From a more applied point of view, we may use these fragmentation data in all situations where statistical fragmentation occurs. This is an approximation that was assumed in predictions of fragmentation branching ratios of molecular species electronically excited in interstellar and planetary atmospheres.

Astrochemistry deals with the study of the content and evolution of the molecular material in astrophysical environments. Modeling of these environments requires the knowledge of a huge amount of data including kinetic data, rate coefficients and also branching ratios for many physical and chemical processes [START_REF] Wakelam | A kinetic database for astrochemistry (kida)[END_REF].

In [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF] it was shown how it was possible to predict those branching ratios through a semiempirical method based on the construction of breakdown curves (internal energy dependent branching ratios). The method, initially applied to carbon and hydrocarbon molecules, has been extended to the case of n and n `molecular systems studied in this thesis (n=2-3).

The plan of the manuscript is the following:

In chapter 1 are presented the experimental tools used in this work: the Tandem accelerator for producing high energy (MeV) molecular species n `; the AGAT setup for recording their excitation and fragmentation following collision with helium atoms, based on the multicoincident detection of all fragments, including the neutral ones. The choice of n `molecules was motivated by their presence in interstellar environments (The Astrochymist * , Cologne Database † , 2018) whereas the choice of helium was motivated by the fact that it is a rather simple partner with only two electrons.

In chapter 2 are presented the methods used for data reduction: the DP2 software allowing the visualization and counting of multicoincident events, the methods for determining the number of impinging fragments on the same detector (resolution of a so-called pile-up event), the determination of absolute target density and absolute cross sections.

Chapter 3 is devoted to the theoretical modelisation of the collision. It describes the Independent Atom and Electron (IAE) model that was used to reduce the molecule-atom collision to several independent ion-atom collisions. Besides we present the results of the Classical Trajectory Monte Carlo (CTMC) method used for calculating impact parameter probabilities of basic electronic processes in those ion-atom collision systems.

Chapter 4 presents the experimental results concerning the cross sections associated to various electronic processes: single and multi-ionisation cross sections of n `projectiles, dissociative electronic excitation cross sections, neutralization cross sections (by single electron capture) and anionic production cross sections (by double electron capture). Comparison with predicted cross sections by the IAE/CTMC model is presented and discussed.

In chapter 5 we present fragmentation branching ratios (BR) for the n Qs pecies with variable charge state (Q=-1,0,1,2,3). For cations (Q=1) we compare the internal energies deduced from measured BR with calculation within the IAE/CTMC model. Results concerning ion pair dissociation (IPD) BR are also presented.

Chapter 6 is devoted to the application of these experiments to astrochemistry (paper). Semi-empirical breakdown curves of 2 , 3 , 2 `and 3 `molecules are presented and used to predict and to recommend products branching ratios of some processes of astrochemical interest to be included in the KIDA ‡ (Kinetic Database for Astrochemistry) database. Some conclusions and perspectives are given at the end. Two appendices relating to chapter 3 and chapter 5 are joined. ‡ http://kida.obs.u-bordeaux1.fr/ Chapter 1

Experimental tools

1.1 Principle of the experiment The first advantage is that during an inelastic process, the deposited energy is low (a few eV) compared to the energy of the particles (few M eV) and thus the velocity of the center of mass is very little modified. In the laboratory frame, for a fragment of mass m emitted at 90 ˝from the beam axis with a kinetic energy c (eV), the angle of angular opening is simply written as:

" ´1`a 2 c { p ˘(1.1)
where p is the projectile velocity. Typical value of is around 1 ˝. It is due to this property that we obtain a solid angle of detection of 4 in the projectile frame with a few (ď10) detectors of reasonably small sizes.

In addition to this geometrical aspect, the second advantage of this set-up is the ability to detect all the fragments including the neutral fragments and to identify their mass with silicon detectors. At these velocities, the detectors have an efficiency of 100 %. For an incident fragment of mass m and velocity the detector outputs the kinetic energy. The velocity of the fragments can be considered to be constant before and after fragmentation (a few eV difference compared to few 10 6 eV of incident kinetic energy), then the measured energy is proportional to the mass of the fragment.

Each detector intercepts particles of a specific charge to mass ({) ratio. Thus we could identify the charge of the impinging fragment by knowing its mass. By doing the same for all the detectors measured in coincidence, we can determine, event by event, the total charge of the molecule and thus go back to the process involved in the collision. For example, since the incident projectile is a cation with " 1, " 0 after collision corresponds to a single electron capture process, " ´1 to a double electron capture process, " 2 (resp.

General view of the experiment

In this chapter, a description of the experimental set-up is given. The experiment comprises of essentially 3 parts (see Figure 1.2):

1. Ion source for the production of n ´p ď 4q beams.

2. The Tandem accelerator to produce and accelerate the n `molecules.

3. AGAT set-up with the associated electronics for collision and data collection.

Chopper C n N - {C n N q+ } ≤ 15M V N 2 gas AGAT Cs C n N - Analyzing Magnet (35 • ) Ion Source Terminal Analyzing Magnet (1 • 3 ′′ ) C n N +

The ion source

A schematic view of the ion source is presented in Figure 1-3. The source HICONEX is one of the sources of ions intended for the production of negative beams at the Tandem d'Orsay. It is mainly dedicated to heavy ions and to atomic ensembles. That's the source we used to get the whole experimental measurements of this thesis. This is a Middletron-type sputtering source. Cesium, heated in a oven at a temperature of the order of 140 ˝C, will vaporize and then ionize when its passage through a sintered tungsten pellet which is brought to a temperature between 800 ˝C and 1050 ˝C. The The beam is magnetically deflected according to the magnetic rigidity '' defined as 1.5 3000 5 ´p74q

1.1 3276

Table 1.1: Beam intensities obtained with a cone made of 50 % of and 50 % of graphite

As Table 1.1 predicts, the magnetic field depends linearly with the square root of mass (see Figure 12345).

During the second run of February 2016 we realized that 4 `beam was essentially `coming from the selection at the source of ´instead of 4 ´(both having the same mass and ´being much more intense). In October 2016, we tried new cones with (Tantale Nitride) mixed with graphite at various concentrations. Unfortunately the n ´beam intensities with these cones were too small and we had to renounce to a proper 4 `study. As some information is nevertheless possibly extractable with this projectile (although not done in this thesis) we will still present in the following some results associated to these species.

As already discussed in previous works on ń clusters (Mezdari, 2005) and n ḿ hydrocarbon molecules [START_REF] Jallat | Fragmentation de molécules carbonées d'intérêt astrophysique auprès des accélérateurs[END_REF] the species produced by sputtering are having some internal energy ˚correlated to the source temperature s . From these works s can be estimated to be s " 3300 K. The most probable internal energy of a canonical system in thermal equilibrium at a temperature s is given by [START_REF] Andersen | On the concept of temperature for a small isolated system[END_REF]):

p " s p3 ´q (1.3)
where s is the temperature of the system, is the number of atoms in the molecule, " 5 (resp. 6) for linear (resp. non-linear) molecules and is the Bolzmann constant.

By knowing the temperature of our source to be " 3300 K, we get the most probable internal energy of the molecule (for linear species) reported in Table 1.2. For large molecules, the internal energy distribution is of Gaussian shape with the standard deviation given by [START_REF] Andersen | On the concept of temperature for a small isolated system[END_REF]:

" s ? 3 ´ (1.4)
Values of are also given in Table 1.2 for linear species. Finally it is interesting to compare the species' internal energy with its electron affinity . Indeed if the internal energy is higher than a very small intensity is to be expected. 0.88 3.11 [START_REF] Garand | Slow photoelectron velocity-map imaging spectroscopy of C 2 N ´, C 4 N ´, and C 6 N ´[END_REF] Table 1.2: Species most probable internal energy, standard deviation for the internal energy distribution and n electron affinity.

After selection of the desired n ´species with the 35 ˝magnet, the selected anion is injected in the Tandem accelerator at about 200 keV. Before the Tandem entrance, a chopper allows to pulse the beam (see Figure 1-2). The chopper produces beam pulses of 150 ns large with a frequency of 2.5 MHz or less ( {). Large values allow to reduce the beam intensity (we worked with a few thousands of projectile/s or even less when using the CCD camera). With this chopper we also could stop the beam when needed. (see Section 1-6-1-2).

1.4 The Tandem accelerator

Description

The accelerator in the Figure 1-6 is a Van de Graff type electrostatic accelerator. It was commissioned in 1972 by Societe High Voltage Engineering Corporation. The first experiment was conducted on January 1973 [START_REF] Vergnes | Tandem physics in orsay[END_REF] with atomic ions and in the late 90's with 60 clusters. The accelerator is comprised of the following parts:

• The accelerator tube, where the particles are transported.

• The voltage terminal and a system to transport charges (Laddertron) in order to increase or decrease the terminal potential. ( max "15 MV)

• A gaseous stripper ( 2 ) placed at the terminal to produce cations from anions by stripping away electrons

• A tank filled with 8 bars of 6 gas to isolate the high voltage terminal from surroundings.

Production of `beams

The negative ions injected into the accelerator at an energy in by the injector undergo a first acceleration towards the center of the accelerator by positive high voltage t . At the center, the ions are passed through a thin layer of 2 gas which acts as an electron stripper and render the species positive. They will then be accelerated again till the end which is grounded.

The final energy of the particles is given by:

" in ` t ` t (1.5)
Where in is the energy of anions at the entrance of the accelerator ("200 keV), t

is the potential at the terminal, is the charge of electron and is the number of positive charges after stripping ( " 1 in our case since n `cations are selected).

Numerical application is presented in Table 1.3 using Equation 1.5 for . Exception arises for `, which cannot be produced from ´which is highly unstable (ground state self ionizes in 10 ´14 s and some excited levels within ns [START_REF] Andersen | Atomic negative ions: structure, dynamics and collisions[END_REF]). `beam was then produced by fragmentation of `at the stripper. It is worth noting that in the stripping process the projectile may gain a little bit of internal energy attributed to the ionization of inner valence shells (Mezdari, 2005).

Typical value for the internal energy gained in the stripping process is 1 ´1.5 eV.

At the exit of the Tandem accelerator the beam is reduced using various slits.

With the entrance slits of the AGAT set-up, this allows to work with a beam of very small angular divergence (see below). Taking into account the stripping process and the cuts in the beam size reduce considerably the intensity of cations as compared to anions (roughly 10 3 times smaller).

The AGAT set-up

The experimental device AGAT (named for AGregat-ATome collision) was schematised in Figure 1-1 and shown on the photo of Figure 1234567.

AGAT is composed of:

• a collision chamber hosting an effusive jet of helium where the collision takes place

• an analysis chamber hosting an electrostatic deflector that deflects the fragments according to their { ratio

• a detection chamber where all the detectors are properly positioned in order to detect all the fragments in coincidence

We will describe the successive parts the beam traverses.

The entrance slits

There are two pairs of slits at the entrance of AGAT to reduce the beam size and the beam emittance. We work on a beam size of about 0.1 mm x 0.1 mm and a typical beam angular divergence of less that 0.15 mrad. Before entering the collision chamber, a set of two vertical and horizontal movable slits are used to achieve this.

Beam of small dimensions is desirable. Along the vertical axis it allows to cross the jet very near the capillary end where the density is the higher. Along the perpendicular direction the beam dimension should be smaller than the jet size in order to perform a jet profile (see below), necessary for the extraction of absolute cross sections. He jet. The gas injection system is presented in figure 1.9. The flow rate of the He jet is controlled electronically which operates from 0-2 sccm with a precision of 0.02 sccm. sccm is an acronym for standard cubic centimetre per minute at standard temperature (0 ˝C) and pressure (1). In the experiments typical flow rates were between 0.25 and 1.1 small enough as to ensure (with the exception of anionic production; see Chapter 2) the single collision condition. For each beam three different flow rates were performed. In order to record event coming only from the jet (and subtract event coming from collision with the residual gas) we used a similar capillary placed on the side of the chamber (see Figure 1.9). The beam will not cross this jet but only the residual pressure induced by the jet in the same conditions as when the beam crosses the vertical jet (same capillary, same flow rate). The procedure to achieve the 'background subtraction' is the following : the experiment is first ran with the vertical jet crossed by the beam by opening The deviation dev of an ion of charge , mass in a constant electric field perpendicular to the ion velocity (see Figure 1.12) has the following expression:

dev " ∆ 2 ` 2 `˘ (1.7)
" Separation between the plates.

" is the distance from the output of the plates to the detector where the deviation is measured.

∆ " 2 " Potential difference.

" Length of the plates. The deflection angle of the ion is given by:

" ´1` dev `L 2 ˘(1.8)
Except the charge and mass , all the other parameters are maintained constant in the experiment. It is thus { or "charge to the mass" ratio alone that determines the deflection of the particles. The particles thus deflected (negative will also be deflected by towards the positive plate) will enter into the detection chamber.

Fragment Angle deviation ( ˝) Position fragment (mm) (at the position detector `L 2 in mm) we put a "finger" which is a steel wire of 60 mm length and 0.5 mm cross section radius (see . Its main function is to stop the incident beam to keep the detector from damage and also to allow the fragmentation events to be recorded (otherwise the acquisition would be always busy with the incident beam, 100 times more intense than the fragments). This finger is removed during normalisation runs (see chapter

2).

The detectors

All the detectors in these experiments are solid-state silicon semiconductor detectors.

A semiconductor is defined as that whose electrical conductivity is around mid way between that of the metals (, ...) and that of the insulators (wood, rubber solids. The electrons in the solid is theorized to be in either conduction band or valence band. Those in the conduction band is responsible for electrical conductivity and those in the valence band do not contribute to the conductivity. The conduction band and the valence band are further separated by a "forbidden band" of which the width of it is usually termed as the "band width" or "band gap". Note here that the "width of band" is expressed in energy. In layman terms, for an electron in a valence band to contribute for conduction, it must gain sufficient energy to "jump" across the forbidden band. In metals, the conduction band and the valence band overlap which amounts to their high conductivity. Whereas in the insulators, the band width is too large for the electrons to jump to the conduction band to contribute to conductivity.

In semiconductors, the band gap is in the intermediate energy range (1.12 eV for silicon, 0.66 eV for germanium), so that it is possible for the electrons to jump across the gap by gaining energy from the ionising radiation. The semiconductor detectors are composed of two joined silicon semiconductors, the P-type and N-type. Doping a semiconductor is a process of adding impurities such that the impurities increase or decrease the band-width. There are two types of doping:

• -N-type doping: Increasing the population of negative charge carriers (donor of electrons), e.g. adding pentavalent atoms.

• P type doping: Increasing the population of positive charge carriers (acceptor of electrons), usually by adding trivalent atoms (boron).

At the P-N junction between these two semiconductors, the electrons of the doped region N will diffuse in the doped region P. The opposite occurs for the carriers of the positive charges. There are thus no more free charge carriers at the P-N junction also called depletion zone. A potential barrier is thus formed in this zone, which prevents the free charges from crossing it. In order to increase the efficiency of the detector, an inverse electrical potential is applied at its terminals, the depletion zone is thus enlarged, as shown in Figure 1-14.

When the P-N junction is hit by a particle, its kinetic energy is transferred to the creation of electrons and holes. If the particle traverses the dead layer (which is before the depleted zone) with a small energy loss and if it is fully stopped in the depleted zone , as is in our case, the efficiency of detection is 100%. The total number of electrons e is proportional to the kinetic energy of the incoming particle.

If is the energy required to create one electron-hole pair then, the number of electrons created e is given by e "

(1.9)

In silicon "3.6 eV. It is much greater than the energy gap (1.12 eV) because a part of the projectile kinetic energy is not used for electron-hole production (but recombinations, phonons ...). The number e is very large in our case and so are the fluctuations of this value (governing, with the noise level, the energy resolution of the detector). The detectors we used (except the detector of neutral fragments) were commercial ion-implanted detectors provided by ORTEC (Ultra ion-implanted detec-

Initial depletion zone

Depletion zone at reverse bias N-type P-type -+ before the runs (see Figure 1-15).

The detector of neutral fragments

There are two detectors for neutral species, one is a home-made silicon detector developed at IPNO and made for optimizing the current shape analysis technique (see Section 2.5). The other one is an original CCD camera developed recently in the team [START_REF] Chabot | Detection of atomic and molecular mega-electron-volt projectiles using an x-ray charged coupled device camera[END_REF]. 1.5.4.3.2 The CCD camera The CCD was invented in 1970 by [START_REF] Boyle | Charge coupled semiconductor devices[END_REF]; [START_REF] Amelio | Experimental verification of the charge coupled device concept[END_REF]. This type of detector is generally used for the detection of photons. In order to be able to integrate these detectors with spacecraft, the damage that cosmic rays can produce has been studied since the early 1990's . In recent experiments the team showed that this detector was able to detect particles and then to combine the position information with the mass information [START_REF] Chabot | Detection of atomic and molecular mega-electron-volt projectiles using an x-ray charged coupled device camera[END_REF]. We used the C4742-98-26KADVS camera manufactured by Hamamatsu Photonics. This camera is designed for direct x-ray detection applications.

It is mechanically attached to an experimental chamber by a vacuum flange and cooled down to ´55 ˝C for reducing thermal noise. The CCD of the camera is an S7170 manufactured by Hamamatsu Photonics as well. S7170 has 512 ˆ512 pixels of 24 µm pitch, leading to an active area of 12.3 ˆ12.3mm 2 , (see Figure 1 -16).

With the aim of extending capabilities for this experiment, this customized version benefited from an extended full well capacity (FWC) of 400 000 electrons per pixel as compared to 340 000 electrons per pixel for the "standard" version. The FWC of the CCD is defined as the amount of signal electrons that can be properly collected.

The camera functions as a pixelated silicon detector. The fragments are spatially resolved and each of their kinetic energy is measured. The two limitations of this detector are the following: the detector needs 160 ms for treating an event; it then reduced our counting rate, normally of 300 s ´1, to 6 s ´1. Also the camera needs to be externally triggered, which was done by sending a signal from the MCP recoil detector as mentioned before.

The detector configurations

The configuration (number of detectors, sizes, positions) is always a delicate matter.

We want to detect every fragments and to distinguish fragments impinging in the same detector. The result (detector configuration) is shown in Table 1.6 (and the corresponding Figure 1-17) for the run of March 2015 and Table 1.7 (and Figure 1-18) for the run of February 2016. In October 2016, the configuration was identical to February 2016, exception made of the neutral fragments detector replaced by a CCD camera and the corresponding EPI detector put in the PA rail in place of detector of negative species (due to the very low counting rate imposed by the CCD camera, negative species could not be detected, their abundance is about 1000 times lower than cations).

In Table 1.6 is presented the detector configuration installed in March 2015 for studies with incident `and 2 `beams. The detectors for anions were both placed on the rail 1(PA) but at different distances: respectively ( L 2 `) = 1027 mm for " ´" detector and ( L 2 `q " 1081 mm for the " ´" detector. In Figure 1-17 is shown the photography of this configuration. The configuration of February 2016 is presented in Table 1.7 and a photography presented in Figure 1-18. On this figure the "finger" is clearly visible in front of the " `" detector.

In order to separate 3 ``from `{ 2 we made a separate run in which we displaced by 35 mm all detectors so that these fragments were incident on the neutral detector. Now dividing the voltage by 2 we could have in the neutral detector, `ànd `{ `, then resolving these two species as well. fragments' energy (mass) with the best accuracy and a current signal pq used for shape analysis studies. The current signal is of poor quality for commercial detectors, but of very good quality for EPI Neutral detector equipped with a pre-amplifier PACI manufactured at IPNO. With PACI, the current amplifier preserves the shape of the signal allowing shape analysis studies to be conducted.

Electronics and acquisition

• 3 I(CN + ) • 5 I(C + /N + ) • Numériseur 2 • Q(CN 0 ) 4 • Q(CN + ) 6 • Q(C + /N + )
From

Acquisition

The way the acquisition works is illustrated in Figure 1-20.

Three workstations control the data acquisition : IPNLINTDM6, AZ4PI and PC AGAT. They are running on Debian OS and we use NARVAL interface on all the three systems. NARVAL (Nouvelle Acquisition temps-Réel Version Avec Linux) is a software developed by [START_REF] Grave | Narval a modular distributed data acquisition system with ada 95 and rtai[END_REF], containing the experiment parameters.

It acts as a conductor: it sends directions to modules called 'actors'. It oversees the acquisition, it routes the data in real time so that we can monitor the progress of the experiment. 'Actors' can be producers, intermediaries or consumers. Producers, as their name implies, produce the data. Intermediaries distribute these data to consumers. As for the consumers, they process the data.

We interact directly with two computers IPNLINTDM6 and PC AGAT. It is from these computers that we start, stop and order the acquisition. The acquisition is first started at the camera via PC AGAT. The camera must be initialized and cooled down to ´55 ˝C before it can start recording. Once the camera is ready, the acquisition is Narval is transferred to the acquiris transmitter.

The camera transmitter generates the images from the camera. For this, it captures the image and the timestamps, that is to say, it delimits the size of the event that will include: the acqiris data, the image and the time. The event builder collects primary role is to compare the two times, to be sure that the data of the detectors and the camera come from the same event. The event builder will then concatenate the two events that match and sent them to the three consumers that are:

• The data receiver that receives the stream of images sent by the camera and then displays the images in a window of SDL (Simple Direct media Layer) control.

We can see in real time the images recorded by the camera.

• CVISU that receives the data flow from the acquiris transmitter and then generates the desired spectra. This 'actor' allows us to visualize during the experiment in real time the detector spectra (see .

• The disk receiver that writes the data concatenated by the event builder on a hard disk. These are the raw data that will be analysed later.

If the detection of the neutral fragments is done with the EPI detector and not with the camera, then the operation of the acquisition is simplified. The camera transmitter and acqiris transmitter are not in operation.

Chapter 2

Data analysis

Data formatting and data treatment

The data collected from our experiments are of two types depending on whether or not the camera was used to detect neutral fragments. If the camera has not been used, then each event constitutes a word formed by the values of the sixteen Camac ADC followed by the eight traces of current signals digitized by the acqiris scanner.

If the camera was used, then a table of 512 ˆ512 (number of pixels) is added to the previous word. The data will then be reduced (formatted) to a multidimensional matrix called NDB by a code written by IPNO engineers. NDB files are especially arranged as to be easily treated by a data visualization software DP2 developed by L.Tassan-Got and JF.Rabasse from IPNO. In the same code it is possible to make a basic treatment of the digitized current signals. samples on points, this filter is written as:

av pq " 1 `1 n{2 ÿ i"´n{2 p `q (2.1)
The running average returns to convolute the signal pq by a square function:

av " 1 `1 b n (2.2) n pq " $ ' & ' % 1, || ă n 2 0, || ą n 2 (2.3)
But the Fourier transform of the product of convolution of two functions corresponds to the product of the Fourier transforms of these functions. Consequently, the application of this linear filter amounts to multiplying the Fourier transform of the signal by the Fourier transform of the square function, that is to say by the cardinal sinus function pq " sinpxq x . This linear smoothing of the signal therefore modulates its frequency spectrum by the function. The higher the number of bridges chosen for running average, the lower the filter cutoff frequency. But the noise frequencies are rather in the high-end spectrum. Therefore, is chosen judiciously to reduce the noise without deteriorating the frequencies containing the information on the signal.

