High order cross derivative computation for the differential cross section of double ionization of helium by electron impact

The double ionization of an atom or a molecule is strongly dependent of the quality of the description of the initial state of the target. Recently, absolute measurements have been reported for the double ionization of helium by 5.6 keV electron-impact. Since the incident (and scattered) electron is very fast, one may apply the usual first Born approximation. Calculations with the first Born approximation lead to an overall magnitude that is about 50% larger than experiment when a simple (one term) Hylleraas wavefunction describes the initial state. Two numerical approaches are available to tackle an accurate (18 terms) Hylleraas wavefunction: a 6-dimensional numerical quadrature (expensive in computer time), or a 2-dimensional quadrature applied to high order cross derivatives (up to the order 9). Automatic differentiation tecnhiques allow for high order derivative computations. Nevertheless existing differentiation tools do not deal with codes written in complex arithmetics and explicit cross derivative computations. This paper first describes the high order differentiation (based on recursive rules) and the extraction of cross derivatives. An operator oveloading library is constructed for the differentiation work. Numerical results, obtained at a lower cost than the sextuple integral, show the pertinence of our approach

Etudes en structures électroniques par collisions (e,2e) asymétriques

Not availableDans le cas de la collision asymétrique (électron diffuse beaucoup plus rapide que l'électron éjecté), on peut négliger les effets d'échanges quantiques qui proviennent de l'indiscernabilité des électrons et, en régime impulsionnel, atteindre la structure électronique de la cible en déterminant la densité d'impulsion, simplement proportionnelle à la section efficace triplement différentielle mesurée. Pour les conditions hors du régime impulsionnel, établissement d'un modèle basé sur une méthode de type perturbation, dont le 1er terme représente la situation impulsionnelle. Obtention d'une convergence rapide malgré l'importance de la correction à réaliser et reproduction des résultats expérimentaux connus sur He, Ne et Ar, et des maximums de la surface de Bethe-Ehrhardt. Extension possible à des énergies incidentes plus basse

Etude de l'ionisation de la molécule d'eau par impact d'ions

Nous avons étudié dans cette thèse l ionisation de la molécule d eau par des ions chargés (H+, He2+ et C6+ ). Trois modèles théoriques ont été développés afin de prendre en compte les diverses interactions coulombiennes existant entre la particule diffusée, l électron éjecté et la molécule d eau ionisée. Dans ce travail nous avons utilisé une fonction d onde monocentrique développé par Moccia pour décrire l état fondamental de la molécule d eau. Les résultats de nos modèles sont comparés aux diverses expériences existant sous la forme de sections efficaces doublement différentielles, sections efficaces simplement différentielle et sections efficaces totales.The ionisation of water molecule by ions (H+, He2+ et C6+) has been studied in this work. Three theoretical models have been investigated in order to take into account for the coulomb interactions between the scattered particle, the ejected electron and the ionised water molecule. We have used a one-center molecular wave function developed by Moccia to describe the initial state of the water molecule. The theoretical results have been compared to different experiments such as double differential, simple differential and total cross sections.METZ-SCD (574632105) / SudocSudocFranceF

Etude de la double ionisation d'atomes par impact d'électrons (élaboration et utilisation du modèle A6C)