In the Figure 2 of the signal (for the shape analysis method) and the time of the signal (time at which it reaches a given % of its amplitude) that we used for noise removing in the case of a very noisy detector.

The DP2 software

DP2 is a 2D visualization and analysis software for multi-dimensional data, and for making grids and contours over the displayed data. The raw data is first treated as outlined before and made into a readable format called NDB compatible with DP2. NDB is a tree structure data format which is useful in working with large dataset and many parameters. The list of parameters that DP2 can treat is made of ADC values for each detector, amplitude, integral and time at which signal rises for each numerical current signal. Most of the information is extracted from ADC that provide the information energy (mass) of the fragments. Prior to looking at coincidences between ADC, an essential work consists in calibrating precisely all ADC.

DP2 allows to extract monodim (1-dimension) spectra from ADC. Figure 23shows the ADC spectrum of the " `" detector during a 3 `` run. As seen in Figure 2-3, the " `" detector could detect `, `, ``and any combination of those.The curly brackets on t ``u means that the molecule can be intact ( ``) or broken ( `{ `). Using the absolute calibration between channel and energy performed before the runs with the tri-alpha source, it is easy to correlate the channel number of ADC from detector " `" with the fragment's mass (see result of calibration on Figure 2-4 andin Table 2.1). The calibration curve is given below. DP2 allows to visualize coincidences between two ADC (2D spectrum). Figure 2-5

shows such a 2D spectrum between ADC from neutral detector and ADC from "

`"

detector. The data used here is from 3 `` collisions. This 2D representation gives the coincidence between the two detectors such that each point on this 2D plane represents an event in which a fragment was detected on the neutral fragment detector and another fragment on the " `" detector. Using calibrations made for each detector it is easy to identify each spot of the Figure 2-5. The notation with curly brackets (for example t 2 u, t u, t 3 u or t 2 u) means that the species may be intact or fragmented. This convention will hold in the whole manuscript.

The resolution of the fragmentation for these species is discussed in section 2.5 and section 2.6. The encirclements are what we call 'grids' in DP2. It defines an area on the 2D plane. DP2 is able to do a 'contour integration', which essentially gives the total number of points inside the contour.

In the Figure 2-5 we encircled with contours complete events (a complete event is having the same mass as the incident 3 `projectile). DP2 could also look for coincidences with 3 or more detectors. In the Figure 2-5, there are many peaks that are incomplete in mass, because a third (or fourth) fragment was detected on another detector. For example for the `{ `{ spot, since we work with incident 3 `, the missing fragment should be ´, ``or ```. DP2 allows to select one of this fragment (selection of the corresponding ADC range, see the list of parameters with their range on the right vertical column of Figure 2345) and the displayed 2D spectrum will now be coincident with this selection. Alternatively it is possible to events. From the `run we could rapidly suspect `not to be fully detected as incomplete events with q`p " 0 ´3q were detected (with a rate of 15% up to 50% depending on ) whereas no incomplete events with q`a lone p " 0 ´3q were measured. Such a result could be explained if the " `" detector was badly positioned towards lower { value. We made a simulation of the fragmentation with a Fortran code for `{ q`f ragmentation channels p " 1 ´3q. The fragmentation energy was assumed to arise from the coulomb explosion. We took a Gaussian energy distribution centered on the coulomb point charge formula c (see Equation 2.4) with "1.17 Å in ` [START_REF] Peterson | Accurate multireference configuration interaction calculations on the lowest 1 ř `and 3 ś electronic states of C 2 , CN `, BN, and BO[END_REF] and standard deviation taken from Table 2.2:

c " 14.41 (2.4) and 1 are in atomic units (au), c is in eV and is in Å.

Channel c (eV) (eV) p `qC `{N q`for " `" detector's Experimental loss rate shift "´2 mm p `qC `{N q `{ `12.3

6.2 0.25 0.34(30%)

`{ ``24.6 8.1 0.33 0.45(20%)

`{ ```3 6.9 9.4 0.37 0.49(30%)

Table 2.2: Comparison between simulated and measured loss rates of `in `{ qf ragmentation channels Equation 2.4 was found to be valid in similar experiments [START_REF] Sampoll | Dissociation of multicharged CO molecular ions produced in collisions with 97-MeV Ar 14`: Total-kinetic-energy distributions[END_REF][START_REF] Caraby | Ionisation et dissociation de la molecule de monoxyde de carbone par impact d'ion lourd rapide multicharge[END_REF][START_REF] Béroff | Fragmentation of multiply charged hydrocarbon molecules C n H q`( ď 4, ď 9) produced in high-velocity collisions: Branching ratios and kinetic energy release of the H `fragment[END_REF]. Standard deviations were taken by assuming their ratio to the centroid value to be equal to measured values in similar systems ( molecule ionized by highly energetic charged ion [START_REF] Caraby | Ionisation et dissociation de la molecule de monoxyde de carbone par impact d'ion lourd rapide multicharge[END_REF]. We defined the loss rate of `in the `{ q`f ragmentation as:

p `qC `{N q`" qà lone qà lone ``{ q`( 2.5)
As seen in Table 2.2 simulated p `q are close from measured ones if assuming a shift of the `detector "´2 mm. In this direction, `detection is not affected and the loss of `fragment was found null as in the experiment. This value "´2 mm was also found in agreement with the examination of the positioning: the detector was not centered on the support by ´2 mm. Note that a very small loss of events is also arising from the fact that the " `" detector (14 mm ˆ14 mm) is a bit too small. In During the analysis of negative species produced in 3 `` data, we found that the mass spectrum (1D ADC spectrum) of " ´" detector was full of noise, as demonstrated in the Figure 23456789. With this noise we could not see any of the expected 3 , 2 ´and 3 ´fragments. We then decided to make a time selection for the signal issued from the " ´" detector. For that we followed the procedure described in section 2.1 i.e., background subtraction, filtering and search of time at which the current signal rises (defined as CN ´). This time selection allowed to keep only signals above a physical threshold i.e. eliminating all background. We show in the Figure 2-10 the mass spectrum when CN ´is selected around its physical value.

Coincident spectra exhibit the same effect. In We found that the shapes of and 2 , as well as and were identical with our detector (see . Then since the energy (mass) of the sum is the same (2{ has the same mass as {) we could not separate the two channels by the shape analysis method. This was the case for a number of channels (for instance 2 over 7 for t 3 u, 2 over 13 for t 3 `u). For that reason, we used a CCD camera whose treatment is presented below.

The CCD treatment

The treatment of data from the CCD camera has been performed by Tijani IdBarkach is obtained by summing the charges delivered by the pixels belonging to the same impact (typically 20 pixels per impact). As seen in Figure 2-17 , the mass resolution of the camera is not as good as the mass resolution of commercial detectors (see for instance Figure 2-3 for the " `" detector). In Figure 2-17, the cut at which a mass separation will be performed is around channel 3400 with some errors (˘150). This will introduce error on the countings and on dissociation BRs. Another source of error is to determine whether two impacts originate from an intact impinging molecule or from a fragmented system. Due to the two carbon foils placed before the camera, all molecules are vaporized into atoms. In Figure 2-18 we show the distribution of distances between two impacts recorded during 2 `´ runs. The very small distances (less than 30{40 pixels, one pixel is 24 µm large) are due to intact 2 whereas the distribution of larger distances originate from 2 fragments, as predicted by simulation of the explosion. Still, the exact limit at which to separate between intact and fragmented species is around 35 pixels, with some error p˘5q, that will introduce another error on counting and branching ratios. On the whole, except some channels for which the camera is the only way of resolving the fragmentation, it was possible to compare the CCD results with the shape analysis method for a number of channels. As seen in Table 2.3 (case of t 2 u), the agreement is pretty good. Let inc be the number of incident particles in a run, process the number of events associated to a given process. The probability for the process process to happen is given by process " process inc (2.6) Recall that we use a 'finger' to stop the incident beam during counting runs. This effectively left us handicapped in directly measuring the incident particles without which all of the physical quantities couldn't be found out. We use a method called 'Normalisation' to find the incident number of particles. For this, we perform, for each flow rate, 'Normalisation runs' with the finger removed. The incident beam intensity is lowered to about 150 events/sec which is about 100/200 times less than during the counting runs The data is collected and analyzed as usual. The idea is to find a conserved quantity in the experiment of which one of the factor is inc . The conserved quantity used here is the probability of a significant channel. Significant channel here refers to a channel with high statistics in order to minimize the experimental error.

Let SN be the probability of a significant channel in 'normalisation run' and S is its counterpart in a counting run. Now, since both the experiments were conducted with the same parameters, these two probabilities must be equal. (2.9)

All the quantities in the right side is known and thus the incident particles.

Background subtraction

As mentioned in chapter 1, we do two distinct experimental runs for each flow rate apart from the normalisation run. One with the beam passing directly through the jet, one with the beam travelling unhindered by the jet, jet being introduced in a lateral direction inside the collision chamber. Probabilities are calculated 'with jet'

p jet q and 'without jet' p back q. The probability of a process due to the jet only (i.e background subtracted) is then:

" jet ´back (2.10)

Dissociation branching ratios (BRs)

For a process say, single capture, the molecule after collision may or may not be fragmented. Consider single capture,

2 `` Ñ t 2 u t 2 u could be {{ , 2 { , { , 2
Branching ratio pq for a given channel is defined as Thanks to the jet-beam overlap profile that is measured during the experiment, we will be able to extract the cross sections associated with each process. A detailed description of the method is given in [START_REF] Wohrer | A method for "on-line" determination of beam-jet overlaps; application to cluster fragmentation studies[END_REF]. A brief description is as follows. In the single collision condition the cross section pq of a given process is given as:

channel " channel t C 2 N u (2.
" jet ´back jet (2.12)
Where, jet is the 'beam-jet overlap' (expressed in units of cm ´2) expressed as:

jet " ż ż ż p, , q 0 p, , q (2.13) p, , q is the flux of incident projectiles, 0 is the total number of incident particles per second and p, , q the density of the jet. Following [START_REF] Wohrer | A method for "on-line" determination of beam-jet overlaps; application to cluster fragmentation studies[END_REF], jet can be written as:

jet " exp λ th (2.14)
λ is a factor close from 1 depending of the flow regime of the gas in the capillary, th is the thermal velocity of the helium gas in this jet for room temperature, dN dt is the flow rate of atoms and exp is given by Equation 2.15. exp " p 0 q ş pq (2.15) p 0 q is the probability measured at the beam position 0 and ş pq is the integral of the jet profile extracted using a Gaussian fit, see Figure 2-20. We give in Table 2.4

the values of jet we derived in the runs and that were used for extracting absolute cross sections. As the dimension of the jet is typically 1 mm we see that the density of the jet at the beam crossing is, for 3 ˆ10 13 at{cm 2 , of the order of 10 ´2 Torr.

Beam

The special case of anions

From the dependence of anion production probabilities with jet , we could conclude that this production is partly related to double collisions. Indeed, unless Equation 2.12 predicts, we found that the anion production probability is quadratic with jet as illustrated for instance in Figure 2-21 for ´{ { { `. Anions are produced through the following processes.

1 Double electron capture (DEC) in a single collision

n `` Ñ t n ´u ` `2
Ion-pair relaxation (IPR) of excited t n q`u species, for example following single electron capture (SEC, Q=0) (single collision process): 3 Single electron capture onto neutral fragment (SECN) in a second collision following a first excitation process, for example dissociative excitation (double collision process),

n `` Ñ t n u `
n `Ñ { `{ { in the first collision, ` Ñ ´` `in the second collision.
The probability of anionic production t n ´uwrites:

" DEC jet `SEC SECN 2 jet 2 (2.16)
The first term in the Equation 2.16 corresponds to single collision process whereas the second one is associated with double collisions in the jet. In order to reduce the quadratic dependence of with jet in the equation to a linear one, normalized probabilities N are introduced defined as

N " SU M (2.17)
Where SU M refers to the sum of probabilities of 'large' processes (Single ionization, excitation etc.) which are directly proportional to jet . For runs with incident 3 ẁe choose SU M to be equal to the complete channels of Figure 2-5 that are linear with jet (see . We have, for the associated cross section, SU M " SU M jet (2.18) and then:

N " DEC SU M `SEC SECN SU M jet 2 (2.19)
The above formula render itself to extract,from the jet dependence of N , σ DEC σ SU M (ordinate of the origin) and σ DEC σ SECN σ SU M (slope of the curve) quantities as seen in (1997) and more recently in the 2 and 2 dimers by [START_REF] Kim | Orientation dependence in multiple ionization of He 2 and Ne 2 induced by fast, highly charged ions: Probing the impact-parameterdependent ionization probability in 11.37-MeV/u S 14`c ollisions with He and Ne[END_REF]. On the other hand the ability of this simple model to predict absolute cross sections is another interesting topic. In a recent work [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF] probabilities were introduced in the IAE model without any adjustment and IAE predictions for various electronic processes (single and multiple ionization and electron capture) occurring in ǹ -, collisions ( " 1-5, "2.25 ua) compared to the experiment. The IAE model is tested here for n"1,3 `-collisions at the same "2.25 a u velocity.

Description of the IAE model

The dynamics of the molecule-atom collision is described in the framework of the impact parameter approximation [START_REF] Bransden | Charge Exchange and the Theory of Ion-Atom Collisions[END_REF] in which the projectile, whose centre of mass is characterized by the impact parameter b with respect to the target, follows rectilinear trajectories with constant velocity v (see Figure 3-1).

The IAE model assumes the following : • The electrons in each atom are treated independently following the so-called Independent Particle Model (IPM) [START_REF] Mcguire | Independent electron approximation for atomic scattering by heavy particles[END_REF] and [START_REF] Lüdde | Comment on inclusive cross sections[END_REF] widely used in collisions physics.

The atoms are positioned at the proper molecule geometry and do not move during the fast p" 10 ´16 q collision. For instance to the page [START_REF] Wohrer | Swift cluster-atom collisions: experiment and model calculations[END_REF]. In the independent atom approximation the IAE probabilities consist of products of atomic probabilities. For instance the He-induced neutralization probability N eutr of a n `molecule ( n `Ñ t n u molecule) is expressed as:

N eutr pbq " n ÿ i p1q Capt p i q ˆn ź i"1 p1 ´ion p i qq ź j‰i p1 ´Capt p j qq `« n ÿ i"1 p2q Capt p i q `n ÿ i"1 ÿ jąi 2 p1q Capt p i q p1q Capt p j q ff ˆ« n ÿ i"1 p1q ion p i q ź j‰i p1 ´ion p j qq ff (3.1)
where i stands for the impact parameter of the -th centre with respect to the target, p1q

Capt p i q, p2q Capt p i q and Capt p i q stand for the probabilities of single-electron, doubleelectron and total electron capture on centre , and p1q ion p i q, ion p i q stand for the projectile single ionization and total ionization for centre p, `or q. The first term of Equation 3.1 represents the dominant contribution to the neutralization probability, which is from single-electron capture without projectile ionization (described in the p1 ´ion q terms). The second term, amounting to a few per cent at most, corresponds to double-electron capture concomitant with projectile single ionization.

The atomic probabilities of processes occurring in -, `-and -collisions are computed assuming independence of the electrons. Furthermore, only valence electrons of the projectile and{or the target are assumed to be active within the dynamics. The probabilities entering Equation 3.1 can thus be written as:

p1q capt p i q " 2 c p i qp1 ´c p i qq (3.2) p2q capt p i q " c p i q 2 (3.3) `1 ´capt p i q ˘" p1 ´c p i qq 2 (3.4)

Cross sections calculations

Suppose we want to calculate the cross section whose expression is given in figure 3.2 b). To calculate the cross section we generate , , :

• is generated with a uniform probability pq " 1 2π

• is generated with a probability pq " pq

• b is generated with a probability pq " 2b b 2 max
Where max is the maximum value of b that we generate in the code; the value of max is set when results are independent of its value (convergence of the results).

Suppose we are interested in the cross section pmq for removing m electrons from the projectile. The cross section is calculated as :

pmq " 2 max ř bďbmax ř θď π 2 ř αď2π pmq b,θ,α try (3.7)
Where pmq pb,θ,αq is equal to 1 if m electrons have been ionized during the try p, , q and 0 otherwise. At each event (collision) we draw for each electron a random number r p0 ď ď 1q. For the electrons of the projectile the random number is compared to the probability of ionization i p i q and the probability of excitation exc p i q ( i is the impact parameter for the atom to which the electron belongs). These probabilities for the , `, , `-collision systems have been calculated using the Classical Trajectory Monte Carlo (CTMC) method (see next section). If ď i p i q the electron is ionized, if i p i q ă ď i p i q `exc p i q it is excited ; if ą p i p i q `exc p i q) it remains on its initial atomic (ionic) shell. The same is done for the electrons of the target where the random is compared to target ionization and electron capture probabilities. All electrons of all atoms are so tested and a final result of the collision is registered. This number will be divided by the number of tries (collisions), typically equal to 10 6 events, and multiplied by the geometrical cross section 2 max following Equation 3.7.

Energy deposit by electronic excitation calculation

The probability of exciting an electron is calculated as explained above. When the collision is finished, excitation is obtained if one or more electrons have been excited whereas no projectile ionization nor electron capture has taken place. As will be seen in the next section, excitation into specific p, q final states are calculated with the CTMC method. By relating these final states to the corresponding excited energy , it is possible to derive differential in energy dpexc dE probabilities. The differential in energy excitation cross section is then obtained as (case of the linear molecule):

" ż ż ż exc p, , q (3.8) and calculated as explained before. The variation with E of dσ dE provides the energy deposit distribution that we will present in chapter 5.

Atom(ion)-atom collisions : Classical Trajectory

Monte Carlo (CTMC) calculations

The CTMC approach

A complete quantum mechanical calculation of the probabilities and cross sections of the various processes involved in collision is impractical because of the immense computational resources that it demands. It is also the case in semi-classical calculations where the size of the basis required to describe all elastic and inelastic channels often renders the method impractical. This is where a purely classical description of the process is called for in the case of ion-atom collisions. CTMC (Classical Trajectory Monte Carlo method) is the most widely used method which treats the ion-atom collision as purely classical. This was developed by [START_REF] Abrines | Classical theory of charge transfer and ionization of hydrogen atoms by protons[END_REF] and later used successfully by [START_REF] Olson | Charge-transfer and impact-ionization cross sections for fully and partially stripped positive ions colliding with atomic hydrogen[END_REF] to calculate the ionization and capture cross sections for positive ions colliding with atom at intermediate energies.

Many authors have since then used the CTMC method and recent developments have concerned the application of CTMC to ion-molecule collisions [START_REF] Illescas | Classical treatment of ion-H 2 O collisions with a three-center model potential[END_REF] or the switching method between 4-body and 3-body collisions for the treatment of two active electrons [START_REF] Jorge | Switching classical trajectory monte carlo method to describe two-active-electron collisions[END_REF].

Before moving on to the description, the validity of such a deviation from a physically 'accurate' (i.e, quantum-mechanical) method needed to be addressed. CTMC considers the interacting particles as classical objects in the sense that they obey classical laws of motion. Typical processes not classical are tunneling (ionization at low and high impact velocities) and interference effects (for instance for electron capture at small impact velocities). It then results that the velocity range where CTMC is valid is typically [1 a.u -4 a.u] for electron capture and [1 a.u -6 a.u] for ionization (Illescas, private communication). This is near the assumption of Bransden and Mc-Dowell (1992), which is 1 ď vp ve ď 4, where p is the velocity of the projectile and e is the velocity of the target electron. In our case p "2.2 au and e " 1.7 au (active electron of helium). The method is outlined below.

Dynamics

The collision is treated within the impact parameter approximation (see Figure 3-3), valid at these energies [START_REF] Palacios | Theoretical treatment of inelastic processes in atomic collisions involving one and many electron systems[END_REF]. In a purely classical framework, one introduces a phase-space distribution pr, p, q which satisfies the Liouville equation:

B B " ´ , e ( " ´B Br B e Bp `B Bp B e Br (3.9)
, e ( is the Poisson's bracket with e is the electronic Hamiltonian function.

To describe and solve the problem of an atom and an electron, a statistical collective of " 10 6 non-interacting electrons is defined for each nuclear trajectory:

pr, p, q " 1 N ÿ j"1

Initial conditions

Different classical initial distributions have been proposed through the years (Jorge Palacios, 2017). In the microcanonical distribution all electrons are having the same energy corresponding to the ionization potential i of the active electron we want to describe [START_REF] Reinhold | Classical ionization and charge-transfer cross sections for H ``He and H ``Li `collisions with consideration of model interactions[END_REF]:

M pr, pq " p i ´2 2
´ pqq (3.11) where is the delta function, is the normalisation constant and p 2 2m ´ pq is the Hamiltonian of the isolated atom. It can be shown [START_REF] Reinhold | Classical ionization and charge-transfer cross sections for H ``He and H ``Li `collisions with consideration of model interactions[END_REF]) that is confined between 0 and 0 where 0 satisfies: i " p 0 q (3.12)

In order to generate an initial condition for the active electron, two transformations must be performed [START_REF] Reinhold | Classical ionization and charge-transfer cross sections for H ``He and H ``Li `collisions with consideration of model interactions[END_REF]):

• Transforming Cartesian pr, pq Ñ p, , r , p , r , p q

The Cartesian coordinates of position-momentum phase space is related to the new coordinates as:

" p1 ´2 r q 1 2 r " p1 ´2 r q 1 2 r " r x " r2p ´ pqqs 1 2 p1 ´2 p q 1 2 p y " r2p ´ pqqs 1 2 p1 ´2 p q 1 2 p z " r2p ´ pqqs 1 2
The intervals of the variables are given by: " i ; P r0, 0 s; r , p P r´1, 1s; r , p P r0, 2s

• a second transformation is performed introducing by:

pq " ş r 0 1 2 p2r i ´ p 1 qsq 1 2 1
The variables are selected at random from the intervals: P r0, p 0 qs, r , p P r0, 2s, r , p P r´1, 1s

A good initial distribution must reproduce as well as possible the quantum radial and momentum densities. The microcanonical distribution is known not to reproduce well the radial density as illustrated for instance in Figure 34. This behaviour (sharp boundary at the classical turning point) will induce limitations to a good description of processes in the low and medium velocity range [START_REF] Palacios | Theoretical treatment of inelastic processes in atomic collisions involving one and many electron systems[END_REF] and [START_REF] Jorge | Calculation of ionization and total and partial charge exchange cross sections for collisions of C 6 and N 7 with H[END_REF] where dynamical processes involve electrons located at the tail of the For the `-(or `-) collision:

1e

´" 2 2 ` He ``e mod p t q ` C ``e mod p p q (3.14) mod are the model potentials describing the interaction of the active electron with frozen projectile and/or target cores. They are built as explained in section 3.2.1.5.

Because, ´is not stable [START_REF] Hotop | Binding energies in atomic negative ions: II[END_REF], , the final collision processes are selected by applying the well known energy criteria.

1
The final energies of the electron will associate each electron trajectory to a different process. Electrons with positive energies with respect to the target p T ą 0q and projectile p P ą 0q will imply ionization, and the bound states will be differentiated as electron capture ( P ă 0 and T ą 0) and elastic/excitation ( P ą 0 and T ă 0)

processes. Once this energy criteria has been applied, the probability corresponding to a process (ionization, capture or excitation in the 1 electron scheme) will be obtained simply dividing the number of trajectories giving rise to this process, i , by the total number of considered trajectories, .

i p, q " i (3.16)

For a given collision velocity , the integration of the opacity function i p, q over all impact parameters will lead to the associated total cross section:

i " 2

ż 8 0 i p, q (3
.17)

Two electron calculations

Here, one electron each of the projectile and the target take part in the collision.

For `-collision, the Hamiltonian writes:

2e ´" 2 1 2 ` pHe ``eq mod p 1T q ` pX 2``e q mod p 1P q (3.18) `2 2 2 ` pHe ``eq mod p 2T q ` pX 2``e q mod p 2P q `1 |r 1T ´r2T |
and for -:

2e ´" 2 1 2 ` pHe ``eq mod p 1T q ` pX ``eq mod p 1P q (3.19) `2 2 2 ` pHe ``eq mod p 2T q ` pX ``eq mod p 2P q `1 |r 1T ´r2T |
In the case of two active electrons, the initial distribution pr 1 , r 2 , p 1 , p 2 , Ñ ´8q consists of the product of microcanonical sets He pr 1 , p 1 q X `,X pr 2 , p 2 q of dimension " He X `,X [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF]. Integration of the Hamilton equations is Indeed in the case of electron capture, there is in the final state 2 electrons on the same atom, which is classically unstable. A recent switching method was proposed by [START_REF] Jorge | Switching classical trajectory monte carlo method to describe two-active-electron collisions[END_REF] to solve this problem, but it was not applied in the present work.

With two active electrons, we can distinguish between an exclusive process where the state of the two electrons is known from an inclusive process where the state of only one electron is defined (i.e consisting of a sum of at least two exclusive processes).

The model potentials

When the active electron is located in the He target, the model potential to describe the interaction of the valence electron with He `ionic core, is of the form:

mod p `` ´q " ´ ´ ´1 ` ´2αr (3.20)
where , and are the atomic number, number of electrons in the frozen core and radial distance from the center of the atom to the active electron and is set to its variational value, " 1.6875.

For the projectiles, the mod is of the form, mod pq "

´

´

´ ´Br `p ´q p´Crq (3.21)

, and are the parameters of the model potential. These parameters are optimised so as diagonalization of the 1 ´Hamiltonian " ´1 2 ∇ 2 `mod pq yields bound eigenenergies in close agreement with those tabulated at NIST. This is illustrated in Tables 3.1 and 3.2 for the cases of and `respectively. Furthermore, the consistency of the mod description can be checked by comparing the radial densities of the fundamental states to those which are issued from conventional Hartree-Foctk calculations. This consistency is illustrated in Figure 3.5 for the prototypical and `cases. Finally, the A, B and C parameters associated to all atoms and ions considered in the present work are listed in

CTMC probabilities results

In the following we will discuss some specific points, illustrated with some probabilities results. On the other hand, the whole set of CTMC probabilities used in the IAE simulation is presented in Appendix A. While the number of electron trajectories can be easily enlarged in 1 ´-CTMC calculation where only 6 Hamilton equations, associated to the active electron, are integrated, the number of trajectories in 2 ´-CTMC calculations has to be further controlled because of the inherent 12 coupled underlying Hamilton equations.

In Figure 3-6 we report impact parameter probabilities for various processes obtained in such 2 ´calculations for `p2q -system as a function of the number of trajectories employed in the computations. We choose to look at exclusive processes of low probabilities. The statistics are too low, as is evident, for 100x100 trajectories and 500x500 trajectories. To be sure of the convergence with 1000x1000 trajectories, we compared it with 1500x1500 trajectories and the convergence was satisfactory. We worked with 1000x1000 trajectories for all the results presented hereafter.

Overview of process probabilities (1 ´calculations)

Being in the intermediate velocity regime ( p " e ) we anticipate that all electronic processes will have similar importance. Indeed we find (see Appendix A) that (target and projectile) ionization is very large but not far are projectile excitation (especially 2s excitation) and electron capture. The only exception is attachment on neutral atom () which is very small. Note that pq of Appendix A are given per electron.

This will favor of course projectile ionization and projectile excitation over the other processes in the atom, and even more, in the molecule.

Comparison between 1 ´and 2 ´calculations (target ionization and excitation)

It is important to check the consistency of 1 ´and 2 ´CTMC calculations when both of them are able to yield probabilities for the same process. As a first example we present in Figure 3.7 a comparison between 1 ´and 2 ´CTMC calculations for target ionization in p2pq- † collision. We see that the inclusive ionization probability predicted by the 2 ´calculation is very close from the 1 ´calculation.

The situation is a little bit different in the `-collision (see Figure 3.8). In the case of `´ collision, inclusive target ionization differs between 1 ´and 2 †Note that results with p2q are found identical to those with p2q for inclusive target ionization whereas exclusive components differ (in particular target ionization + projectile excitation is larger with p2q and target ionization alone accordingly smaller). calculations but target electron loss (target ionization + electron capture) are close (see Figure 3.8). The difference can be attributed to the smaller electron capture in 2 ´model as compared to 1 ´model. The underlying reason for this difference is the fact that the 2 ´-captured electron makes the system unstable due to the increased repulsive potential from the other electron. In any case, capture is not expected to be well calculated in 2 ´calculation so that we always used only 1 ´calculation in our simulations for target ionization, electron capture and attachment. For target excitation a similar behaviour to target ionization was observed between 1 ´and 2 ćalculations.

But target excitation was not introduced in our simulations.

Comparison between 1 ´and 2 ´calculations (projectile ionization and excitation)

For projectile ionization and excitation 1 ´calculation requires to introduce a potential between an electron and the He atom. We discuss it below. Before finding this potential, we performed 2 ´calculations. In simulations both 1 ´and 2 ´calculations were used and compared.

The electron-He model potential for 1 ´calculations

A parametrized form of target potential for neutral ´´s ystem exists on experimental and theoretical grounds [START_REF] Valiron | Model-potential methods for the calculation of atom-rare-gas interaction: application to the h-he system[END_REF]. We present 3 potentials extracted from that paper in Figure 3-9 V1(red), V2(black) and V1 with null dipole polarizability (blue). On comparing the force experienced by the electron of which the magnitude is given by the first derivative of the potential, we find a stark difference between 1 and 2, (see inset in Figure 3456789). In the latter case, there is a big bump in the force experienced by the electron in the range of distance P p0.75, 1.25qau. This is the result of the localized attractive well in 2. We chose to work with 1 potential where the dipole polarizability is not neglected p ‰ 0q, this potential giving results in good agreement with the experiment (see discussion of Figure 1 in [START_REF] Valiron | Model-potential methods for the calculation of atom-rare-gas interaction: application to the h-he system[END_REF]). 1 ´CTMC calculations, using Hamiltonians similar to that of Equation 3.15, allowed us to obtain projectile ionization and excitation of p2, 2q, `p2, 2q, p2, 2q and `p2, 2q. Capture to helium has been found to be zero as expected since formation of ´is unlikely compared to competing (ionization and excitation) processes. ones (correlated to the higher binding energy) it is seen that the ionization probability from the same shell is higher in 1 ´calculations. Figure 3-11 presents the projectile excitation probabilities calculated with 1 ´CTMC using 1p ‰ 0q and compared to the 2 ´CTMC calculations for the same system. The excitation probability from the same shell is lower in 1 ´calculations. This observation is in direct opposition to what had been observed in the ionization probabilities and was observed for all projectiles (see Appendix A). We will present and discuss both 1 ´and 2 ´calculations results when comparing to experiments (Table 3.5 and Table 3.6 and in chapter 4). We already note that discrepancies are bigger for small impact parameter ď 1 a.u such that these discrepancies will be somewhat washed out at the level of cross sections involving the opacity functions pq. Concerning and , the classical-quantum correspondence is more involved, and the partition of the continuous classical phase-space must be considered.

3.2.2.5.1

The classical p, q to quantum p, q correspondence

In the CTMC calculation, the final energy E of the electron and its kinetic momentum L is known. In case the electron is bound (Eă 0) a classical quantum number c is calculated by the hydrogenic formula:

c " c ´p ´ q 2 2 (3.22)
Where p ´ q is the effective charge felt by the active electron (Z atomic number, N number of frozen electrons). A quantum counterpart to the classical c is quant "

d ´p ´ q 2 2 quant (3.23)
where quant is the energy of the quantized p, q subshell. If we want to keep the fact that the quantum volume occupied by a p, q electron is proportional to p2 `1q we must consider a domain for c in terms of adjacent r min c , max c s intervals, such that for valence and unoccupied subshells. However it is clear that there is a satisfying quantum-classical correspondence which can be used to derive p, q-selective cross sections, using a procedure similar to Equation 3.16. When calculating projectile 2s excitation we were faced with the fact that the 2s 2p being adjacent, very large cross sections were obtained. This results from the fact that any small perturbation, induced for instance as the He target lies at infinity from the `p2q projectile, is classically sufficient to pass from the 2s bin to the 2p one. This is quantum mechanically prohibited since quantum trajectories are entangled, unlike the classical ones so that the whole set of 2s quantum trajectories remain in the 2s bin. To tackle this problem we checked, by comparing to quantum calculations (Errea As seen on this figure a reasonable agreement between classical and quantum results is obtained when the classical bin for 2p is reduced from r " 1, " 2s to r " 1.2, " 2s.

All projectile excitation probabilities were then extracted with this latter condition.

3.2.2.5.3 CTMC predictions for p, q cross sections Thanks to the classical to quantum correspondence projectile excitation into final pq states could be calculated. This was done up to " 6 and for ě 7 and the results are shown in Appendix A (for probabilities into final states summed over ).

The p, q distributions are used in the energy deposit calculation that we present in chapter 5. It is noticeable that the distributions show the importance of non dipolar transitions (∆ " 0, 2) in these medium velocity collisions.

Projectile excitation probabilities do decrease rapidly with n, especially for 2s excitation. Table 3.4 gives, for 1 ´calculation p 1, ‰ 0q, the percentage of excitation ( ş pq) into the n final state for 2 and 2 excitation in ´ collision p "2.25 auq. The distribution of final states is found little dependent on n. For p2q excitation, the percentages into levels are typically 7% for " 0, 60% for " 1 and 33% for " 2 p1 ´calculation 1, ‰ 0q, emphasizing non-dipolar (short-range) behaviour.

Process

System Formula calc Experiment Single Capture N+-He 2 c p1 ´c q 7.99 10 ´17 N+ Ñ N N+-He 2 c p1 ´c qp1 ´2s ion q 2 p1 ´2p ion q 2 5.24 10 ´17 3.74 10 ´17 p60%q Single Capture C+-He 2 c p1 ´c q 7.72 10 ´17 C+ Ñ C C+-He 2 c p1 ´c qp1 ´2s ion q 2 p1 ´2p ion q 5.4 10 ´17 C -He 2 c p1 ´c q 0.41 10 ´17 C ÑC-C -He 2 c p1 ´c qp1 ´2s ion q 2 p1 ´2p ion q 2 0.2 10 ´17 0.55 10 ´17 p30%q C+ Ñ C-C+-He p cc q 2 p1 ´2s ion q 2 p1 ´2p ion q 4.79 10 ´18 8.0 ´20 p40%q 4.38 10 ´17 3.74 ´17 p60%q C+ÑC C+-He 2 c p1 ´c qp1 ´2s ion q 2 p1 ´2p ion q 4.73 10 ´17 3.5 10 ´17 p30%q CÑC-C-He 2 c p1 ´c qp1 ´2s ion q 2 p1 ´2p ion q 2 0.17 10 ´17 0.55 10 ´17 p40%q C+ÑC-C+-He p cc q 2 p1 ´2s ion q 2 p1 ´2p ion q 3.98 10 ´18 8.0 10 ´20 p40%q N+ÑN++ N+-He Made in the code 0.94 10 ´16 1.7 ´16 p40%q N+ÑN+++ N+-He (projectile ionization without electron capture) 2.10 10 ´17 0.99 10 ´17 p50%q C+ÑC++ C+-He " 0.98 10 ´16 1.5 ´16 p64%q C+ÑC+++ C+-He 1.33 10 ´17 CÑC+ C-He 2 2s p1 ´2s qp1 ´2p q 2 `2 2p p1 ´2p qp1 ´2s q 2 1.89 10 ´16 1.77 10 ´16 p0.36qC ÑC++ C-He 2 2s p1 ´2p q 2 `2 2p p1 ´2s q 2 `4 2s 2p p1 ´2s qp1 ´2p q 5.39 10 ´17 2.99 10 ´17 p0.60qT able 3.6: Comparison between measured and calculated cross sections with 1 ´calculation for projectile ionization. All experiments were performed at AGAT except (*) by Nakai and Sataka (1991) 3.2.2.6 Comparison between CTMC and experiment for total cross sections (, `, `´ collisions)

In Table 3.5 andTable 3.6 is presented a comparison between measured cross sections and CTMC calculated cross sections. Experimental error bars are given at "2 sigma" i.e with a 95% confidence. The two Tables differ by the type of calculation for projectile ionization : 2 ´calculation for Table 3.5 and 1 ´calculation (V1, ‰ 0) for Table 3.6.

Looking at Table 3.5 andTable 3.6 we see that projectile ionization cross sections are higher in 1 ´calculations than in 2 ´calculations. The difference is of the order of 20% for single ionization but amounts to 80% for double ionization. We see that the larger p(b) at small impact parameters for 1 ´calculations are having a larger effect on double ionization than on single ionization, as expected. According to the large error bars, both calculations are compatible with the experimental results, with the exception of single ionization of `(2 ´calculation) and double ionization of `(1 ´calculation).

Target (He) ionization is well reproduced by the CTMC calculations (always 1 ćalculations)

with the exception of double ionization in thecollision (experiment of [START_REF] Dubois | Single and double ionization of helium by neutral-particle to fully stripped ion impact[END_REF]) where the calculation is 4 times too high. The IPM may be questionable. A new experiment would also be desirable.

Experimental neutralisation (single electron capture without projectile ionization) cross sections in `-and `-collisions are well reproduced by both 1 ´and 2 ´projectile ionization CTMC calculations . It is much better than what we found in `-collision [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF]. Note that the reduction of single electron capture by the "no projectile ionization" was larger in the `-collision ("60%) than in the present systems ("35% in `-and "40% in `-). In the case of attachment without projectile ionization Ñ ´both CTMC calculations (1 ánd 2 ´) are providing a cross section roughly two times smaller than experiment.

We believe CTMC to be too small in its prediction for that process. Looking now to anionic production cross sections `Ñ ´(double electron capture without 99 projectile ionization) we find that both 1 ´and 2 ´CTMC calculations predict cross sections that are too large roughly by a factor 50. This is an equivalent result to what was obtained in `´ collisions [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF]. The IPM may be incorrect, but may not be the only cause of discrepancy (see chapter 4).

In conclusion, there is an overall reasonable agreement between experiment and CTMC calculations in , `, `´ collision systems, especially for one electron processes i.e with the exception of some double ionization processes ( `Ñ ``à nd Ñ ``) and exception made of the peculiar `Ñ ´process leading to a final anion. as dominant if 2 `and 3 `cross sections are compared. This saturation of SI cross sections is compensated by the increase of multi-ionization cross sections (see for instance the relative triple over single ionization cross sections in the last column of the Tables 4.1 to 4.3). The second more probable process is dissociative excitation amounting roughly to 40% of the single ionization whatever the molecule. This ratio of excitation over ionization is typical of this velocity range [START_REF] Vernhet | Excitation in swift heavy ion-atom collisions[END_REF].

As mentioned before multi-ionization cross sections increase relatively to SI cross sections when the molecule size increases. By contrast neutralization cross sections, of the order of a few 10 ´17 2 , decrease relatively to SI when the projectile size increases. The cross sections for anionic production ( n `becoming n ´) have orders of magnitude of 10 ´20 2 . Two electrons are captured by the projectile and we expect small cross sections. In fact we find results very close from what we get with incident carbon clusters ǹ of the same velocity in collision with He (see Figure 8 in [START_REF] Béroff | Anion production in high-velocity cluster-atom collisions; the electron capture process revisited[END_REF] i.e a decrease of the anionic production cross section with the molecule size.

Process

`´ collision `´ collision Proj. single ionization 1.5 10 ´16 p64%q 1.7 10 ´16 p40%q cross section (SI) 2 (rel. err) Proj. double ionization 0.99 10 ´17 p50%q cross section (DI) 2 Ratio DI/SI (rel. err) 0.06 p28%q Neutralization cross 3.5 10 ´17 p30%q 3.74 10 ´17 p60%q section 2 (rel. err) Anionic production 8.0 10 ´20 p40%q cross section 2 (rel. err) Table 4.4: Measured cross sections for various electronic processes in the `´ (second column) and `´ (third column) collision (v=2.2 au); confidence in error bars: 95%. Partial report from Table 3.6 of Chapter 3.

Comparison with IAE/CTMC predictions

Geometries of `molecules

In the IAE model the geometry of the incident n `molecule is needed. We used the calculations performed by N. Aguirre and S. Diaz-Tendero from the Universidad Autonoma de Madrid. Geometry optimization and harmonic frequencies have been obtained at the DFT-B3LYP/6-311++G(3df,2p) level of theory. More accurate electronic energies were computed over the geometry previously optimized at the DFT level by using single (S) and double (D) excitations, adding triple (T) excitations in a perturbative way, with the same basis set: CCSD(T)/6-311++G(3df,2p). For each molecule, several geometrical conformations and the two lowest spin state isomers have been considered (singlet/triplet and quadruplet/doublet). These calculations were carried out with the Gaussian09 package. The same type of calculations has been previously performed on n m hydrocarbon molecules by the same authors [START_REF] Sánchez | Structure, ionization, and fragmentation of neutral and positively charged hydrogenated carbon clusters: C n H qm (n=1-5, m=1-4, q=0-3)[END_REF]. In Figure 4.1 is presented a general view of the geometries for the lowest energy and excited isomers of n `molecules (CnN.q1) and n `molecules (CnN.q2). In the calculations the linear lowest energy isomers were introduced but the shape effect (variation of the results with the molecule shape) is discussed in Section 4. Processes with a star are directly comparable to the experiment. function of the charge position for linear 3 `and for 2 ´CTMC calculations. It is seen that the charge position has a sizeable effect when it is positioned on C3 i.e at the end of the chain (see Figure 4.5). These results (also obtained with the 1 ´CTMC calculations) are understandable: when the charge is on C3 the projectile multiionization is increased (taking into account the fact that passing between two neutrals is more efficient than passing between a neutral and an ion) and the projectile single ionization is accordingly reduced. Then, whereas single electron capture onto the ion does not depend on the charge position, the single electron capture without projectile ionization, dominated by single electron capture without projectile single ionization, is larger when the charge is on C3. A similar effect is observed on Neutralization and Anionic production cross sections. As a consequence, an average of predicted cross sections with the charge positioned in C1, C2 and C3 was performed before comparing to experiment.

The role of the molecule shape

As already noticed [START_REF] Chabot | Multi-ionization cross-sections of small ionic carbon clusters by particle impact as a tool to investigate their shapes[END_REF] the shape of the molecule has some effects on the results. Whereas predicted cross sections are not sensitive to a little modification of the interatomic distances, the compactness of the molecule (i.e linear versus cyclic) may induce sizeable modifications on multi-ionization cross sections. In Table 4.8 we present IAE/CTMC predicted cross sections when considering the cyclic isomer of 3 `(Figure 4.6). This cyclic isomer is situated 1.1 eV above the lowest energy isomer according to N.Aguirre calculations. Since the internal energy of 3 `is estimated to be around 2 eV (see Table 1.2 in Chapter 1) it is likely to be populated in the experiment. It is interesting to note that the charge position does not matter in the cyclic case, which makes sense. In the last column of Table 4.8 is reported the ratio between predicted cross sections (averaged over the charge position) for the cyclic isomer divided by results with the linear isomer. As expected the projectile triple ionization is larger with the cyclic isomer and the projectile single ionization accordingly smaller but the effect is modest (" 10 ´15%) on this small molecule. An effect of the same order of magnitude is observed for the cyclic 2 `as compared to the linear 2 `. Nevertheless, the first cyclic 2 `, situated 2 eV above the linear ones is not expected to be very much populated since the internal energy of 2 ìs around 1 eV. Since this is difficult to estimate the quantitative contribution of the cyclic isomers in the experiment and since the effect is rather small we compare in sections 4.2.5 to 4.2.8 the experiment to the IAE/CTMC calculations performed with the lowest energy isomers.

The role of inner shells

In the preceding chapters we presented CTMC impact parameters probabilities for processes affecting only the valence shells of the C, C `, N and N `atoms (ions). This is because, at this velocity, the probability of ionising inner-shells is about 100 times smaller. We show in Figure 4.7 the carbon K-shell ionization cross sections measured in `-He collisions as a function of the projectile energy (collision velocity) 4.8: Role of the molecular shape on predicted cross sections; Predicted cross sections for cyclic 3 `and CTMC 2 ´calculations. In the last column, ratio between cross section with cyclic isomer divided by the cross section with linear 3 `.

by [START_REF] Toburen | Experimental and theoretical study of the electron spectra in 66.7-350-keV/u C `+He collisions[END_REF]. At 0.12 MeV/u (v=2.2 a.u) the cross section is about 10 ´18 2 (i.e 0.5 10 ´18 2 per electron) as compared to 0.5 10 ´16 2 per valence shell electron (1.5 10 ´16 2 for total ionization in the valence shell, see Table 4.4).