Ce travail concerne l étude théorique de la double ionisation d atomes par impact d électrons. Nous avons élaboré un modèle tenant compte des phénomènes d échange possible entre l électron diffusé et les électrons de la cible concernés qui seront éjectés lors de la collision. Chaque électron dans la voie finale (électron diffusé et éjectés) est décrit par une onde coulombienne tenant compte de son interaction continuelle avec le noyau résiduel. Les interactions répulsives entre électrons sont prises en compte par des facteurs de Gamow (modèle A6C). Une première partie est consacrée à l étude de la double ionisation de l hélium où une comparaison avec les résultats du groupe d Orsay (Pr. A. LAHMAM-BENNANI) est effectuée. Puis dans une deuxième partie notre modèle est confronté aux dernières expériences du même groupe d Orsay qui sont relatives à la double ionisation directe de l argon associé à l effet Auger.This work is about the theoretical study of the double ionization of atoms by electron impact. A model including exchange effects between the incoming electron and the two active electrons of the target is described. Each electron in the continuum (the scattered one and the two ejected ones) is described by a coulomb wave which takes into account for the interaction with the residuel nucleus. The interactions between each electron in the continuum have been included by Gamow factors (A6C model). A first part is about the double ionisation of helium and a comparison has been made with recent experiments of LAHMAM-BENNANI et al. then, in a second part, our model has been compared to the recent experiments of LAHMAM-BENNANI et al about the double ionization of argon (direct double ionization + Auger effect).METZ-SCD (574632105) / SudocSudocFranceF

High order cross derivative computation for the differential cross section of double ionization of helium by electron impact

The double ionization of an atom or a molecule is strongly dependent of the quality of the description of the initial state of the target. Recently, absolute measurements have been reported for the double ionization of helium by 5.6 keV electron-impact. Since the incident (and scattered) electron is very fast, one may apply the usual first Born approximation. Calculations with the first Born approximation lead to an overall magnitude that is about 50% larger than experiment when a simple (one term) Hylleraas wavefunction describes the initial state. Two numerical approaches are available to tackle an accurate (18 terms) Hylleraas wavefunction: a 6-dimensional numerical quadrature (expensive in computer time), or a 2-dimensional quadrature applied to high order cross derivatives (up to the order 9). Automatic differentiation tecnhiques allow for high order derivative computations. Nevertheless existing differentiation tools do not deal with codes written in complex arithmetics and explicit cross derivative computations. This paper first describes the high order differentiation (based on recursive rules) and the extraction of cross derivatives. An operator oveloading library is constructed for the differentiation work. Numerical results, obtained at a lower cost than the sextuple integral, show the pertinence of our approach

Double ionization of neon by electron impact: use of correlated wave functions

A model including correlation both in the initial state and in the final state is applied to the case of the double ionization of neon. The results of our model are compared to the available experimental data performed at high incident energy. Fully (fivefold) differential cross sections (FDCS) have been studied by applying the first Born approximation. Four ion states of Ne++, which are not resolved in the experiments, have been included in our calculation

Theoretical study of (e, 2e) process of atomic and molecular targets

Triple differential ionization cross sections (TDCSs) by electron impact are calculated for some atomic and molecular targets by using several models where Post Collisional Interaction (PCI) is taken in account. We also investigate the effect of the short range potential and describe the ejected electron either by a Coulomb wave or by a distorted wave. Significant differences are observed between these models. A better agreement with experimental data is achieved when the short range potential and distortion effects are included

Ionization of phenol by single electron impact: triple differential cross sections

International audienceTriple differential cross sections (TDCS) for the ionization by single electron impact of the highest and next-highest occupied molecular orbitals of phenol are provided in this work. A first Born approach is used, describing the ejected electron by a distorted wave. The molecular wave functions are developed in a single-center form using the computational chemistry program Gaussian. The TDCSs are calculated for an unknown molecular orientation with the proper average (PA) approach and using four different models. In the distorted wave model (DW) the atoms positions do not intervene in the interaction potential between the incoming electron and the molecular target, while in the distorted wave multi-center model (DW-MC) they are taken into account. In the DW-Gamow and the DW-MC-Gamow models, the repulsion between the outgoing electrons is described by adding the Gamow factor to the DW and DW-MC models. In general, all results are in good agreement with the experimental data. A small difference is observed between the DW and DW-MC results in the recoil region. Adding the Gamow factor improves the angular position and the relative amplitude of the two peaks observed in the binary region. When the TDCSs are compared to other theoretical results relying on the orientation averaged molecular orbital (OAMO) approximation, the improved agreement with the experimental data reinforces the importance of the PA approach