Still, if now interested in multiple ionization, it appears that inner shell ionization, followed by Auger de-excitation, becomes more and more important and competitive with valence shell ionization as illustrated in Figure 4.8. In this Figure 4.8 it is seen that inner-shell ionization amounts about to 10% of the triple ionization in 3 `´ collisions at v= 4.5 a.u. Since the K shell ionization is larger at v=4.5 a.u as compared to v=2.2 a.u (see Figure 4.7) and valence shell smaller, we can safely assume that inner-shell ionization will contribute negligibly to projectile ionization up to triple ionization. As a consequence comparison of experimental projectile ionization cross sections with IAE/CTMC predictions will be restricted to projectile ionization up to triple. Inner shell ionization can be included easily in the IAE code and this is only by a lack of time that it has not been done in the present work.

Comparison between experiment and IAE/CTMC model for projectile ionization

We now compare, process by process, the experimental and theoretical cross sections.

In Figure 4.9 and 4.10 is presented the case of projectile ionization. In order to visualise the results obtained in the different systems, cross sections of Tables 4.1 to 4.4 are presented as a function of the number of atoms in the projectile n atom , putting arbitrarily for visualisation purposes the `projectile at n atom =1.2. We see that pre- dictions are in rather good agreement with the experimental results, especially when using the CTMC 2 ´calculation for atomic ionization. The strong increase of double ionization when going from the atom to the diatomics, observed experimentally, is well reproduced by the IAE model and explained by the possibility for the helium atom to ionise the two components of the molecule when passing between, their half separation ("1.1 a.u) corresponding roughly to the impact parameters where probabilities are at their maximum. The saturation of ionization cross sections with the molecule size is also reproduced by the model. It is found that a small difference of single ionization cross sections in the atoms (1 ´predicting roughly a cross section 30% higher than the 2 ´calculation) is having a large effect on the multi-ionization cross sections, especially for the small systems. It would be interesting to measure the triple ionization of the atoms to constrain more the model.

Comparison between experiment and IAE/CTMC model for projectile excitation

In Figure 4.11 is presented the comparison between experiment and IAE/CTMC model for projectile excitation cross sections. In the experiment, the dissociative excitation only is measured whereas in the model the total excitation (single and multiple), calculated on the basis of atomic excitation, is considered. In atomic C, `, N the first spin allowed transitions begin above 7. 5, 9.3 and 10.3 eV respectively (see Tables 5.20,5.21 and 5.22 in Chapter 5), then depositing enough energy for dissociation (dissociation energy is around 5/6 eV for n `molecules, see Chapter 5). In order to be comparable to the experiment (no change of the projectile charge state) the calculation has to be for excitation without projectile ionization. This correction is large, reducing the inclusive excitation cross sections by roughly 60% (an almost constant reduction with the molecule size, slightly larger with the 1 ĆTMC calculation as compared to the 2 ´calculation). Also the double process of single projectile ionization together with electron capture has to be (and was) added. This last "correction" is much smaller, giving rise to an increase of the cross sections between 13% and 26% depending on the molecule and type of calculation. In the end, the very good agreement between experiment and model is remarkable. We will test in more detail this atomic approach to the excitation process with the use of measured dissociation branching ratios. In Figure 4.12 are compared measured and predicted cross sections for projectile neutralization. This process (change of the projectile charge from +1 to 0) is due to electron capture without projectile ionization. Again this last restriction (no ionization) leads to very large reductions of electron capture cross sections: from 30% for `2 ´calculation up to 73% for 3 `1 ´calculation. As expected the reduction is larger with 1 ´calculation (larger projectile ionization probabilities) and for largest sizes (since projectile ionization increases with the size). Altogether the agreement between the experiment and the model for projectile neutralization is satisfactory.

Comparison between experiment and IAE/CTMC model for projectile neutralization

Comparison between experiment and IAE/CTMC model for projectile anionic production

In Figure 4.13 are compared measured and predicted cross sections for anionic production cross sections. This process (change of the projectile charge from +1 to -1) is due to double electron capture without projectile ionization. This last restriction (no ionization) leads to reductions of cross sections of the order of 60%-70% for 2 `and 3 `and 40%-50% for `(depending on 1 ´or 2 ´CTMC calculation for projectile ionization). As seen in this figure there is a strong overestimation of IAE/CTMC predictions as compared to the experiment (a factor 50 to 100), as already obtained in `-collisions [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF].

One point to discuss is the fact that, with the exception of `, all double electron capture processes are spin forbidden for ground state to ground state (GS to GS) double transfer. Indeed, since GS of Helium is singlet, it is found that a spin allowed process requires the spin of n `to be equal to the spin of n ´, which is not the case except for `(compare Table 4.6 and Table 5.19). On the other hand, there are close in energy states in n ´allowing to perform the double electron transfer such as the final 1 1 states, situated respectively at 0.04eV ( 2´) and 0.2 eV ( 3´) above the GS [START_REF] Pascoli | Are C n N ´clusters really bent?[END_REF] . Whether these states are stable or not is not discussed by the authors. Note that in ´only the GS is stable [START_REF] Khamesian | Formation of CN ´, C 3 N ´, and C 5 N ´molecules by radiative electron attachment and their destruction by photodetachment[END_REF] whereas in ´there exists, apart from the 4 , a 2 loosely bound (33 meV) state [START_REF] Andersen | Atomic negative ions: structure, dynamics and collisions[END_REF]. In this last case, calculations of double electron transfer towards this excited 2 state using a semiclassical atomic orbital close coupling (SCAOCC) calculations taking into account electron correlations (static and dynamic) gave good results [START_REF] Labaigt | Electron capture and ionization processes in high-velocity C ǹ , C ´Ar and C ǹ , C ´He collisions[END_REF]. Such a calculation for double electron capture towards the GS of ´would be instructive.

Indeed, another source of disagreement between experiment and model could be related to the fact that the outer electron is captured in a non stable state and is ejected before entering in the analysis chamber (i.e within 80 ns). There are indeed some indications in the experiments of spurious trajectories for anions that could be explained by the loss of the outer electron during the path within the electrostatic analyser. An extensive and careful analysis of this phenomenon has to be done.

Conclusions and future

In conclusion, comparisons of experimental single, double and triple projectile ionization as well as dissociative excitation and neutralization with the IAE/CTMC model showed a very reasonable agreement. For projectile ionization, the 2 ´CTMC calculations give better results. We recall that there are no adjustable parameters in the theoretical modelization, apart from the basic approximations of IAE. By contrast, the anionic production cross sections are overestimated by the theory by such a factor that we suspect some incomplete detection of the anions in the experiment.

In the future various points should be investigated: Measured dissociation BR of neutral species, produced by electron capture in ` , 2 `´ and 3 `´ collisions, are reported in Tables 5.1, Table 5.2 andTable 5.3 respectively. Also reported in these Tables are: the channel dissociation energy (column 3) i.e the energetical cost of the channel starting from the ground state of n species calculated using total energies of Table 4.6 ; the number of fragments f of the considered channel (column 4); BR( f ), the branching ratio in number of emitted fragments, obtained by summing all BR corresponding to the same value of f (column 5). The BR( f ) distribution is a good indicator of the species internal energy. Indeed (see Table 5.3) two-fragments channels all require around 6 eV of internal energy for being open whereas three-fragments and four-fragments channels require around 12 eV and 18 eV respectively. Then the knowledge of BR( f ) could in principle allow to extract the species internal energy f(E ). In Figure 5.1 are presented the f(E) distributions that were found to match measured BR of Tables 5.2 and5 Within a given f , the higher dissociation BR corresponds to the channel having the smaller energetical cost (smaller dissociation energy). This result is typical of a statistical fragmentation behaviour. It will be interesting to compare these BR to calculations performed within such approach, for instance, Microcanonical Metropolis Monte Carlo method (M3C, [START_REF] Aguirre | M3C: A computational approach to describe statistical fragmentation of excited molecules and clusters[END_REF]) that are presently underway by the collaborators from Madrid.

Singly charged molecules `(n=1-3)

Measured dissociation BR of singly charged species, produced by projectile electronic excitation in `´ , 2 `´ and 3 `´ collisions, are reported in Tables 5.4, Table 5.5 and Table 5.6 respectively. As indicated before, the BR of intact n species are not measured in the experiment. As in the case of neutrals, BR( f ) may be used to extract the species internal energy. We anticipate distributions shifted towards higher energies as compared to neutrals since BR( f ) are the largest for f =3, at variance with neutrals where that was for f =2. This is what is obtained as shown in figure 5.2. In the section 5. As in the case of neutrals, within a given f , the higher dissociation BR corresponds to the channel having the smaller energetical cost (smaller dissociation energy). Calculations within the statistical fragmentation model M3C [START_REF] Aguirre | M3C: A computational approach to describe statistical fragmentation of excited molecules and clusters[END_REF]) are under study.

Doubly charged molecules ``(n=1-3)

Measured dissociation BR of doubly charged species (dications), produced by projectile single ionisation in `-He, 2 `-He and 3 `-He collisions, are reported in Tables 5.7, Table 5.8 and Table 5.9 respectively. Due to the coulombic repulsion between the two charges, n ``states are not stable i.e do have exothermic dissociation channels: `` `for ``(-4.5 eV), `+ `for 2 ``(-1.03 eV) and 2 `+ `for 3 ``(-3.0 eV). The ``dication has been theoretically studied and its ground state found to be metastable due to a barrier of 0.84 eV [START_REF] Fiser | A theoretical study of spectroscopy and metastability of the CN 2`d ication[END_REF]. We were not able to distinguish ``from `+ `in the `-He collisions but we managed, in the 3.82 C +N + ``7.7e-3 (3.9e-4) 15.92 C +C + ``1.2e-3(9.3e-5) 2.16 e-4(2.2 e-5) 30. 4Table 5.9: Measured dissociation BR of excited 3 ``species produced by projectile single ionisation in 3 `-He collisions; the first line refers to the BR for non fragmented (intact) species; negative dissociation energies correspond to exothermic channels.

In the experiments, 2 ``and 3 ``were detected with non negligible BR (8% and 3% respectively), meaning that a part of this population was surviving the 80ns separating the collision from the fragment analyser. Sizeable barriers to the dissociation are then highly probable in these molecules but we could not find any theoretical study on these systems, to the best of our knowledge. As a general behaviour on these dissociation BR of dications, we note the preference towards an equal sharing of the charge between the fragments, which is indeed less costy in energy.

5.1.4

Highly charged molecules `( n=1-3, q>2)

Measured dissociation BR of highly charged species (q>2), produced by projectile multiple ionisation in `-He, 2 `-He and 3 `-He collisions, are reported in Tables 5.10, Table 5.11 and Table 5.12 for q=3 and Tables 5.13, Table 5.14 and Table 5.15 for q=4.

For q ě 3 no intact species were detected. It is found that vaporisation prevails, where the number of emitted fragments is equal to the number of atoms in the molecule. In fact the criterium for vaporisation depends qualitatively on q/n, in agreement to what was quantitatively obtained on carbon clusters [START_REF] Chabot | Scaling Law for the Partitioning of Energy in Fragmenting Multicharged Carbon Clusters[END_REF].

As in the case of the dications, the sharing of the charge is preferred in the Channel BR (abs.err) f BR( f ) (abs.err) ``+ `0.60(0.05) 2 1(0) `+ ``0.39(0.05) ```+ N 4 e-3(5 e-4) C + ```8 .4 e-4(7 e-4) Table 5.10: Measured dissociation BR of excited ```s pecies produced by projectile double ionisation in `-He collisions.

Channel BR (abs.err) f BR( f ) (abs.err) `+ ``0.023(0.002) 2 0.03 (0.003) 2 + ``1.7 e-3(1.2 e-4) CN + ```5 .6 e-5 (1.7 e-5) `+ `+ `0.792(0.045) 3 0.97 (0.06) N + `+ ``0.083(8 e-3) C + `+ ``0.061 (3 e-3) C + `+ ``0.037 (4.2 e-3) C +N + ```1 .4 e-4 (4.4 e-5) C +C + ```8 .3 e-5 (2.6 e-5) Table 5.11: Measured dissociation BR of excited 2 ```s pecies produced by projectile double ionisation in 2 `-He collisions.

dissociation. When the sharing leads to unequal charges on the different atoms, the charge onto C is preferred as compared to the charge onto N, for energetical reasons.

Anionic molecules ´(n=1-3)

Measured dissociation BR of anionic species, produced by double electron capture in `-He, 2 `-He and 3 `-He collisions, are reported in Tables 5.16, Table 5.17 and Table 5.18 respectively. Dissociation energies, reported in the columns 3, were Channel BR (abs.err)

f BR( f ) (abs.err) 2 ``+ `0.018(1.3 e-3) 2 0.031(4 e-3) 2 `+ ``6.63e-3(1.6 e-3) `3 + `6.00e-3(5 e-4) 3 + ``6.85e-4(9 e-5) 2 `+ `0.147(0.010) 3 0.304(0.03) 2 + `+ `0.142(0.010) ``+ `+CN 3.9e-3(1 e-3)

2 +N + ``3.38e-3(1.20 e-3) `+ ``+C 2.93e-3(1 e-3) ``+ `+ 2 1.57e-3(4 e-4) 2 + ``+C 1.48e-3(1.5 e-4) ``+ `+ 2 1.42e-3(1.4 e-4) ( ```+ 2 +N)+( ```+ CN +C)
1.41e-4(3 e-5) 2 `+ `+C 0.425(0.03) 4 0.665(0.06) 3 `+N 0.184(0.013) ``+ `+C +N 0.035(9 e-3) ``+ `+2C 0.014(4 e-3) ``+ `+2C 6.93e-3(7 e-4) ```+ 2C +N 5.22e-5(2 e-5) ```+ 3 3.65e-5(2 e-5)

Table 5.12: Measured dissociation BR of excited 3 ```s pecies produced by projectile double ionisation in 3 `-He collisions.

Channel BR (abs.err) f BR( f ) (abs.err) ``+ ``0.83(0.02) 2 1(0) ```+ `0.10(0.02) `+ ```0 .07(0.03) Table 5.13: Measured dissociation BR of excited ````s pecies produced by projectile triple ionisation in `-He collisions.

Channel BR (abs.err) f BR( f ) (abs.err) `+ ```1 e-3 (2 e-4) 2 1.3 e-3 (3 e-4) 2 + ```3 e-4 (8. e-5) `+ `+ ``0.745(0.02) 3 0.999 (3 e-4) `+ `+ ``0.195(0.02) N + ``+ ``0.033 (2 e-3) C + ``+ ``0.017 (2 e-3) `+ ```+ N 4 e-3 (1 e-3) C + `+ ```3 e-3 (2 e-4) C + `+ ```2 e-3 (5 e-4) Table 5.14: Measured dissociation BR of excited 2 ````s pecies produced by projectile triple ionisation in 2 `-He collisions.

Channel BR (abs.err)

f BR( f )(abs. err) 2 ``+ ``2.06e-4(2 e-4) 2 3.84 e-4(4 e-4) 2 `+ ```8 .50e-5(9 e-5)

`3 + ``5.01e-5(5 e-5) 3 + ```4 .25e-5(4 e-5) `+ `+ ``0.015(4 e-3) 3 0.03(9 e-3) `+ 2 + ``0.011(3 e-3) `+ 2 + ``5.52e-3(1 e-3) `+ ```+ CN 4.67e-4(2 e-4) C + 2 + ```3 .51e-4(2 e-4) 2 ``+CN 3.08e-4(1.5 e-4) C + `+ ```2 .55e-4(9 e-5) `+ ```+ 2 2.43e-4(1 e-4) ``+ ``+ 2

1.64e-4(4 e-5) N + 2 + ```1 .62e-4(8 e-5) `+ ```+ 2 2.23e-5(1 e-5) 3 `+ `0.641(0.045) 4 0.97(0.12) C + `+ `+ ``0.175(0.044) N +2 `+ ``0.098(0.025) C +2 `+ ``0.044(4 e-3) 2 ``+C +N 4.82e-3(2 e-3) ``+ ``+2C

2.57e-3(7 e-4) `+ ```+ C +N 6.20e-4(3 e-4) `+ ```+ 2C 4.93e-4(2 e-4) `+ ```+ 2C 2.57e-4(1.2 e-4)

Table 5.15: Measured dissociation BR of excited 3 ````s pecies produced by projectile triple ionisation in 3 `-He collisions.

obtained using energies of if the internal energy exceeds the neutral electron affinity (EA), the electron will be emitted. In [START_REF] Béroff | Anion production in high-velocity cluster-atom collisions; the electron capture process revisited[END_REF] we evaluated this so-called thermionic emission (statistical emission) within the Weisskopf formalism and found the rate to be very large (typical 10 11 s ´1 at E*=5 eV), much larger than dissociation as illustrated in Figure 5.3 where the ratio of dissociation over (dissociation + electron emission) is reported (case of ń clusters). The relaxation following double capture can then be summarized as follows, as a function of the internal energy E:

-for E ď EA, n ´stays intact -for EA < E < diss ( diss dissociation energy of the anion) 100% of the relaxation occurs by electron emission

-for E ě diss a few % of the relaxation occurs by dissociation, and the rest by electron emission

On the other hand we cannot prove from results of Tables 5.16-5.18 that this electron emission is taking place. We see for instance that BR( f ) are rather close from those obtained for neutrals (see Table 5.1 to 5.3), exception made of / but the difference could be explained by the fact that diss is equal to 10 eV in ánd only 7 eV in . An experimental study of electron emission is then mandatory for concluding.

Looking now at specific channels we note that, whereas 2 was a populated fragment in the dissociation of ń clusters, this is here ´that appears dominant. We have a very large BR for intact ´(more than 97%), and channels with ´fragment are by far dominant: the ´+C channel for relaxation of 2 ´(BR=51%)

and channel ´+ 2 for relaxation of 3 ´(69%). Its strong stability (dissociation energy of "10 eV) may explain it.

Interpretation of dissociation of `molecules

using the energy deposit calculation performed within IAE/CTMC model.

The principle of the calculation is the following: we introduce in the IAE code the excitation into final (n,l) states on each atom (n, l principal and orbital angular momentum quantum numbers), using the probabilities exc calculated with CTMC (only 1e calculation of exc will be presented here). Because n,l (b) are noisy and not so easy to fit, we calculated in the code the probability of excitation into a n level, n (b), then used relative (n,l) cross sections to determine in which (n,l) state is the electron excited. This approximation is valid if the shapes of the n,l (b) do not depend much on l, which is approximately the case. At each final state (n,l) is associated a given energy E (see below) so that we have the dPexc dE to be introduced in the formula 3.8 of chapter 3.

Correspondence between the final (n,l) state and the energy of the transition

The energies of the transitions have been taken from the NIST database. We present only final states that may be populated according to the following selection rules :

△ " 0; △ " 0, 1, 2; △ " 0, 1, 2
Where S, L, J are respectively the spin, orbital angular momentum and total angular momentum of the considered state. In Tables 5.20,5.21 and 5.22 are presented the states that may be populated according to these selection rules in the case of C, `and N respectively. When many terms 2S`1 J contribute to a same one-electron transition, the energy of each term is introduced in the code that contributes with a weight (2J+1).

Final configuration Transition

Term (Energy in eV) 2s 2 2p 3s 2p Ñ3s

Discrete spectra

Having introduced the energies associated to the (n,l) final state in the code, we obtain a spectrum for the energy deposit which is composed of discrete lines. In Figure 5.4 we show such a spectrum (with an interval between the points of 0.2 eV) obtained in the case of excitation of 2 `where single excitation has been selected and autoionizing states are not included. The highest peaks correspond to 2s-2p excitation into C atom (8 eV, 9.3eV), `ion (9.3 eV, 13.7eV) and N(11 eV).

The spectrum stops before the IP of `(24.4 eV). In figure 5.5 the energy deposit associated to single and multiple excitation into 2 `is presented. It is seen that new peaks appear after 15 eV up to 40 eV (and above). The intensities of the peaks are small because the multiple excitation (roughly 10% of single excitation in 2 `) is shared between many different energies. to dissociation) , the lines should not be included because the molecule would change its charge and would not be selected as excited molecule. On the other hand, fragmentation could occur before autoionization, especially when the molecule is excited into repulsive states as for instance in double excitation. This is why we present both case. In this situation new lines appear (around 28 eV) but the modification of the spectrum is modest. In order to compare to the internal energy distribution extracted with BR( f ) (see figures 5.1 and 5.2), we have to degrade seriously the resolution. We made a convolution between the discrete spectrum and a gaussian curve of 4 eV of standard deviation placed at the position of the peaks. In fact, because the molecules are having already some internal energy before the collision, we shifted all the peaks by the mean energy of the projectile i.e 0.3 eV for `, 1.2 eV for 2 `and 2.1 eV for 3 `(see Table 1.2 in chapter 1).

Convoluted spectra

Results of convoluted spectra for `, 2 `and 3 `are shown in figures 5.7, toionizing states are reported, both including the total single and multiple excitation. In figure 5.10 the semiempirical distribution (solid line) is peaked at higher energy than the calculated ones but, being narrower, the mean internal energy is close (15.9 eV as compared to 14.6 eV and 16.1 eV for calculated long dashed and dotted distributions). The opposite is observed in Figure 5.11. Here the semiempirical distribution (solid line) peaks near the calculated ones but, being broader, includes lower energies than the calculated ones. The mean energy, 15.04 eV, is close from the calculated ones (14.6 eV and 16.1 eV for calculated long dashed and dotted distributions). The calculated distributions are very close between 2 `and 3 `, which is normal since the only difference comes from difference in multiple excitation, which is small in any case. Nevertheless, the agreement between the semiempirical distributions and the calculated ones is rather good taking into account the errors on the semiempirical distribution (1 eV for centroid, 2 eV for the width); it provides a qualitative explanation for the semiempirical distributions and the dissociation branching ratios of 2 ànd 3 `measured in the experiment.

Ion Pair dissociation

Ion pair dissociation (IPD) is a relaxation process of highly excited molecules proceeding through emission of an anionic and one (or several) cationic fragments. Due to the energetical cost of the process and the very few density of final states, it is a process with a very small probability as compared to the "normal" dissociation (i.e without emission of anions). In a recent work [START_REF] Launoy | Ion-pair dissociation of highly excited carbon clusters: Size and charge effects[END_REF] the AGAT team showed that the branching ratio for IPD is roughly constant with the species charge and size. We have measured IPD BR for numerous channels in n Q`s pecies and reported the results, not yet interpreted, in Appendix B. We only present in Figure 5.12 the sum of these BR (sum over all channels of same Q value) as a function of the molecule size and charge. We obtain results that are close to those obtained on qǹ clusters (see Figure 5.13) i.e showing a weak dependence as a function of the size and charge except for 2 Q`Q =2-3. In this latter case, as N does not carry an extra electron, the other fragments must be multicharged which is energetically costy, then less favorable.

Figure 5-12: Measured BR for IPD dissociation of n Q`s pecies as a function of Q for different species: Q`( circles), 2 Q`( squares) and 3 Q`( triangles).

channels were measured for all species and for various charges (Q=0-3). IPD as compared to "normal" dissociation was found to be equally probable whatever the size and the charge of the species, except when the IPD dissociation involves doubly charged fragments. In the future it would be interesting to:

-Compare the BRs of neutral n and cations n `with M3C statistical fragmentation predictions.

-Interpret the BR of multicharged species , and stimulate M3C calculations.

-For anions n ´, look at electron emission in data and stimulate M3C calculations including the process of electron ejection.

-Interpret IPD dissociation.

Chapter 6

Application to astrochemistry (paper)

Introduction

Breakdown curves are energy dependent dissociation branching ratios of an excited molecule (Vekey, 1996). BDCs are specific to the molecule, its size, charge (see below), then constitute a kind of identity card of the molecule that reflects its intimate electronic structure. The usefulness of BDC resides in the fact that, based on their knowledge, it is possible to predict dissociation branching ratios of the molecule following any physical or chemical process if the associated energy deposit is known. In a recent work [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF]) we showed how it was possible to construct, on both experimental and theoretical grounds, semiempirical BDC for carbon and hydrocarbon molecules and to use those to predict product branching ratios for reactions of astrochemical interest. Whereas the method has its own limitations, it allows to go beyond the usual first order prediction consisting to affect a BR equal to 1 to the most exothermic reaction. This approximation is common in astrochemical databases involving thousands of reactions that should somehow be given a value. With a more realistic estimate, the improvement may be substantial. Indeed, not only is the number of products much larger than 1 in most cases but the main channel is not always the most exothermic one as will be seen below.

In this paper we intend to pursue the work presented in [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF] whose aim is to furnish product branching ratios to the astrochemical databases, in particular the recent KIDA database dedicated to the interstellar chemistry [START_REF] Wakelam | A kinetic database for astrochemistry (kida)[END_REF]Wakelam et al. 2015). In place of carbon and hydrocarbon molecules we focused on this paper on C n N radicals and their cations C n N + (n =2-3). Some of them have been detected in the interstellar medium (ISM) : CCN in IRC + 10216 Nebula (Anderson and Ziurys, 2014), CCCN in the Taurus dark cloud (Friberg et al. 1980). Despite the large number of molecules containing both carbon and nitrogen in the ISM, the chemistry of nitrogen containing molecules is not well documented, exception made of the chemistry relevant to Titan's atmosphere (Dutuit et al. 2013). In Loison et al. (2014a) the chemistry in dark cloud chemical models of carbon chains containing H, O, N atoms was reviewed, amongst them the C n N (+) families. For the latter ones, reported values of products BR are based on calculations or estimates but not on experiments. Generally speaking the numerous works on C n N (+) , mostly theoretical, refer to structure calculations in the ground (Ding et al. 1998;Maclean et al. 2007) or excited (Sadlej and Roos, 1991;Zhang et al. 2014) electronic states but very few on the stability and dissociation BR of these species. This is why the experimental dissociation branching ratios we present in Section 2.2 for excited C 2 N (+) and C 3 N (+) may be of fundamental interest as well.

The plan of the paper is as follows :

In Section 2 the method of construction of semiempirical BDC is presented. It covers the general principle of the method which is summarised from [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF], the description of the experiments with the associated results and the presentation of semiempirical BDC. In Section 3 we use the obtained BDC to predict product BR for various processes leading to the formation of C 2 N (+) or C 3 N (+) adducts. It includes some neutral-neutral, ion-molecule reactions, dissociative recombination (DR) process and charge exchange with He + process. In each case we will compare the model predictions with the literature and what is presently reported in KIDA. In Section 4 we comment the effect these new BR could have in cold cores environments and conclude.

Semiempirical method

Principle and validity

The principle of the method has been detailed previously [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF]) and only a brief summary will be given here. The semiempirical method is based on both experimental and theoretical ingredients. From the experimental point of view, we measured all fragmentation branching ratios of C 2 N (+) and C 3 N (+) molecules excited in high velocity collisions with Helium atoms (see Section 2.2). From the theoretical side, we assumed that this fragmentation was of statistical nature, i.e. only depending on the molecule internal energy. This assumption was found valid for carbon C n (Martinet et al. 2004) and hydrocarbon C n H ( Aguirre et al. 2018) molecules. This allowed to express the fragmentation branching ratio along channel j, BR j as :

∫ = ∞ BR BDC (E)f(E)dE j 0 j (1)
where f(E) is the normalised internal energy distribution of the excited molecule and BDC j (E) the energy dependent dissociation branching ratio along channel j, also referred as to breakdown curve for channel j (Vekey, 1996). As branching ratios, BDC j verify, at each energy :

∑ = BDC (E) 1 j j (2)
Since we measured in the experiments BR j for all channels j and since f(E) was also determined following the procedure recalled in Section 2.2, we could extract BDC j (E) for all channels j by inversion of Eq. ( 1). As explained in [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF], the BDC j curve was taken the following form :

= ∑ BDC (E) aG(E) aG(E) j jj j jj (3)
where G j has the generic form depicted in Fig. 1.

The significance of the G j form is the following : the probability of decaying along channel j opens at E diss (which is the minimum required energy), reaches its maximum at E sat and then start to disappear at E disap when further dissociation of one of the fragments opens. E diss and E disap quantities have been calculated using the Coupled cluster CCSD(T)/6-311 + + G(3df,2d) method for the molecule whose geometry was optimised at the DFT B3LYP/6-311 + + G(3df, 2d) level. Vibrational energies, entering in the zero-point energy correction, were performed at the same DFT level. A large number of isomers and spin states was investigated. Electronic ground states of the atoms and molecules together with symmetry of the lowest energy isomers of molecules of interest here are presented in Table 1. Similar calculations have been recently reported for hydrocarbon molecules (Sanchez et al. 2016).

The (E sat -E diss ) and (E disap -E end )d i fferences, which provide the steepness of the ascent and descent of the G j curve, were estimated also on theoretical grounds. We used BDC calculations performed by some of the authors using the Microcanonical Metropolis Monte Carlo (MMMC) (Diaz-Tendero et al. 2006) and M 3 C ( Aguirre et al. 2017) statistical fragmentation theories as a guide to estimate these differences. Typical values are 1 to a few eV depending on the number of emitted fragments of the considered channel [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF]. Values of E diss ,E sat ,E disap and E end that enter in the construction of the G j functions are given in the appendix (Table A-1) for all channels j of each molecule.

Having constructed the G j (E) functions, the a j scaling factors were extracted by minimization between measured and predicted BR j using the j coupled Eqs. ( 1)- (3). By this manner semiempirical BDCs were obtained. The errors come from experimental error bars on BR measurements, f(E) distributions and error bars on the (E sat -E diss ) and (E disap -E end ) values. In the Tables of Section 3, we give the error bars for all channels calculated by running the minimization code with slightly different inputs : within experimental error bars for measured BRs, with different f(E) distributions compatible with the measurements and with 25% uncertainties for (E sat -E diss ) and (E disap -E end ) quantities.

In all cases where a comparison between experiment and model predictions was possible, a good agreement was found for products branching ratios [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF]. This was the case for dissociative recombination (DR) of C 4 + ,C 2 H + and C 3 H 2 + measured nearby storage rings. Also the semiempirical BDC were found in very good agreement with BDC calculations performed within the more sophisticated Microcanonical Metropolis Monte Carlo (MMMC) method for the C n carbon clusters (see the case of C 7 in [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF].

The statistical approach is expected to work when many states contribute to the studied process. According to Herbst (1978) this is the case in Dissociative Recombination and in chemical reactions already in very small systems (triatomics) when concerned with integrated properties such as products branching ratios irrespectively of their internal state. A statistical approach appears meaningful also in the case of photodissociation by a broad photon energy range. By contrast, photodissociation at specific energy may exhibit some strong dynamical response (see for instance the phototodissociation of CH 4 near the Lyman-α in Gans et al. 2011) that the model, as all other dynamical processes, is unable to treat.

2.2. Experiments : dissociation BR, internal energy distribution of C 2 N (+) and C 3 N (+) Experiments have been performed at the Tandem accelerator in Orsay with beams of C n N + molecules of, respectively, 4.6 MeV (n =2) and 6.0 MeV (n = 3) kinetic energy colliding with helium atoms. Both projectiles have the same impact velocity v = 2.2 a.u (120 keV/amu). The exact value of v does not matter much, the main goal being to produce in the collision excited molecular species of known internal energy and to measure the associated dissociation branching ratios. It was found that dissociation branching ratios of C n (n ≤ 5) were not dependent on v, within experimental error bars, over the [2][3][4] a.u velocity range [START_REF] Wohrer | A method for "on-line" determination of beam-jet overlaps; application to cluster fragmentation studies[END_REF]. It reflects the fact that there is little change of internal energy with v in this velocity domain. In the collision, excited C n N + and C n N species were produced by electronic excitation and charge transfer processes respectively. The associated fragmentation was recorded using the dedicated AGAT spectrometer [START_REF] Launoy | Ion-pair dissociation of highly excited carbon clusters: Size and charge effects[END_REF]. Briefly, AGAT consists of a collision chamber hosting the helium jet, an electrostatic analyser for deflecting fragments according to their charge over mass ratio and a detection chamber where 10 solid-state silicon detectors, suitably positioned, intercepted the fragments. The time window for detection of fragments was [0-150 ns], long enough so as to record the total fragmentation. It was theoretically checked (Diaz-Tendero, 2005) for the dissociation of a C 5 cluster excited in similar conditions and analysed with the same setup. On the other hand, the evolution with n of C n dissociative branching ratios let us deduce that it is the case at least up to sizes n =10 (Mezdari 2005). The current signals issued from the detectors were used to extract the masses of the fragments. Because the current signal shapes for N and C were very close, some of the channels could not be resolved by the shape analysis method [START_REF] Chabot | Shape analysis of current pulses delivered by semiconductor detectors: A new tool for fragmentation studies of high velocity atomic clusters and molecules[END_REF]. In order to get all channels resolved, we used for detection of neutrals an original CCD position sensitive detector associating the position and mass information [START_REF] Chabot | Detection of atomic and molecular mega-electron-volt projectiles using an x-ray charged coupled device camera[END_REF].

In Tables 2345are presented measured dissociation branching ratios for C 2 N, C 3 N, C 2 N + and C 3 N + excited in HVC. Dissociation branching ratios for all channels j have been measured and reported. Their number is increasing with the size and the charge of the molecule. The rate of intact cations is not measured in the experiment. Being reported in the third columns of Tables 2345are the dissociation energies calculated as explained in Section 2.1. These dissociation energies are computed for the lowest energy isomers of both the parent and the fragments. This is a kind of approximation since the isomer state of the fragment is not known in these experiments. Accordingly the channel notations of Tables 2-5 should be understood as isomer unresolved notations.

An instructive information comes from the number of fragments N f of the dissociation channel, reported in columns 4 of Tables 2345. Indeed this number strongly correlates with the internal energy of the species Measured dissociation branching ratios BR j of the excited C 2 N molecule along channel j (second column) and as a function of the number of fragments N f (last column). The BR j for intact (non fragmented) molecule is given in the first line.

In the third column is reported the calculated dissociation energy of channel j i.e. the minimum energetical cost for dissociation along this channel. Measured dissociation branching ratios BR j of the excited C 2 N + molecule along channel j (second column) and as a function of the number of fragments N f (last column). In the third column is reported the calculated dissociation energy of channel j i.e. the minimum energetical cost for dissociation along this channel. since channels with two fragments (N f = 2) typically require 6 eV whereas channels with N f = 3 and N f = 4 require around 12 eV and 18 eV respectively (with the exception of C 2 N + for which all energies are shifted by 3 eV towards higher values). Experimental BR(N f ), obtained by summing experimental BR j associated to the same value of N f (see columns 5 in Tables 2345), were used to extract the internal energy distribution of the species f(E). This was done by using Eq. ( 1) in which BR j is replaced by BR(N f ) and BDC j (E) replaced by BDC Nf (E) (BDC Nf (E) is the sum of BDC j (E) for channels j having the same N f value).

An analytical form for f(E) was assumed, made of two half Gaussian distributions centered and joining at E0 and having standard deviation σ L (low energy side) and σ H (high energy side). This form is flexible enough to reproduce all possible shapes and physically meaningful distributions (in particular the decrease of the distribution at high energy). The values we found for E0, σ L and σ H in the case of the four studied molecules are reported in Table 6. They show quite broad energy distributions peaking around 5/8 eV for neutral molecules, 13/ 14 eV for cationic molecules and extending up to 25 eV (neutrals) and 40 eV (cations). Note that the distributions obtained with cations are perfectly explained by the excitation process of atoms composing the molecule (Mahajan et al. 2018). This distribution is not expected to change more with the collision velocity, especially in the high velocity range (v ≥ 2-3 a.u). Indeed, in ion-atom collisions, probabilities of excitation processes decrease with v but the relative populations of {n,l} final states (n, l principal and orbital angular momentum quantum numbers respectively) are basically unchanged (Kirchner et al. 2000).

As a general remark on these results of Tables 2345we note that, within a given number of emitted fragments, channels requiring the lowest energy are having the larger BR. Exception arises for the C 3 +N channel which is having a very small BR although the dissociation energy is close to the lowest energy one (see Table 3). In fact the existence of a barrier along the C 3 + N reaction coordinate has already been invoked in the literature (Loison et al. 2014a) and estimated to be about 1 eV in KIDA (Smith and Loison, 2011). We checked the height of this barrier by calculating the energy profile of the C 3 N( 4 A") → C 3 ( 1 Σ g + )+N( 4 S u ) reaction. Results are shown in Fig. 2. Relative energy as a function of the reaction coordinate (a.u) computed at the B3LYP/6-311 + + G(3df,2p) level of theory is shown in black. The blue points in Fig. 2 correspond to relative energies at the critical points in the reaction (reactant, transition state and products) computed at the CCSD(T)/6-311 + + G(3df,2p) level over the B3LYP geometry. The CCSD(T) calculations provide a barrier height of 0.4 eV for the reverse reaction, smaller than previously estimated. In any case this barrier is likely to reduce the C 3 + N outgoing channel reported in Table 3 since the required energy is not 5.57 eV but 5.97 eV. It is seen in Fig. 3 that BDCs exhibit well separated energy domains associated to a different number of fragments. This justifies the procedure used for extracting the internal energy distribution described previously. It is important to recall here that this energy is from electronic origin (electron capture and electron excitation) and is centered on quite large values (see Table 6). Accordingly, the constructed BDCs are presumably applicable to any type of energy deposit, electronic or vibrational (part of the electronic energy being rapidly converted into vibrational energy, especially in large systems).

The BDC are specific to each molecule, size and charge. If the internal energy of the adduct is taken as a delta function (case of the processes considered in Section 3, the energy is called E a ), it is easy to predict the products branching ratios by placing E a on the x-axis of Fig. 3. Obviously the accuracy of the predictions will be better if this energy is in a «flat domain» and far from curve crossings. In case there is an internal energy distribution f(E a ) associated to the studied process, BR are obtained using Eq. ( 1).

Semiempirical products branching ratios

Using BDCs of Fig. 3, products branching ratios for physical and chemical processes leading to excited adducts C 2 N (+) and C 3 N (+) of known internal energy E a were predicted. The processes we considered below are neutral-neutral reactions, ion-molecule reactions, dissociative recombination (DR) and charge exchange reaction with He + .

In the calculation of the internal energy of the adduct E a , we supposed that the reaction occurred between reactants in their electronic ground states towards the adduct in its electronic ground state. This energy is equal to the dissociation energy of the adduct in its electronic ground state towards reactants in their electronic ground states (reverse pathway, see Eq. ( 4)). The E a energies are reported in bold in Tables 78910. Similarly, the exothermicity ΔE of the reaction (reactants to products) was calculated by supposing that the products were in their electronic ground states. ΔE has been calculated by difference between the adduct internal energy and the dissociation energy of the adduct towards the considered outgoing channel (or the dissociation energy increased by a barrier height when pertinent), see Eq. ( 5). Exothermicities are reported in the last column of Tables 78910; positive values correspond to exothermic reactions.

Table 6

Parameters of the internal energy distributions (see text) of C 2 N, C 3 N, C 2 N + and C 3 N + molecules fragmenting along Tables 2345.

=- → ∆E E E (adduct products) ad i s s (4)
These assumptions are not always valid. Ground state to ground state reaction is sometimes forbidden, for spin conservation violation or symmetry breaking reasons. We checked, for all reactions, whether the reaction between reactants and products was spin allowed and whether the adduct was possibly the lowest energy isomer of the molecule in its electronic ground state. For that, we used the electronic ground states characteristics of atoms and molecules involved in the processes (presented in Table 1) and the known selection rules (see appendix B of [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF]. We indicate in the legend of Tables 7-10 when the reaction is spin forbidden ( ¶) and also when spin and/or symmetry considerations preclude the formation as an adduct of the lowest energy isomer of the molecule in its electronic ground state (*). In the first case ( ¶), since the model is not able to predict whether a spin forbidden reaction will be closed, slowed down or will occur with a normal rate (Schwarz, 2004) we introduced this uncertainty in the error bars of the predicted values. We recommend to use in chemical models the predicted values with the associated large unsymmetrical error bars given in Tables 78910. When the adduct cannot be the lowest energy isomer in its electronic ground state, we checked whether the adduct could possibly be a close-in-energy isomer of the molecule in its electronic ground state (calculations of many isomers were performed as indicated before). In all cases an excited isomer of the adduct was found to be compatible with spin and symmetry considerations. Then, symmetry considerations never precluded strictly the reaction to occur. We recommend to use the predicted branching ratios for these reactions identified with the * sign.

Neutral-neutral reactions

Reactions between neutral reactants leading to intermediate C 2 N and C 3 N adducts are reported in Table 7. In addition to the adduct internal energy E a and reaction exothermicities ΔE, given in column 5 and 6 respectively, we present in column 3 semiempirical product branching ratios predicted by the model and in column 4 values found in the KIDA database.

Considering reaction with C 2 + N reactants we note that a single outgoing channel different from the entrance one, C + CN, is open so that the BR of this one has to be 1. For this reaction the adduct cannot be C 2 N in the lowest energy isomer and in its electronic ground state for spin and symmetry reasons. According to our calculations of isomers, there exists an isomer having a 4 A "(Cs) ground electronic state, situated 1.107 eV above the lowest energy one (CNC in the 2 Π g state), through which the reaction could occur. The complete pathway of this reaction has been recently elucidated (Loison et al. 2014b).

We consider next the CNC + C and CCN + C reactions because CCN + C is the reaction treated in KIDA. It is possible to treat different reactants isomers within the model since, depending on the isomer, we may get different E a values and then different model predictions. By contrast, because the experimental results of Section 2.2 are isomer unresolved, we have generally no access to the products isomers. Model predictions are identical between the two reactions and give C 2 +CNas very dominant, in accordance with KIDA. Prediction for C 3 + N is associated with a large error bar so that it is difficult to estimate the role of the barrier height of 0.4 eV in this reaction. Note that without barrier the model prediction for C 3 + N is 0.11 (0.03). Although a minor channel we may mention that the reaction leading to C 3 + N products cannot occur through the electronic ground state of the C 3 N lowest energy isomer for spin and symmetry considerations. But the reaction can proceed through the 4 A'' (Cs) state of an excited C 3 N isomer situated, according to our calculations, 3.90 eV above the lowest energy one. The C 3 +N→ C 2 + CN reaction has not been reported in the Table 7 because this spin forbidden reaction is unlikely to occur due to the barrier of 0.4 eV preventing the addition of N to C 3 .

Ion-molecule reactions

In Table 8 are reported model predictions for ion molecule reactions leading to intermediate C 2 N + and C 3 N + adducts. As mentioned before the isomer state of the products cannot be derived from the model; unresolved isomer product is indicated in brackets (for instance [C 2 N + ]). We note that, for a given couple of reactants, many outgoing channels with significant branching ratios are predicted by the model, at variance with KIDA where often one channel only, corresponding to the largest exothermicity, is supposed to be populated. This channel is sometimes corresponding to our main outgoing channel (case of CN + + C reactants for instance) but sometimes not (cases of C 2 +N + and CN + +C 2 reactants). The C + + CCN reaction is of interest because predictions for two products channels are reported in KIDA, based on the work of Loison et al. (2014a). In this work, DFT calculations showed no barrier for CCCN + and CCNC + formation. Calculated branching ratios are in good agreement with the model predictions for [C 2 N + ] + C and C 2 + + CN products . The reaction leading to C 3 + +N products, of rather small branching ratio (∼10% as predicted by the model), is not considered in Loison et al. (2014a).

For a few cases in Table 8 (identified by the sign ¶), reaction from reactants in their electronic ground states towards products in their electronic ground states is spin forbidden. As explained before uncertainties on these reactions are completely included in the error bars.

As in the case of neutral-neutral reactions, the intermediate complex involved in the reaction could sometimes not be the adduct of Table 1. This concerned six channels, identified by the * sign. In all cases an adduct satisfying spin and symmetry considerations was found. Those adducts were : 3 B 2 (C2v), situated 2 eV above the adduct of Table 1, for the five first reactions stamped with * leading to a C 2 N + adduct ; 1 A'(Cs), situated 0.6 eV above the adduct of Table 1, for the last reaction stamped with * leading to a C 3 N + adduct.

Dissociative recombination (DR)

In Table 9 are reported branching ratios predictions following DR in electron-CNC + , electron-CCN + and electron-C 3 N + collisions. The internal energy of the neutral adduct E a has been taken equal to its ionization potential (IP), assuming that the DR process proceeds mainly with electron kinetic energy small as compared to IP (Mitchell, 2015).

Although the internal energy of the neutral adduct differs in CNC + +e -and CCN + +e -reactions, it is seen from Fig. 3 that both reactions lead to equal model predictions for BR. This is in agreement with estimations of Loison et al. (2014a) reported in KIDA. The model predicts a strong dominance of the C + CN products channel, as reported in KIDA.

For C 3 N + + e-, the main products are found to be C 2 +CN as predicted by the model and reported in KIDA. The role of the barrier along the C 3 + N outgoing channel is found rather small since, without barrier, the predicted BR is 0.07 (0.02). It is in any case a small This last reaction has a BR far from being negligible and should then be considered in databases.

Charge exchange reactions with He +

In Table 10 products of charge exchange between CNC, CCN, C 3 N and He + are reported. As well known from ion-atom collisions, charge exchange at low velocity occurs between electronic states of equal energy (energy matching) (Olson, 1981). The same is found for ion-molecule collision as shown for instance in a recent investigation of the charge exchange reaction betweeen He + and dimethyl ether (Cernuto et al. 2017). Helium, which has a large IP (24.6 eV), captures then an electron from an inner valence shell of the molecule, resulting in a large internal energy of the molecular ion ΔIP = IP (He)-IP (molecule) [START_REF] Chabot | Scaling Law for the Partitioning of Energy in Fragmenting Multicharged Carbon Clusters[END_REF]. The adducts of interest here are the excited molecular ions CNC + , CCN + and C 3 N + after charge exchange and not the intermediate complexes [C 2 NHe + ]or[C 3 NHe + ] that are formed during the collision. Accordingly we have for those E a = ΔIP. We used our calculated IP of CNC, CCN and C 3 N (equal to 9.66 eV, 10.67 eV and 11.76 eV respectively footnote 1 ) in order to extract E a values, reported in bold in column 5 of Table 10. Exothermicities of the reactions ΔE were calculated with Eq. ( 5) as before.

Due to the large internal energies of the molecular ions, fragmentation into three fragments is rather important, exception made of CCN + whose internal energy (13.92 eV) is close from the opening of the first three-fragment channel (C + + C + N that requires 13.71 eV). That was already noted in C n ,C n H and C 3 H 2 +He + reactions [START_REF] Chabot | Reactions forming C p0,`q n"2,10 , C n"2,4 H p0,`q , and C 3 H p0,`q 2 in the gas phase: Semiempirical branching ratios[END_REF]) whereas, from mass spectra and the abundance of HCO + , authors from (Cernuto et al. 2017) could estimate a very large contribution of channels with three or four fragments as well. Fragmentation along channels with three fragments has a large energetical cost. Accordingly the corresponding exothermicity of the reaction is rather small. This behavior is apparently non statistical. In fact within a pure statistical fragmentation process it is found that the system prefers to spend the internal energy for breaking chemical bonds (producing more fragments) rather than by dissipating the energy in fragment's internal energy or fragments kinetic energy (Diaz-Tendero et al. 2006). In that respect channels reported in KIDA as main products and corresponding to maximum exothermicities (two-fragments channels) are out of the game. The database should be updated for these charge exchange reactions.

Discussion about the astrophysical implications and conclusions

Using the Nautilus astrochemical model, we simulated the expected abundances of C n N molecules in cold cores conditions. Nautilus is a gasgrain astrochemical model. Based on micro-physical parameters (such as rate coefficients for gas-phase reactions), this numerical model computes the species abundances in interstellar conditions as a function of time by solving a set of kinetic differential equations. The model includes a large number of chemical processes in the gas-phase. It also takes into account the interactions with the interstellar grains (adsorption on the surfaces and desorption from the surfaces) and the reactions at the surface of the grains (treated with the Langmuir-Hinselwood approach). The model is described in details in Ruaud et al. (2016) while the chemical parameters are described in Loison et al. (2017). For this work, the gas-phase network has been updated with the new branching ratios presented in this paper. We have run the model for typical cold core conditions, i.e. a gas and dust temperature of 10 K, a proton density of 2 × 10 5 cm -3 , and a high visual extinction preventing any direct photochemistry. Fig. 4 presents the results of our simulations for CN, CCN, C 3 N, and C 5 N. In fact, under cold core conditions, the model results are not affected by the chemical updates. Indeed, species having an abundance of more than 10 -12 (with respect to H) were modified by less than 5% at all times, which is not significant. One interesting point however is that the CCN predicted abundance is the same or higher as the ones of the two other detected species (i.e. C 3 N and C 5 N). This molecule has been detected in the circumstellar envelop of IRC + 10216 (Anderson and Ziurys, 2014) where the conditions are different from cold cores but, as far as we know, not in cold cores. We however could not find any published upper limits. In our model, CCN is formed by the dissociative recombination of CH 2 CN + and CH 3 CN + , and the neutral-neutral reaction N + CCH -> H + CCN. Note that errors on the predicted abundances of Fig. 4 may be important due to uncertainties on the rates of contributing processes. Their estimates would require an extensive work, that goes beyond the scope of this paper. On the other hand, observational constraints on CCN abundance in cold cores would be of great help to constrain the model.

In this paper, we have presented new branching ratios for a number of reactions involved in the chemistry of the interstellar molecules C n N. Despite the fact that the new values do not significantly change the model results, they will be included in the KIDA databases and should be included in current astrochemical models. In fact, because of the non-linear behavior of these models, the importance of the reactions depends on the specific network used and the physical conditions (Wakelam et al. 2010).

Footnotes :1 : Recent measurements give 9.78 (0.04) eV and 10.82 (0.03) eV for CNC and CCN molecules respectively (Garcia et al. 2017). Chapter 7

Conclusion

In conclusion we studied collisions between n `projectiles (n=0,1,2,3) and He atoms in the intermediate velocity regime (v=2.25 a.u), focusing on both the collisional aspect (cross sections for various electronic processes) and molecular relaxation (fragmentation) aspect. In addition, some application of these experiments to astrochemistry was performed.

The experimental tools have been described in chapter 1 and 2: The Tandem accelerator of Orsay was used to provide the molecular ions at the given velocity. A dedicated setup, AGAT, was used to perform and analyse the collision, in particular through the recording of all projectile fragments of known charge and mass including negative, neutral and positively charged ones. In chapter 2 were described the analyzing tools for identification, counting, background subtraction, normalization and extraction of absolute cross sections and absolute dissociation branching ratios.

Chapter 3 was devoted to the collision modeling, using the IAE/CTMC model based on a representation of the molecule in terms of independent atoms and using the independent electron approximation. For this, extensive calculations of impact parameter probabilities for electronic processes in C, C `, N, N `-He collisions were performed within the classical CTMC approach and presented. This included (target and projectile) ionization, electron capture and projectile excitation in (n,l) states.

Comparison between measured and CTMC cross sections in these systems showed a reasonable agreement, validating its use in the IAE calculation, with the exception of double electron capture giving rise to anionic C

´.

In chapter 4, experimental cross sections for projectile ionization, dissociative excitation, projectile neutralization and projectile anionic production cross sections were presented and compared to predictions of the IAE/CTMC model. A good agreement was generally observed, which is notable as no adjustment parameter exists in the calculation, apart from the basic approximations. On the other hand, as is the case for C ´, anionic production cross sections were grossly overestimated by the model.

In chapter 5 dissociation branching ratios of excited C n N q`s pecies (q= -1,0, 1,2,3,4) were presented and discussed. Branching ratios in number of fragments were used to estimate the internal energy distribution (simulated with two half gaussians) for the case of C n N and C n N `species, using theoretical dissociation energies. In the C n N case, the distributions were compared to predictions of the IAE/CTMC model, using the CTMC probabilities for excitation into (n,l) states and the energy levels of excited C, C `, N atoms (ion) from the NIST. A good agreement was observed, furnishing a qualitative interpretation for the internal energy of C n N `molecules following electronic excitation and measured dissociation branching ratios.

Chapter 6 (paper to appear in "Molecular Astrophysics") is describing some application of our experiments to astrochemistry, namely, the construction of breakdown curves (energy dependent dissociation branching ratios curves) for C 2 N, C 3 N, C 2 N ànd C 3 N `molecules and their use for predictions of products branching ratios of some physical and chemical processes involving these excited adducts. This included some neutral-neutral reactions, ion-molecule reactions, dissociative recombination and electron transfer in collisions with He `processes. For those, recommendations for new products branching ratios to include in databases, in particular the KIDA database, were done. Nevertheless, inclusion of the new products branching ratios in a cold core astrochemical model did not change the model predictions significantly.

In the future various aspects should be investigated. From the collisional point of view, understanding the disagreement between experiment and model for anionic production cross section is an important point. This would require experimental (check if some electron is lost before or during the pass through the electrostatic analyser) and theoretical (two active electron calculation) works. Also, it would be interesting to introduce the molecular character of the projectile, for instance by doing CTMC calculations with a multi-center potential. From the fragmentation point of view, we expect our measurements to be soon compared to calculations performed within the statistical fragmentation model M3C [START_REF] Aguirre | M3C: A computational approach to describe statistical fragmentation of excited molecules and clusters[END_REF]. Also, we measured all branching ratios for Ion Pair Dissociation of C n N q`s pecies (q=0, 1,2,3), not yet interpreted.

From the astrochemical point of view it would be interesting to construct BDC for more strategic molecules for which the potential impact on interstellar chemistry has been demonstrated. Résumé: Abstract: This thesis studies the aftermath of collision between singly positively charged Nitrogenated carbon species C n N + (n=0,1,2,3) and neutral Helium atom at a velocity of 2.25 au. At this velocity, close to the velocity of outer electrons in atoms and molecules, several electronic processes take place and are near their maximum of probability such as ionisation (single, double, triple. . . ), electronic excitation and electron capture (single and double). We looked at their cross sections and how their evolution with the molecule size. Following the collision the molecule can fragment, which leads to another interesting aspect, the fragmentation branching ratios.

Collision experiments were done using a Tandem accelerator at Orsay that produced the C n N + projectiles and a dedicated set-up, AGAT, to capture the flying fragments/intact molecule after collision according to their charge to mass ratio. Knowing the number of particles that are shot and the fact that our set-up allows no loss of fragments/intact molecule, we could get the probabilities of various fragments formed. Using these probabilities and a knowledge of the Helium jet profile used, we could measure their cross sections. The probabilities alone are sufficient to obtain the fragmentation branching ra-tios. The next step was to use a theoretical model to simulate the collision. We used Independent Atom and Electron (IAE) model coupled with Classical Trajectory Monte Carlo (CTMC) method to calculate the desired cross sections. A general good agreement was obtained, with the exception of double electron capture. The model could also predict, through the calculation of the species internal energy, the fragmentation branching ratios of cations C n N + after electronic excitation. Also, the branching ratios were used to construct semi-empirical Breakdown Curves (BDCs), which are internal energy dependent dissociation branching ratios specific to each molecule, type, size and charge. With those, we could recommend products branching ratios to be used for various processes of astrochemical interest. The products branching ratios will be made available for a wider network of researchers under the international Kinetic Database for Astrochemistry (KIDA). This thesis was realized under the doctoral programme of École Doctorale Ondes et Matière (EDOM) with Institut des Sciences Moléculaires d'Orsay (ISMO) where the author was given an office and Université Paris-Sud (Université Paris-Saclay) where the author is formally enrolled.

Université Paris-Saclay Espace Technologique / Immeuble Discovery Route de l'Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France

  laire restreint et de les identifier et détecter avec 100% d'efficacité. Les expériences ont été effectuées auprès de l'accélérateur Tandem d'Orsay avec des faisceaux moléculaires C n N `de quelques MeV d'énergie cinétique. Le dispositif AGAT a permis de réaliser les collisions (en condition de collision unique) et de mesurer tout à la fois les sections efficaces des processus et la fragmentation associée. Parallèlement nous avons simulé ces collisions d'un point de vue théorique en utilisant le modèle à Atomes et Electrons Indépendants (IAE) couplé à des calculs CTMC (Classical Trajectory Monte Carlo). Dans ce modèle la molécule est supposée composée d'atomes (ions) indépendants, placés à la géométrie d'équilibre de la molécule qui est gelée pendant la collision rapide (10 ´16 s). Les probabilités des processus d'excitation électronique, ionisation et capture électronique dans les collisions entre les constituants atomiques et l'Hélium, fonctions du paramètre d'impact de collision, ont été calculées par la méthode CTMC. Sur cette base, nous avons prédit les sections efficaces des différents processus électroniques qui se sont trouvées être en bon accord avec les mesures, à l'exception de la double capture d'électrons. Avec le même modèle IAE/CTMC nous avons calculé le dépôt d'énergie dans les molécules associé au processus d'excitation électronique. Pour faire ce calcul nous avons utilisé les probabilités d'excitation électronique dans différents niveaux d'excitation calculées par la méthode CTMC et l'énergie associée à ces niveaux d'excitation atomique extraite des tables NIST. Un bon accord a été obtenu lors de la comparaison avec la distribution d'énergie obtenue en utilisant les rapports de branchement de dissociation mesurés. Ces expériences nous ont permis de construire des «Breakdown Curves»(BDC), véritables cartes d'identité des molécules qui permettent de prévoir, dans le cadre d'une fragmentation statistique, comment va fragmenter un système dont on connait l'énergie interne. Avec ces BDC nous avons pu prédire et recommander des rapports de branchement pour les voies de sortie de différents processus physiques et chimiques d'intérêt astrochimique impliquant la formation de complexes moléculaires C n N (n=2-3) et C n N `(n =2-3). Les réactions considérées sont : les réactions ionmolécule, les réactions neutre-neutre, la recombinaison dissociative avec des électrons et le processus d'échange de charge en collision avec He `. Les prédictions de notre modèle seront insérées dans la base internationale d'astrochimie «Kinetic Data Base for Astrochemistry»KIDA http://kida.obs.u-bordeaux1.fr. Cette thèse a été réalisée dans le cadre de l'Ecole Doctorale Ondes et Matière (EDOM) à l'Institut des Sciences Moléculaires d'Orsay (ISMO), à l'Université Paris-Sud Paris Saclay. This section for acknowledgement section begins and ends with the director of my thesis Dr. Karine Béroff. From the process of my application of Ph.D to the deposit of this thesis to the library of Université Paris-Sud, Karine along with her meticulous nature is of great help. I thank Dr. Béroff for guiding me and helping me in properly installing, in finishing administration and in introducing me to other prominent researchers in the area. I wish to extend my thanks along with my supervisor to Dr. Marin Chabot and his doctoral student Tijani IdBarkach for the smooth and uninterrupted conduct of experiments at the Tandem accelerator at Orsay. The author wish to acknowledge Dr. Arnaud Le Padellec, Dr. Thibaut Launoy, Dr. Maëlle Bonnin and all the others who helped in conducting the collision experiments at the Tandem accelerator. I thank Dr. Aurélie Jallat for helping me with the data analysis code during the initial phase of my PhD. I thank Dr. Laurent Tassan-Got for introducing me to DP2, the data analysis software used in this work. Dr. Tassan-Got is credited to be a principal author of this software. It filled in me with great joy and respect to discuss with him the various aspects of DP2. The author used several techniques acquired from Dr. Tassan-Got during the course of this work. I thank my PhD defence jury; Dr. Alain Dubois, Dr. Jean-Christophe Loison, Dr. Patrick Rousseau, Dr. Séverine Boyé-Péronne and Dr. Bernard Pons for going through the thesis carefully, suggesting corrections and recommendations and being present at the defence to evaluate and assess the extend of this work and the presentation. I also thank the jury for their valuable comments on the various techniques and tools used in this work. I thank Dr. Sergio Díaz-Tendero and Dr. Nestor Aguirre for calculating the structure of the projectiles used in this thesis. The author did the Classical Trajectory Monte Carlo (CTMC) (a theoretical model used here) calculations at Madrid and Bordeaux. I thank Universidad Autónoma de Madrid and Centre Lasers Intenses et Applications, Université de Bordeaux for hosting me and providing with a peaceful working environment during the CTMC calculations. The first phase of the CTMC calculations was done at UAM Madrid.

3. 1

 1 Molecule-atom collisions : the Independent Atom and Electron (IAE) model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Description of the IAE model . . . . . . . . . . . . . . . . . . 3.1.2 IAE code: Cross sections calculations and energy deposit calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2.1 Cross sections . . . . . . . . . . . . . . . . . . . . . . 3.1.2.2 Energy deposit by electronic excitation . . . . . . . .

3. 2

 2 Atom(ion)-atom collisions : Classical Trajectory Monte Carlo (CTMC) calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The CTMC approach . . . . . . . . . . . . . . . . . . . . . . . 3.2.1.1 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1.2 Initial conditions . . . . . . . . . . . . . . . . . . . . 2 3.2.1.3 One electron calculations . . . . . . . . . . . . . . . 3.2.1.4 Two electron calculations . . . . . . . . . . . . . . . 3.2.1.5 The model potentials . . . . . . . . . . . . . . . . . . 3.2.2 CTMC probabilities results . . . . . . . . . . . . . . . . . . . 3.2.2.1 Convergence of probabilities with the number of trajectories (2 ´calculations) . . . . . . . . . . . . . . .

4. 1

 1 Experimental results on cross sections . . . . . . . . . . . . . . . . . . 4.2 Comparison with IAE/CTMC predictions . . . . . . . . . . . . . . . 4.2.1 Geometries of n `molecules . . . . . . . . . . . . . . . . . 4.2.2 The role of the charge position . . . . . . . . . . . . . . . . . . 4.2.3 The role of the molecule shape . . . . . . . . . . . . . . . . . . 4.2.4 The role of inner shells . . . . . . . . . . . . . . . . . . . . . . B Ion pair dissociation (IPD) branching ratios B.1 Relaxation by IPD of { Q`} species (Q=0,1) . . . . . . . . . . . . B.2 Relaxation by IPD of { 2 Q`} species (Q=0,1,2,3) . . . . . . . . . . B.3 Relaxation by IPD of { 3 Q`} species (Q=0,1,2,3) . . . . . . . . . .

  Excitation and fragmentation of `(n=1-3) molecules in collisions with He atoms at intermediate velocity;fundamental aspects and application to astrochem-

Figure 1 - 1 :

 11 Figure 1-1: Schematic diagram of the AGAT setup .

Figure 1 - 2 :

 12 Figure 1-2: A general view of the experimental set-up

Figure 1 - 3 :Figure 1 - 4 :

 1314 Figure 1-3: View of the HICONEX 384 ion source

Figure 1 - 5 :

 15  Relation between mass and magnetic field for the species of Table1.1

Figure 1 -

 1 Figure 1-6: A picture of the Tandem accelerator

Figure 1 - 7 :

 17 Figure 1-7: Outside view of AGAT set-up

Figure 1 -

 1 Figure 1-8: Interior of the collision chamber

4

 4 and closing 7 (all other valves open except 8 and 9 used for pumping), then a second run is performed with 4 closed and 7 open which will be subtracted from the first one. In order to extract the absolute target density crossed by the beam necessary to extract absolute cross sections a beam profile is performed. It consists in recording an event probability (for instance electron capture probability) as a function of the lateral position of the jet along (see Figure 2.19).

Figure 1 -

 1 Figure 1-9: Gas injection system

Figure 1 -

 1 Figure 1-13: Schematic view of the interior of the detection chamber

Figure 1 -

 1 Figure 1-14: Enlargement of the depletion zone

Figure 1 -

 1 Figure 1-16: Sketch of a cross section of the CCD sensor. The structured electrode at the bottom allows to collect and transfer charges created locally at the pixel level.

2

  and {{ for example. But, in the experiments, we were not able to separate between { and 2 { which motivated us to use the camera for their branching ratios.

Figure 1 -

 1 Figure 1-17: View of the detectors in runs of March 2015

able 1 . 7 :

 17 Detector configuration of February 2016 (∆ " 42 ); range of detection may be non-symmetrical in case there is a (slight) masking by another detector.

Figure 1 -

 1 Figure 1-18: View of the detectors in runs of February 2016. The "finger" is seen in front of the detector " `".

Figure 1 -

 1 Figure 1-21: A live CVISU during the run

Figure 2 -

 2 1 shows a current signal from the detector. The signal treatment is done with, subtracting the background, smoothing by -point running averages, time calculation and finding the amplitude and integral of the signal. The background is subtracted by subtracting the average of a region of no signal, for example, an interval of r500, 900s in the Figure 2-1. The signals are filtered using a linear smoothing filter to reduce noise. This filter makes a running average of the signal on `1 points. Thus each sampled point of the signal is substituted by the average value of the n 2 values around. For a signal pq that

Figure 2 - 1 :

 21 Figure 2-1: Current signal output before treatment; on x-axis, 0.5 ns per canal.

  Figure 2-2: Amplitude fragmentation resolution of 2 vs 2 as a function of the filtering points number of current signal.

Figure 2 .

 2 Figure 2.2 but the improvement is rather small. Once the signals are smoothed, some signal characteristics may be extracted. The most important ones are the amplitude

Figure 2 - 3 :

 23 Figure 2-3: Energy response of " `" detector at the impact of one or several `,

Figure 2 - 4 :

 24 Figure 2-4: Mass calibration of " `" detector in runs of February 2016 and October 2016 following Figure 2-3

Figure 2 - 6 :

 26 Figure 2-6: Loss rate calculation vs coulomb explosion energy c for `and

Figure 2 - 7 :

 27 Figure 2-7: Simulating the `and `hits for a well centered 14 mm ˆ14 mm detector and for c "18 eV

Figure 2 -Figure 2 - 9 :

 229 Figure 2-8: Comparison between raw (broken line and open symbols), corrected (black line and full symbols) final 2 Q`p robabilities (normalized to " 0) recorded in March 2015 and results of the October 2016 run (red line and red symbols); collision 2 `´

Figure 2 Figure 2 -

 22 Figure 2-10: Same spectrum of Figure 2-9 with timing selection of CN ćoincidence

Figure 2 -

 2 Figure 2-15: Comparison between current signals from (red curve) and 2 (black curve). Top: raw results; down: normalized signals.

Figure 2 -

 2 Figure 2-16: Comparison between current signals from (red curve) and (black curve); top: raw results; down: normalized signals.

Figure 2 -

 2 Figure 2-17: Mass resolution of the CCD camera

Figure 2 -

 2 Figure 2-18: Distribution of distances between two impacts (in pixels, 1 pixel " 24) measured in the collision 2 `´

Figure 2 -

 2 Figure 2-19: Schematic illustration of beam and jet relative positions (from Wohrer et al. (2000))

Figure 2 -

 2 Figure 2-20: An example of beam-jet profile fitted to a Gaussian function.

Figure 2 - 21 :

 221 Figure 2-21: Dependence of ´{ { { `probability with jet

Figure 2 -

 2 . Since SU M and SEC are measured in the experiment, DEC and SECN cross sections can be deduced.

Figure 2 -

 2 Figure 2-22: Probabilities as a function of jet . Top: for sum (Equation 2.18); bottom: for N where the channel studied is ´{ { { `(Equation 2.19).

Figure 3 - 1 :

 31 Figure 3-1: Schematic view of the molecule-atom collision

  4 `is modelled by 4 carbon atoms (ions) shown in black in Figure 3-1 and one atom (open circle) at the end of the chain (see precise geometries in Chapter 4). The collision between 4 `and is treated as 5 collisions (three -, one `-and one -) * operating at different impact parameters. The impact parameters values depend on the inter-atom distances, orientation angle and the polar angle of b in the plane perpendicular

Figure 3 - 3 :

 33 Figure 3-3: A schematic diagram showing a 3 body collision

  performed for the He X `,X pairs of electrons. Main shortcomings of 2 ´calculations

Figure 3 - 5 :

 35 Figure 3-5: Comparison of radial densities in and `with mod (solid line) or with Hartree-Fock (broken line) potential.

Figure 3

 3 Figure 3-6: 2 ´exclusive probabilities as a function of the impact parameter in -, v=2.25 au with 100 ˆ100, 500 ˆ500, 1000 ˆ1000 and 1500 ˆ1500 trajectories.

Figure 3 -

 3 Figure 3-7: Target ionization in p2q-collision. 1 ´calculations: black squares; 2 ´calculation: open triangles up. Components of target ionization in 2 ´calculation: target ionization alone: black circles; target ionization + projectile ionization: black triangles down; target ionization `projectile excitation: open circles.

Figure 3 -

 3 Figure 3-8: Target ionization (squares) and target electron loss (circles) in 1 ´calculation (black symbols) and 2 ´calculation (open symbols). Calculations performed with incident `p2q.

Figure 3 - 9 :Figure 3 -

 393 Figure 3-9: Model potentials and its derivatives for -´system

3. 2 . 2 . 5 . 2

 2252 Figure3-13: 2-2 excitation probability pq as a function of in `-p2q collision p " 2.25q. Comparison between quantum calculations (blue curve) and classical calculations with different bin ranges: Black[1][2], red[1.05-2], green[1.1-2], yellow[1.15-2], pink[1.2-2]

Table 3 . 4 :

 34 Percentage (%) of projectile excitation into final levels for 2 and 2 electron of in -collision p2.25 q; 1 ´calculation p 1, ‰ 0q et al., 2006; Pons, 2000b,a), the bin range in the classical calculation and decided to enlarge the 2s one from [0, 1[ to [0, max [ with max P R, and correspondingly shrink the 2p one to [ max , 2[.

Figure 3 -

 3  shows the result for the `-p2q system and for 2 ´2 excitation.

Figure 4 - 1 :

 41 Figure 4-1: General view of the geometries of the first isomers of n `(n=1-3). In blue, the Nitrogen atom. Calculations by Nestor Aguirre and Sergio Díaz-Tendero (private communications).

Figure 4 - 2 :

 42 Figure 4-2: Goemetry of the lowest energy isomer of `molecule. Distances are given in atomic units. Nitrogen in blue. Mulliken charges in parenthesis.

Figure 4 - 3 :

 43 Figure 4-3: Geometry of the lowest energy isomer of 2 `molecule. Distances are given in atomic units. Nitrogen in blue. Mulliken charges in parenthesis.

Figure 4 - 4 :

 44 Figure 4-4: Geometry of the lowest energy isomer of 2 `molecule in cyclic configuration. Distances are given in atomic units. Nitrogen in blue. Mulliken charges in parenthesis.

Figure 4 - 5 :

 45 Figure 4-5: Geometry of the lowest energy isomer of 3 `molecule. Distances are given in atomic units. Nitrogen in blue. Mulliken charges in parenthesis.

Figure 4 - 6 :

 46 Figure 4-6: Geometry of the lowest energy isomer of 3 `molecule in cyclic configuration. Distances are given in atomic units. Nitrogen in blue. Mulliken charges in parenthesis.

Figure 4 -

 4 Figure 4-9: Comparison between experimental cross sections and IAE/CTMC predictions for projectile ionization; SI (circles), DI (triangles up), TI (squares) refer to single, double, triple ionization respectively; CTMC calculations performed with two active electrons (CTMC 2 ´calculation).

Figure 4 -

 4 Figure 4-10: Comparison between experimental cross sections and IAE/CTMC predictions for projectile ionization; SI (circles), DI (triangles up), TI (squares) refer to single, double, triple ionization respectively; CTMC calculations performed with one active electron (CTMC 1 ´calculation).

Figure 4 -

 4 Figure 4-11: Comparison between measured dissociative excitation cross sections and projectile excitation cross sections predicted by the IAE/CTMC model.

Figure 4 -

 4 Figure 4-12: Comparison between experiment and IAE/CTMC model for projectile neutralization cross sections.

Figure 4 -

 4 Figure 4-13: Comparison between experiment and IAE/CTMC model for anionic production cross sections.

-

  Introduction of inner shell ionization in the model and interpretation of multiionization cross sections (quadruple ionization and above). -Calculation of double electron capture in `with SCAOCC including electron correlations -Search in the data of electron ejection signature in case of anionic fragments -Beyond the IAE model : a new approach is developed in the group of Bernard Pons in Bordeaux in order to introduce the molecule and the stable propagation of electrons in molecular orbitals.

Figure 5 - 1 :

 51 Figure 5-1: Internal energy distribution of 2 (solid line) and 3 (dashed line) extracted from measured BR( f )

Figure 5 - 2 :

 52 Figure 5-2: Internal energy distribution of 2 `(solid line) and 3 `(dashed line) extracted from measured BR( f )

Figure 5 - 4 :

 54 Figure 5-4: Internal energy deposit in 2 `by single electron excitation calculated by IAE/CTMC

Figure 5 -

 5 Figure 5-7: Calculated energy deposit in `without (solid line) and with (broken line) inclusion of the autoionizing states following single and multiple excitation in `-He collisions. The two curves have the same integral.

Figure 5 - 8 :

 58 Figure 5-8: Calculated energy deposit in 2 `without (solid line) and with (broken line) inclusion of the autoionizing states following single and multiple excitation in 2 `-He collisions. The two curves have the same integral.

Figure 5 -

 5 Figure 5-9: Calculated energy deposit in 3 `without (solid line) and with (broken line) inclusion of the autoionizing states following single and multiple excitation in 3 `-He collisions. The two curves have the same integral.

5. 2 . 4

 24 Comparison with the internal energy distribution deduced from experimental branching ratios In this section we compare the internal energy distributions calculated with IAE/CTMC with the distributions extracted with the use of the measured dissociation branching ratios BR( f ). The associated energy distributions (semiempirical distributions) are extracted as explained in the paper of IdBarkach et al. (2018) (see chapter 6). They are presented with solid lines, superimposed to the calculated distributions in Figure 5.10 and 5.11 for 2 `and 3 `respectively.

Figure 5 -

 5 Figure 5-10: Comparison between calculated (long dashed without and dotted with autoionizing states) and semiempirical (solid) internal energy deposits due to single and multiple excitation of 2 `in 2 `-He collisions. The three curves have the same integral.

Figure 5 -

 5  Comparison between calculated (long dashed without and dotted with autoionizing states) and semiempirical (solid) internal energy deposits due to single and multiple excitation of 3 `in 3 `-He collisions. The three curves have the same integral.

Fig. 1 .

 1 Fig. 1. Generic form of the G j function.

2. 3 .

 3 Breakdown curves of C 2 N, C 3 N, C 2 N + and C 3 N + molecules In the Fig. 3 are presented semiempirical breakdown curves for C 2 N, C 3 N, C 2 N + and C 3 N + . The way these BDC are constructed was explained in Section 2.1. For C 3 N the existence of a barrier of 0.4 eV along the C 3 + N reaction coordinate was taken into account by replacing the dissociation energy E diss of Fig. 1 by E diss + 0.4 eV. For cationic species the BDC curves start above the dissociation energy because, as mentioned before, the rate of intact cations is not measured in the experiment.

Fig. 2 .

 2 Fig. 2. Energy profile of the C 3 N( 4 A") → C 3 ( 1 Σ g + )+N( 4 S u ) reaction. Relative energy (eV) as a function of the reaction coordinate (a.u.) is computed at the B3LYP/6-311 + + G(3df,2p) level of theory and shown in black. The blue circles correspond to relative energies at the critical points in the reaction (reactant, transition state and products) computed at the CCSD(T)/6-311 + + G(3df,2p) level over the B3LYP geometry.

Fig. 3 .

 3 Fig. 3. Semiempirical BDC for C 2 N, C 3 N, C 2 N + and C 3 N + molecules.

Titre:

  Excitation et fragmentation des molécules C n N + (n = 1-3) en collision avec des atomes de He à vitesse intermédiaire; aspects fondamentaux et application à l'astrochimie. Mots clés: Molécules, Collisions, Rapports de branchement de fragmentation, Astrochimie, Sections efficaces, La méthode Monte Carlo de trajectoires classiques (CTMC).

Table

  The values are given in Table1.2.

	Molecule	Most probable	Standard deviation (eV) n electron affinity (eV)
		internal energy (eV)
	´0.28	0.28	3.86 (Bradforth et al., 1993)
	2 ´1.14	0.56	2.75 (Garand et al., 2009)
	3 ´1.99	0.74	4.31 (Graupner et al., 2006)
	4 ´2.84

Table 1 . 3

 13

		" p in `t q	14 26	`t		(1.6)
	Element Mass (u)	Run
	`26	March 2015	0.20		1.469	3.138	120.7	2.20
	2 `38	March 2015	0.18		2.191	4.562	120.0	2.19
	2 `38	Oct. 2016	0.17		2.186	4.542	119.5	2.19
	3 `50	Feb. 2016	0.18		2.943	6.066	121.3	2.20
	3 `50	Oct. 2016	0.17		2.942	6.054	121.1	2.20
	4 `62	Feb. 2016	0.18		3.673	7.526	121.4	2.20
	`14	Oct. 2016	0.18		1.083	1.761	125.8	2.24

The energy of `calculates in this case as (velocity is conserved): in pMeVq t (MeV) (MV) (keV u ´1) () : Voltages at the terminal for the production of iso-velocity n `species.

is calculated with Equation

1

.5, except for `with Equation

1

.6 (see text).

Table 2 .

 2 1: Mass calibration of " `" detector following Figure 2-3.

	pℎq " ˆpq	`
	" 13.30
	" ´17.33

Table 2 .

 2 3: Comparison between dissociation BR measured with the CCD camera and with the shape analysis method ( 2 `´ ) collision, October 2016 2.7 Probabilities and dissociation branching ratios

	2 `´

2.7.1 The normalisation procedure

  11)channel and t 2 u are occurrence probabilities of the considered channel and t 2 u where probabilities are calculated following Equation3.1 .. are background subtracted.

2.8 Absolute cross sections 2.8.1 The single collision condition

Table 2 .

 2

	Run	Flow rate (sccm) Flow rate corrected	jet (at{cm 2 )
			from offset (sccm) (relative error bar)
	`March 2015 2 `March 2015 3 `Feb 2016 3 `Feb 2016 `Oct 2016	0.6 1.1 1.1 0.25 1.1	0.53 1.03 1.03 0.18 1.03	2.77 ˆ10 13 p17%) 5.30 ˆ10 13 p14%) 5.28 ˆ10 13 p11%) 9.23 ˆ10 12 p14%) 4.62 ˆ10 13 p18%)

4: Measured jet in the experiments

Table 3 .

 3 3.

	Orbital	mod
	2p	-0.5345 -0.5346
	3s	-0.1548 -0.1541
	3p	-0.1004 -0.1009
	3d	-0.0568 -0.0581
	4s	-0.0621 -0.6240
	4p	-0.0472 -0.0474
	4d	-0.0319 -0.0326

Table 3 .

 3 1: Energy levels of mod compared to NIST values for atom.

	Orbital	mod
	2p	-1.0884 -1.0888
	3s	-0.4094 -0.4047
	3p	-0.3219 -0.3227
	3d	-0.2347 -0.2362
	4s	-0.1923 -0.1906
	4p	-0.1633 -0.1625
	4d	-0.1310 -0.1315

Table 3 .

 3 2: Energy levels of mod compared to NIST values for `atom.

	Projectile Z N	A	B	C
	6 6 1.964 7.136 0.840
	`6 5 1.904 0.808 2.518
	`7 6 2.634 0.899 3.194
	``7 5 2.401 1.264 3.238
	``6 4 2.044 1.256 3.202

Table 3 .

 3 3:The optimised A, B, C parameters for the projectile-electron model potential.

  3.2.2.5 p, q classical cross sections Beyond total probabilities for bound states within capture and (projectile and target) excitation, CTMC is able to provide state-selective, i.e p, q cross sections. However, one has first to link the continuous and || ⃗ || " ||⃗ ^⃗ || classical values to the quantized and numbers. Concerning || ⃗ || and , we simply state, following Rakovic et al. (2001) that all ´trajectory ending with ď || ⃗ || ă `1 belong to subshell.

Table 3 .

 3 5: Comparison between measured and calculated cross sections with 2 ´calculation for projectile ionization. All experiments are done at AGAT except * DuBois and[START_REF] Dubois | Single and double ionization of helium by neutral-particle to fully stripped ion impact[END_REF]

	Process	System	Formula	calc	Experiment
	N+ÑN	N+-He	2 c p1 ´c qp1 ´2s ion q 2 p1 ´2p ion q 2

Table 4 .

 4

	Process (final Q)	Cross section 2 (rel err) norm to proj. single ionization (rel. err)
	Projectile single ionization (Q=2)	2.29 10 ´16 p38%q	1
	Projectile double ionization (Q=3)	5.44 10 ´17 p38%q	0.24p26%q
	Projectile triple ionization (Q=4)	8.28 10 ´18 p36%q	0.04p26%q
	Projectile quadruple ionization (Q=5)	6.52 10 ´19 p38%q	2.8 10 ´3p34%q
	Projectile quintuple ionization (Q=6)	ď 3.10 10 ´20 p38%q	ď 1.3 10	´4
	Projectile dissociative excitation (Q=1)	9.44 10 ´17 p36%q	0.41p26%q
	Neutralization (Q=0) Anionic production (Q=-1)	4.15 10 ´17 p34%q 2.51 10 ´20 p42%q	0.18p22%q 1.10 10 ´4p46%q
	Table 4.1: Measured cross sections for various electronic processes in the `-
	(v= 2.2 au) collision; confidence in error bars: 95%.

2: Measured cross sections for various electronic processes in the 2 `-(v= 2.2 au) collision; confidence in error bars: 95%.

Table 4 .

 4

3: Measured cross sections for various electronic processes in the 3 `-(v= 2.2 au) collision; confidence in error bars: 95%.

Table 4 . 5 :

 45 2.3 by comparing the results obtained with a linear molecule Position of the atoms in the barycentre of the molecules and Mulliken charges.with those obtained with a cyclic (compact) molecule. Precise results concerning the positions of the atoms are given in Table4.5 and Figures 4.2 to 4.6. Also reported in this Table and Figures are the charges on each atom calculated by the Mulliken procedure and provided by the Gaussian package. Whereas the Mulliken procedure is

	Molecule (isomer) Atom X (au) Y (au) Z(au) Mulliken charge
	`iso1 (linear)	C	-1.11	0	0	0.995
			N	1.11	0	0	0.005
	2 `iso1 (linear)	C1	2.35	-0.245	0	0.46
			C2	-2.35	0.245	0	0.46
			N	6 10 ´5	5 10 ´4	0	0.08
	2 `iso3 (cyclic)	C1	0.79	-1.25	0	0.53
			C2	0.62	1.34	0	0.53
			N	-1.40	5 10 ´4	0	0.08
	3 `iso1 (linear)	C1	2.5 10 ´3 -1.29	0	0.26
			C2	-0.39	1.17	0	1.17
			C3	0.08	3.64	0	0.17
			N	0.30	-3.52	0	-0.60
	3 `iso5 (cyclic)	C1	-0.061	1.48	2 10 ´3	0.29
			C2	2.15	0.088	-0.038	0.59
			C3	0.061	-1.48 -2 10 ´3	0.29
			N	-2.15	-0.088	0.038	-0.17
	not expected to be very accurate (Wiberg and Rablen, 1993) we will only retain from
	these calculations that the positive charge of the cation is essentially shared between
	carbon atoms.	Because we need it for the calculation of the dissociation energies

in Chapter 5 we also present in Table

4

.6 the total energies calculated by N.Aguirre and S.Diaz-Tendero for various atoms and molecules of use in this work. The ZPE (zero point energy) is calculated as:

Table 4 .

 4 7: Role of the charge position on predicted cross sections; case of linear 3 `with CTMC 2 ´calculations.

	Process	Charge on C1 Charge on C2 Charge on C3	Average
	Single proj.	3.87 10 ´16	3.82 10 ´16	3.57 10 ´16	3.75 10 ´16
	ion. *
	Double proj.	1.46 10 ´16	1.44 10 ´16	1.45 10 ´16	1.45 10 ´16
	ion.*
	Triple proj.	4.37 10 ´17	4.52 10 ´17	5.08 10 ´17	4.66 10 ´17
	ion.*
	Total proj.	2.20 10 ´16	2.20 10 ´16	2.20 10 ´16	2.20 10 ´16
	Exc.*
	Single electron	7.79 10 ´17	7.76 10 ´17	7.82 10 ´17	7.79 10 ´17
	capture (SC)
	SC without	2.77 10 ´17	2.99 10 ´17	4.04 10 ´17	3.27 10 ´17
	proj.ion.
	Attachment	8.06 10 ´18	8.26 10 ´18	8.37 10 ´18	8.23 10 ´18
	Attachment without	2.70 10 ´18	2.79 10 ´18	2.31 10 ´18	2.60 10 ´18
	proj. ion
	Gain (SC + Attach.)	8.54 10 ´17	8.50 10 ´17	8.60 10 ´17	8.55 10 ´17
	Gain without	3.02 10 ´17	3.24 10 ´17	4.26 10 ´17	3.51 10 ´17
	proj. ion. (Neutralization)*
	Double electron	7.89 10 ´18	8.04 10 ´18	7.85 10 ´18	7.79 10 ´18
	capture (DC)
	DC without	2.48 10 ´18	2.75 10 ´18	3.61 10 ´18	2.95 10 ´18
	proj. ion. (Anionic production)*

Table

	Process	Charge on C1 Charge on C2 Charge on C3	Average	Cyclic/linear
	Single proj.	3.37 10 ´16	3.25 10 ´16	3.38 10 ´16	3.33 10 ´16	0.89
	ion. *
	Double proj.	1.43 10 ´16	1.41 10 ´16	1.42 10 ´16	1.42 10 ´16	0.98
	ion.*
	Triple proj.	5.19 10 ´17	5.42 10 ´17	5.21 10 ´17	5.27 10 ´17	1.13
	ion.*
	Total proj.	1.90 10 ´16	1.91 10 ´16	1.90 10 ´16	1.90 10 ´16	0.86
	Exc.*
	Single electron	7.81 10 ´17	7.78 10 ´17	7.77 10 ´17	7.79 10 ´17	1.00
	capture (SC)
	SC without	2.72 10 ´17	3.20 10 ´17	2.70 10 ´17	2.87 10 ´17	0.88
	proj.ion.
	Attachment	7.95 10 ´18	8.22 10 ´18	8.35 10 ´18	8.17 10 ´18	0.99
	Attachment without	2.33 10 ´18	2.24 10 ´18	2.41 10 ´18	2.33 10 ´18	0.89
	proj. ion
	Gain (SC + Attach.)	8.54 10 ´17	8.52 10 ´17	8.53 10 ´17	8.53 10 ´17	1.00
	Gain without	2.94 10 ´17	3.41 10 ´17	2.93 10 ´17	3.09 10 ´17	0.88
	proj. ion. (Neutralization)*
	Double electron	7.93 10 ´18	7.91 10 ´18	8.01 10 ´18	7.95 10 ´18	1.00
	capture (DC)
	DC without	2.50 10 ´18	2.78 10 ´18	2.43 10 ´18	2.57 10 ´18	0.87
	proj. ion. (Anionic production)*

Table 5 .

 5 .3 respectively. Details of the procedure may be found in IdBarach et al. (2018) (see chapter 6). 1: Measured dissociation BR of excited CN species produced by electron capture in `-He collisions; the first line refers to the BR for non fragmented (intact) species Channel BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)

	Channel BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	CN	0.43(0.02)		1	0.43(0.02)
	C +N	0.57(0.02)	7.32	2	0.57(0.02)
	2	0.36(0.02)		1	0.36(0.02)
	CN +C	0.45(0.02)	4.89	2	0.55(0.03)
	2 +N	0.10(0.01)	6.23
	C+C+N	0.09(0.02)	12.21	3	0.09(0.02)
	Table 5.2: Measured dissociation BR of excited 2 species produced by electron
	capture in 2 `-He collisions; the first line refers to the BR for non fragmented
	(intact) species
	Channel	BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	3	0.22(0.02)		1	0.22(0.02)
	3 +N	0.04(0.01)	5.57	2	0.46(0.05)
	2 +C	0.12(0.02)	6.60
	2 +CN	0.30(0.02)	5.51
	CN+C+C	0.17(0.03)	11.49	3	0.29(0.05)
	2 +N+C	0.12(0.02)	12.82
	N+C+C+C	0.03(0.01)	18.82	4	0.03(0.01)

Table 5 .

 5

3: Measured dissociation BR of excited 3 species produced by electron capture in 3 `-He collisions; the first line refers to the BR for non fragmented (intact) species.

Table 5 .

 5 2 we will compare these distributions to energy 123 deposit calculations performed within the IAE/CTMC model. Channel BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)

	`+ N	0.53(0.05)	4.85	2	1(0)
	C + `0.47(0.05)	8.14
	Table 5.4: Measured dissociation BR of excited `species produced by projectile
	electronic excitation in `-He collisions
	Channel BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	CN+ `0.218(0.015)	6.39	2	0.47(0.03)
	C+ `0.145(0.007)	8.86
	2 + `0.025(0.002)	11.02
	N+ 2	0.086(0.004)	8.24
	C+C+ `0.112(0.005)	17.01	3	0.53(0.03)
	C+N+ `0.414(0.03)	13.71
	2 + +C	0.148(0.003)	4.52	2	0.40(0.03)
	2 +CN	0.086(0.007)	5.43
	`+ 2	0.064(0.005)	6.02
	3 +N	0.052(0.002)	5.45
	`+ 2	0.033(0.003)	7.40
	`+ 3	0.012(0.0015)	8.28
	`+CN +C	0.14(0.01)	10.91	3	0.41(0.03)
	`+ 2 +N	0.076(0.006)	12.25
	2 +N +C	0.108(0.008)	12.76
	`+C+C	0.053(0.005)	13.38
	`+ 2 +C	0.038(0.003)	15.54
	`+N+C+C 0.155(0.011)	18.23	4	0.19(0.02)
	`+C+C+C	0.03(0.003)	21.53

5: Measured dissociation BR of excited 2 `species produced by projectile electronic excitation in 2 `-He collisions Channel BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)

Table 5

 5

.6: Measured dissociation BR of excited 3 `species produced by projectile electronic excitation in 3 `-He collisions

  3 `-He collisions, to do a separate configuration with a detector at current shape recognition: no ``fragment was detected.Table5.7: Measured dissociation BR of excited ``species produced by projectile single ionisation in `-He collisions; the first line refers to the BR for non fragmented (intact) species; negative dissociation energies correspond to exothermic channels.*: the sum of BR for `+ `and ``dissociation is measured.

	Channel	BR (abs.err) Dissociation Energy (eV)	f	BR( f ) (abs.err)
	``Not measured		1
	`+ `(+ ``)	0.91(0.02)	-4.5	2(1)
	``+ N	0.052(0.015	4.3
	C + ``0.024(0.005)	14.0
	Channel	BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	2 ``0.082(0.004)		1	0.082(0.004)
	`+ `0.476(0.046)	-1.03	2	0.52(0.05)
	2 + `0.041(0.002)	1.64
	CN + ``8.6		1.15e-3(1.3e-4)
	2 + ``2e-4(6e-5)	19.5
	C + `+ `0.216(0.033)	7.11	3	0.40(0.04)
	N + `+ `0.174(0.010)

Table 5 .

 5 8: Measured dissociation BR of excited 2 ``species produced by projectile single ionisation in 2 `-He collisions; the first line refers to the BR for non fragmented (intact) species; negative dissociation energies correspond to exothermic channels.

	Channel	BR (abs.err)	Dissociation Energy (eV) f BR( f ) (abs.err)
	3 ``0.03(3 e-3)		1	0.03(3 e-3)
	2 `+ `0.378(0.026)	-3.0	2	0.46(0.03)
	2 + `0.05810(6 e-3)	0.4
	3 + `0.026(1.8 e-3)	1.24
	`3 +N	1.145 e-3(1.14 e-4)	7.0
	2 ``+C	6.574 e-4(6.6 e-5)	6.9
	``+ 2	7.413 e-5(7.4 e-6)	10.6
	``+ 3	3.97 e-5(6 e-6)	19.2
	2 `+CN	0.075 (6 e-3)	3.5	3	0.28(0.02)
	`+ 2 +N	0.072 (5 e-3)	5.2
	`+ `+C	0.057 (4.6 e-3)	5.9
	2 + `+C	0.041(3 e-3)	8.5
	`+ `+ 2	0.03(2.4 e-3)	8.1
	( ``+ 2 +N)+
	( ``+CN +C)	8.4e-4(7 e-5)
	``+ 2 +C	1.85 e-4(1.8 e-5)	26.4
	2 `+C +N	0.133(0.011)	10.8	4	0.23(0.02)
	`+ `+2C	0.095(8 e-3)	14.0
	``+2C +N	1.56 e-3(1.2 e-4)	23.9
	``+3C

Table 4

 4 .6 (chapter 4) and experimental electron affinities (seeTable 5.19).

	Channel BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	´ě0.97 ´+N ď0.03	9.92	1 2	ě0.97 ď0.03

Table 5 .

 5 16: Measured dissociation BR of excited ´species produced by double electron capture in `-He collisions; the first line refers to the BR for non fragmented (intact) species.

	Channel	BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	2 ´0.40(0.04)		1	0.40(0.04)
	´+C	0.51(0.06)	3.8	2	0.58(0.09)
	CN+ ´6.34	0.07(0.02)
	2 +N ´+C+N	ď0.02 0.02(0.01)	4.24 14.3	3	0.02(0.01)

Table 5 .

 5 17: Measured dissociation BR of excited 2 ´species produced by double electron capture in 2 `-He collisions; the first line refers to the BR for non fragmented (intact) species.

	Channel	BR (abs.err) Dissociation Energy (eV) f BR( f ) (abs.err)
	3 ´0.09(0.01)		1	0.09(0.01)
	´+ 2	0.69(0.06)	6.24	2	0.90(0.03)
	2 +CN	0.16(0.06)	6.83
	2 ´+C	0.05(1e-3)	8.44
	( ´+C+CN)+( ´+N+ 2 )	ď0.02	14.82 and 16.5	3	ď0.02

Table 5 .

 5 18: Measured dissociation BR of excited 3 ´species produced by double electron capture in 3 `-He collisions; the first line refers to the BR for non fragmented (intact) species.

Table 5 .

 5 20: Energies of reachable states in carbon atom starting from the ground state 2 2 2 2 3 0 . Ionisation potential of C is 11.26 eV; states with a star are autoionizing. From NIST database.

	3 (7.48)

Table 5 .

 5 21: Energies of reachable states in the `ion starting from the ground state 2 2 2 2 1{2 . Ionisation potential of `is 24.38 eV; states with a star are autoionizing. From NIST database.

Table 1

 1 Electronic ground states (GS) and symmetry point groups (Sym.) of atoms and molecules studied in this work. Reported results are for the lowest energy isomers except CCN which is 0.08 eV above CNC and CCN + which is 1.09 eV above CNC + .

	Species	C	N	C 2		CN	CNC	CCN	C 3		C 3 N
	GS Sym.	3 P g atom	4 S u atom	1 Σ g + D∞h	2 Σ + C∞v	2 Π g D∞h	2 Π C∞v	1 Σ g + D∞h	2 A′ Cs
	Species	C +	N +	C 2	+	CN +	CNC +	CCN +	C 3	+	C 3 N +
	GS Sym.	2 P u atom	3 P g atom	4 Σ g -D∞h	1 Σ + C∞v	1 Σ g	+ D∞h	1 Σ C∞v	2 B 2 C2v	3 A" Cs

Table 2

 2

Table 3

 3 Same legend as Table2for the excited C 3 N molecule.

	Channel j	BR j (abs.err)	Dissociation energy (eV)	N f	BR(N f )(abs.err)
	C 3 N	0.22(0.02)		1	0.22(0.02)
	C 3 + N	0.04(0.01)	5.57	2	0.46(0.05)
	C 2 N + C	0.12(0.02)	6.6
	C 2 + CN	0.30(0.02)	5.51
	CN + C + C	0.17(0.03)	11.49	3	0.29(0.05)
	C 2 + N + C	0.12(0.02)	12.82
	N + C + C + C	0.03(0.01)	18.82	4	0.03(0.01)

Table 4

 4

Table 5

 5 Same legend as Table4for the excited C 3 N + molecule.

	Channel j	BR j (abs.err)	Dissociation energy	N f BR(N f )(abs.err)
				(eV)
	C 2 N + + C	0.148(0.003)	4.52	2	0.40(0.03)
	C 2	+ + CN	0.086(0.007)	5.43
	C + +C 2 N	0.064(0.005)	6.02
	C 3	+ + N	0.052(0.002)	5.45
	CN + +C 2	0.033(0.003)	7.4
	N + +C 3	0.012(0.0015) 8.28
	C + + CN + C	0.14(0.01)	10.91	3	0.41(0.03)
	C + +C 2 + N	0.076(0.006)	12.25
	C 2	+ + N + C	0.108(0.008)	12.76
	CN + + C + C	0.053(0.005)	13.38
	N + +C 2 + C	0.038(0.003)	15.54
	C + + N + C + C 0.155(0.011)	18.23	4	0.19(0.02)
	N + + C + C + C 0.035(0.003)	21.53

Table 7

 7 Branching ratios (BR) for Neutral-Neutral reactions. E a represents the internal energy of the neutral adduct and ΔE the exothermicity of the reaction. * : the reaction cannot proceed through the electronic ground state of the adduct lowest energy isomer.

	Reactants	Products	Model BR (abs.err)	KIDA BR	E a (eV)	ΔΕ (eV)
	C 2 +N	C + CN*	1	1	6.23	1.34
	CNC + C	C 2 + CN	0.90(0.05)		6.6	1.09
		C 3 + N*	0.10(0.05)			0.63
	CCN + C	C 2 + CN	0.90(0.05)	1	6.68	1.17
		C 3 + N*	0.10(0.05)			0.71

Table 8

 8 Branching

	Reactants	Products	Model BR (abs.err)	KIDA BR E a (eV) ΔΕ (eV)
	C 2	+ +N	C + +CN	1	1	8.24	1.85
	CN + +C	C + + CN*	0.72(+ 0.07/-0.05) 1	8.86	2.47
			C 2 + + N*	0.28(+ 0.05/-0.07)			0.62
	N + +C 2	CN + + C*	0.40(0.05)		11.02	2.16
			C + + CN*	0.39(0.05)			4.63
			C 2 + + N*	0.21(0.04)	1		2.78
	C 3	+ +N	[C 2 N + ]+C	1		5.45	0.93
	C 2	+ +CN	[C 2 N + ]+C	1		5.43	0.91
	C + + CNC [C 2 N + ] + C	0.58(0.06)		6.02	1.5
			C 2 + + CN	0.30(0.06)			0.59
			C 3 + + N	0.12(0.04)			0.57
	C + + CCN [C 2 N + ] + C	0.58(0.06)	0.7 ¤	6.1	1.58
			C 2 + + CN	0.30(0.06)	0.3		0.67
			C 3 + + N	0.12(0.04)			0.65
	CN + +C 2	[C 2 N + ]+C ¶	0.35(+ 0.03/-0.35)		7.4	2.88
			C 2 + +CN ¶	0.28(+ 0.03/-0.28) 1		1.97
			C + +[C 2 N]* 0.23(+ 0.77/-0.03)			1.38
			C 3 + +N ¶	0.12(+ 0.02/-0.12)			1.95
	N + +C 3	[C 2 N + ] + C	0.33(+ 0.15/-0.04)		8.28	3.76
			C 2 + + CN	0.25[+ 0.15/-0.03)			2.85
			C + +[C 2 N]	0.22(+ 0.14/-0.03)			2.26
			C 3 + + N	0.11(+ 0.13/-0.02)			2.83
			CN + +C 2 ¶	0.09(+ 0.02/-0.09)			0.88

ratios (BR) for Ion-molecule reactions. E a represents the internal energy of the ionic adduct and ΔE the exothermicity of the reaction. ¤ : this value corresponds to the sum of the two isomers CNC + and CCN + .*:t h e reaction cannot proceed through the electronic ground state of the adduct lowest energy isomer ; ¶ : the reaction is spin forbidden for ground state reactants towards ground state products.

Table 9

 9 Branching ratios (BR) for dissociative recombination. E a represents the internal energy of the neutral adduct and ΔE the exothermicity of the reaction. ¶ : the reaction is spin forbidden for ground state reactants towards ground state products.

	Reactants	Products	Model BR (abs.err)	KIDA BR E a (eV) ΔΕ (eV)
	CNC + +e -C + CN	0.77(+ 0.23/-0.03) 0.95	9.66	4.77
		C 2 +N ¶	0.23(+ 0.03/-0.23) 0.05		3.43
	CCN + +e -C + CN	0.77(+ 0.23/-0.03) 0.95	10.67	5.78
		C 2 +N ¶	0.23(+ 0.03/-0.23) 0.05		4.44
	C 3 N + +e -	C 2 + CN	0.56(0.05)	1	11.76	6.25
		C+[C 2 N]	0.32(0.03)			5.16
		C 3 + N	0.09(0.02)			5.79
		C + C + CN 0.03(0.02)			0.27

Table 10

 10 Branching ratios (BR) following charge exchange reactions in collisions of CNC, CCN and C 3 N with He + .E a values give the internal energies of the adducts CNC + , CCN + and C 3 N + after charge exchange and ΔE are the exothermicities of the reactions.

	Reactants	Products (+ He) Model BR	KIDA BR E a (eV) ΔΕ (eV)
				(abs.err)
	CNC + He + C + + C + N	0.30(0.15)	14.93	1.22
		C + + CN	0.25(0.10)		8.54
		CN + + C	0.25(0.07)		6.07
		C 2	+ + N	0.15(0.05)		6.69
		N + +C 2	0.05(0.02)		3.91
	CCN + He + C + +C+N	0	13.92	0.21
		C + + CN	0.38(0.05)	1	7.53
		CN + + C	0.38(0.05)		5.06
		C 2	+ + N	0.20(0.03)		5.68
		N + +C 2	0.04(0.02)		2.9
	C 3 N+He +	C + + C + CN	0.25(0.04)	12.81	1.9
		C 3	+ + N	0.18(0.04)		7.36
		[C 2 N + ] + C	0.15(0.07)		8.29
		CN + +C 2	0.14(0.03)		5.41
		C 2	+ + CN	0.12(0.06)	1	7.38
		C + +[C 2 N]	0.09(0.05)		6.79
		N + +C 3	0.03(0.01)		4.53
		C + +C 2 + N	0.02(0.01)		0.56

outgoing channel as compared to the C + [C 2 N] of near exothermicity.

Table A . 1

 A1 Values of the E diss ,E sat ,E disap and E end quantitites entering in the G j functions for all channels j of each molecule.

	Molecule	Channel j	E diss (eV)	E sat (eV)	E disap (eV)	E end (eV)
	C 2 NC 2 N		0	0.01	4.89	5.39
		CN + C	4.89	5.39	12.21	13.71
		C 2 + N	6.23	6.73	12.21	13.71
		C + C + N	12.21	13.71	40	42.5
	C 3 NC 3 N		0	0.005	5.51	5.515
		C 3 + N	5.97	6.47	12.82	14.32
		C 2 + CN	5.51	6.01	11.49	12.99
		C 2 N + C	6.6	7.1	11.49	12.99
		CN + C + C	11.49	12.99	18.82	21.32
		C 2 + N + C	12.82	14.32	18.82	21.32
		N + C + C + C	18.82	21.32	40	42.5
	C 2 N +	CN + C +	6.39	6.89	13.71	15.21
		N+C 2	+	8.24	8.74	13.71	15.21
		C+CN +	8.86	9.36	13.71	15.21
		C 2 +N +	11.02	11.52	17.01	18.51
		C+N+C +	13.71	15.21	40	42.5
		C+N + + C	17.01	18.51	40	42.5
	C 3 N +	C 2 N + + C	4.52	4.57	10.91	12.41
		C 3	+ + N	5.45	5.95	12.25	13.75
		C 2	+ + CN	5.43	5.93	10.91	12.41
		C + +C 2 N	6.02	6.52	10.91	12.41
		CN + +C 2	7.4	7.9	12.25	13.75
		N + +C 3	8.28	8.78	15.54	17.04
		C + + C + CN	10.91	12.41	18.23	20.73
		C + +C 2 + N	12.25	13.75	18.23	20.73
		C 2	+ + N + C	12.76	14.26	18.23	20.73
		CN + + C + C	13.38	14.88	18.23	20.73
		N + +C 2 + C	15.54	17.04	21.53	24.03
		C + + N + C + C	18.23	20.73	40	43.5
		N + + C + C + C	21.53	24.03	40	43.5

  Thanks to the development of a versatile new source of cations at the terminal of the Tandem accelerator in Orsay, we should be able to work on more pertinent candidates in the future. 151 B.2 Relaxation by IPD of { 2 `} species (Q=0,1,2,3)Table B.1: Measured branching ratios within ion pair dissociation of 2 excited species. For IPD branching ratios within Q=0 total dissociation, multiply all values by 6.1e-4 (3e-4). Table B.2: Measured branching ratios within ion pair dissociation of 2 `excited species. For IPD branching ratios within Q=1 total dissociation, multiply all values by 1.6e-4 (0.3e-4). * the energetical cost is 27.01 eV for ´+ `+ `and 31.4 eV for ´+ Table B.3: Measured branching ratios within ion pair dissociation of 2 ``excited species. For IPD branching ratios within Q=2 total dissociation, multiply all values by 1e-5 (0.5e-5). Table B.4: Measured branching ratios within ion pair dissociation of 2 ```e xcited species. For IPD branching ratios within Q=3 total dissociation, multiply all values by 2.3e-6 (1.2e-6).B.3 Relaxation by IPD of { 3 `} species (Q=0,1,2,3) TableB.5: Measured branching ratios within ion pair dissociation of 3 excited species. For IPD branching ratios within Q=0 total dissociation, multiply all values by 2.1e-4(1.2e-4).TableB.6: Measured branching ratios within ion pair dissociation of 3 `excited species. For IPD branching ratios within Q=1 total dissociation, multiply all values by 2.2e-4 (0.7e-4).TableB.7: Measured branching ratios within ion pair dissociation of 3 ``excited species. For IPD branching ratios within Q=2 total dissociation, multiply all values by 1.2e-4 (0.2e-4).

	Channel	Channel Experimental BR Required energy of Experimental BR
		(abs. err)	(abs. err)	3 `(eV)
	Channel ´+ ``+ ``1(0) Experimental BR Required energy of ´+C + `+ `0.40(0.07) 31.4
	(abs. err) ´+N +2 `0.28(0.07)		2 (eV) 28.1
	´+ `0.77(0.22) 2 + `+ `0.15(0.02)		12.3 23.4
	´+C + `0.08(0.07) ´+2 `0.08(0.03)		25.5 18.2
	´+ `ď0.08 ´+ 2 + `0.05(0.01)		17.3 26.0
	´+N + `ď0.12 ´+ `+ `ď0.08		22.2 23.3
	2 + `0.04(0.004)		17.5
	Channel	Experimental BR Required energy of
	Channel	Experimental BR Required energy of (abs. err) 3 ``(eV)
	(abs. err) ´+2 `+ `0.96(0.03)	2 `(eV) 23.9
	´+{ ``} 0.96(-0.06/+0.04) Channel Experimental BR Required energy of 27.01/31.4* ´+N + `+ ``0.02(0.01) 33.8
	´+C + ``0.018 (0.002) (abs. err) ´+C + `+ ``0.01(6e-3)	45.3 3 (eV) 42.3
	´+ ``0.016 (0.015) ´+C + `0.27(0.01) ´+C + `+ ``ď0.01		26.9 18.81 37.1
	´+N + ``ď0.008 ´+C +N + `0.19(0.08)		36.8 28.74
	2 +N + `0.12(0.01)		20.73
	2 +C + `0.03(0.02)		24.02
	``Channel ´+ 2 `ď0.27 Experimental BR Required energy of 15.0 ´+CN + `ď0.19 Channel Experimental BR 21.41 ´+C + `ď0.11 (abs. err) 23.88 ´+ `+ `+ ``0.84(0.20)
	(abs. err) ´+ `+ ``0.73(0.27) ´+N + 2 ´+2C + `ď0.10 ď0.10 ´+2 `+ ``0.16(0.14) 2 ``(eV) 29.2 32.03 23.24
	´+ `+ ``0.27(0.27) ´+ 2 ď0.01		35.4 13.33

  TableB.8: Measured branching ratios within ion pair dissociation of 3 ```e xcited species. For IPD branching ratios within Q=3 total dissociation, multiply all values by 5.8e-5(2.6e-5).

  Dans cette thèse nous avons étudié des collisions entre des projectiles C n N + (n=0,1,2,3) et des atomes d'Hélium à vitesse intermédiaire(2.25 u.a). A cette vitesse, proche de la vitesse des électrons sur les couches de valence externe des atomes et molécules, de nombreux processus électroniques prennent place avec une forte probabilité: ionisation (simple et multiple), excitation électronique, capture d'électron (simple et double). Nous avons mesuré les sections efficaces absolues de tous ces processus. Un autre aspect intéressant de la collision concerne la fragmentation des molécules excitées, que nous avons également mesurée précisément grâce à un dispositif dédié. Les expériences ont été effectuées auprès de l'accélérateur Tandem d'Orsay avec des faisceaux de quelques MeV d'énergie cinétique. Le dispositif AGAT a permis de réaliser les collisions (en condition de collision unique) et de mesurer tout à la fois les sections efficaces des processus et la fragmentation associée. Parallèlement nous avons simulé ces collisions d'un point de vue théorique en utilisant le modèle à Atomes et Electrons Indépendants (IAE) couplé à des calculs CTMC (Classical trajectory Monte Carlo). Sur cette base, nous avons prédit les sections efficaces qui se sont trouvées être en bon accord avec les mesures, à l'exception de la double capture d'électrons. Par ailleurs les rapports de branchement de dissociation des C n N + après excitation électronique sont bien reproduits en utilisant la distribution d'énergie interne des espèces calculées avec le même modèle IAE/CTMC. Ces expériences nous ont permis de construire des « Breakdown Curves » (BDC), véritables cartes d'identité des molécules qui permettent de prévoir, dans le cadre d'une fragmentation statistique comment va fragmenter un système dont on connait l'énergie interne. Avec ces BDC nous avons pu prédire et recommander des rapports de branchement pour des voies de sortie de processus physiques et chimiques d'intérêt astrochimique. Ces données seront insérées dans la base internationale d'astrochimie the Kinetic Data Base for Astrochemistry KIDA. Cette thèse a été réalisée dans le cadre de l'École Doctorale Ondes et Matière (EDOM) à l'Institut des Sciences Moléculaires d'Orsay (ISMO), à l'Université Paris-Sud (Université Paris Saclay). Excitation and fragmentation of C n N + (n=1-3) molecules in collisions with He atoms at intermediate velocity; fundamental aspects and application to astrochemistry. Molecules, Collisions, Fragmentation branching ratios, Astrochemistry, Cross sections, Classical Trajectory Monte Carlo.

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" 0.99 where 2 is the goodness of fit.

Acknowledgements

Acknowledgements

Chapter 4

Results on cross sections

Experimental results on cross sections

The experimental results for the cross sections will be presented in this chapter. To recall the experimental conditions, the collision velocity is 2.2 a.u with the projectiles being n `(n=1,2,3) molecules with the target He atom.

In Tables 4.1 to 4.3 are presented experimental cross sections for various electronic processes measured in `-, 2 `´ and 3 `´ collisions. Also reported from Chapter 3 the results obtained with the atomic ions `and `in Table 4.4. The considered processes are projectile ionization, projectile dissociative excitation, neutralization and projectile anionic production. What is measured in the experiment is the projectile charge after the collision. This observable covers in fact multi-electron processes (for instance neutralization is electron capture without projectile ionization; projectile excitation is without projectile ionization but includes electron capture with single projectile ionization) that are estimated within the IAE/CTMC model. In order to compare to this modelling we give in Tables 4.1 to 4.3 experimental error bars "at two sigma" (i.e with 95% confidence).

The single ionization (SI) cross sections are of the order of a few 10 ´16 2 which is the dominant process. The cross sections show an increasing trend in their absolute value as the size of the molecule increases. This can be attributed to the increase in the individual atomic centres, each contributing to the process. This trend is not "

Where i are the vibrational frequencies in the molecule.

The role of the charge position

In the IAE code, only integers can be introduced for the charges carried out by the atoms. In the n `atomic representation of the molecule, the Nitrogen atom has been taken as neutral and the positive charge carried out by one of the carbon atom.

We looked at the effect of the charge position on the results of the IAE/CTMC predicted cross sections. In

Appendix

In this appendix, we give in the Table A-1 the values of E diss ,E sat ,E disap ands E end used for the construction of the G j functions for all j channels of each molecule. These quantities are calculated or derived from theoretical work (see text).

Appendix A CTMC probabilities in , `, , `, -He collisions (v=2.25 a.u)

In this appendix, we present the CTMC probabilities used in the IAE model for extracting cross sections of Chapter 4. All probabilities are given by electron. On the same figure pq is also reported. In red are presented analytical fits used in the code.

Appendix B

Ion pair dissociation (IPD) branching ratios B.1 Relaxation by IPD of { `} species (Q=0,1)

IPD dissociation of CN gives

´/ `only. The BR with respect to total dissociation of CN is 1.8 e-4 (0.9e-4). The required energy of CN is 20.6 eV.

IPD dissociation of `gives ´{ ``only. The BR with respect to total dissociation of `is 1.1 e-5 (0.7e-5). The required energy of `is 36.5 eV.

List of Tables