This thesis presents an extensive computational study of electron-impact scattering and ionisation of atomic hydrogen and hydrogenic ions, which are fundamental to many diverse disciplines, from astrophysics and nuclear fusion to atmospheric physics. The non-relativistic Schrodinger equation describes these collisions, though finding solutions for even hydrogen, the simplest electron-atom collision, has proven to be a monumental task. Recently, Rescigno et al [Science 286, 2474 (1999)] solved this equation in coordinate space using exterior complex scaling (ECS), and presented the first electron-hydrogen differential cross sections for ionisation that matched with experiment without requiring uncontrolled approximation. This method has significant potential for extension to larger collision systems, but its large computational demand has limited its energy range and target configurations, and its application to discrete final-state collisions has been largely unexplored. Using radically different numerical algorithms, this thesis develops methods that improve the computational efficiency of ECS by two orders of magnitude. It extends the method to calculate discrete final-state scattering cross sections and enhances the target description to include hydrogenic ions and excited initial states. In combination, these developments allow accurate solutions over a broad range of energies and targets, for both scattering and ionisation, including the important near-threshold energy region where accurate calculations have been unavailable. The refined ECS method implemented in this work now offers complete numerical solutions of electron-hydrogen collisions, and its computational efficiency will facilitate its future application to more complex targets. The thesis culminates with the first ab initio quantum mechanical confirmation of ionisation threshold laws for electron-hydrogen collisions [Bartlett and Stelbovics, 2004, Phys. Rev. Lett. 93, 233201], which have resisted confirmation through the complete solution of the Schrodinger equation for more than half a century.

Neste trabalho implementamos um programa computacional capaz de descrever passo-a-passo o processo de colisão entre dois átomos confinados numa armadilha magneto-óptica em regime frio. Para isso utilizamos o formalismo de Wigner, que é uma formulação equivalente à mecânica quântica, para encontrar-mos uma aproximação quase-clássica para as equações que descrevem o sistema. Este formalismo permite-nos separar os graus de liberdade externos dos átomos colidentes, que podem ser tratados de maneira quase-clássica, dos graus internos de liberdade, os quais não tem contraparte clássica e, portanto, são tratados quanticamente / In this work we implement a computer program that describes, step by step, the collision process between two atoms confined in a magneto-optical trap in the cold regime. Here we utilize the Wigner-function theory, which is a formulation of quantum mechanics in terms of a phase space, to find a quasi-classical approx¬imation of the dynamical equations that govern the time evolution of the system. This approach allows us to describe the dynamics in terms of external and internal degrees of freedom. The former degrees of freedom are treated quasi-classically, while the latter, because they do not have a classical counterpart, are treated quan¬tum mechanically

Neste trabalho estudamos o processo de foto-ionização associativa(PAI) em uma amostra fria de átomos de sódio com o objetivo entender os efeitos dos estados repulsivos e dimensão da colisão. Realizamos experimentos de PAI com duas cores em uma armadilha magneto-óptica adicionando um feixe de prova com intensidade, frequências e polarização ajustáveis. O formato dos átomos aprisionados também foi uma das variáveis no estudo da PAI. Para os átomos em formação esférica, observamos uma mudança marcante no comportamento da constante de taxa de formação da foto-ionização associativa(K) para um determinado domínio de frequências, e essa mudança no comportamento pode ser atribuída a participação de estados moleculares repulsivos na PAI e a formação de um possível cruzamento evitado entre os níveis moleculares. No atomotron ,armadilha atômica em forma de anel, variamos a polarização do laser de prova e constatamos que a razão entre K das polarizações paralela e perpendicular ao movimento dos átomos é igual a 4. Uma comparação entre K do atomotron e o da armadilha esférica em função da intensidade do feixe de prova, nos mostrou uma diferença no comportamento e no valor da constante de taxa. / Photoassociative ionization (PAI) in a cold sample of sodium atoms was the main subject of our studies as a way to understand the effects of repulsive states and collision dimensions. Two-color PAI experiment were preformed in a magneto-optical trap (MOT) trough the addition of a probe laser beam, the intensity, polarization and frequency of that probe laser were tunable. The shape of the trapped atoms also could be changed. In a spherical shape MOT, we observed a marked change in the PAI rate constant (K) for a definite frequency range, and that change can be attributed to the influence of repulsive molecular states and the a possible formation of an avoided crossing between molecular levels. In atomotron, ring shaped mot, we changed the polarization of the probe beam, and saw that the ratio between K for a polarization parallel to the atoms motion and a perpendicular one is 4. Comparing the K as a function of the intensity between a spherical shaped mot and atomotron showed us a difference in the behavior and the value of the rate constant.

Dans cette thèse, nous étudions deux aspects de la dynamique d'impuretés atomiques interagissant avec des nanogouttes d'hélium superfluide (He) : la photo-excitation d'alcalins sur une nanogoutte et le dopage de nanogouttes contenant des tourbillons (vortex) quantiques avec des atomes de gaz rares. Nous utilisons la théorie de la fonctionnelle de la densité d'hélium ainsi que sa version dépendante du temps pour en faire la description théorique. Le premier aspect a été effectué dans le cadre d'une collaboration avec des expérimentateurs sur la photo-excitation du rubidium (Rb). Les alcalins sont une sonde très intéressante des gouttelettes d'hélium car ils résident dans leur zone de surface, où il a été prédit qu'un taux de condensation de Bose-Einstein de 100% était possible en raison d'une densité inférieure à celle de l'hélium superfluide. Nos simulations montrent que les états excités 5p et 6p désorbent à des échelles de temps très différentes, séparées par 2 ordres de grandeur (~100 ps et ~1 ps pour 5p et 6p respectivement). Ces résultats sont en accord avec ceux de l'expérience pompe-sonde à l'échelle femtoseconde qui a étudié la photodesorption d'atomes de Rb. Cependant, dans nos simulations, l'excitation vers 5pPi_{3/2} aboutit à un exciplexe RbHe lié à la surface, contrairement à l'expérience où RbHe est éjecté. L'introduction de la relaxation de spin de Pi_{3/2} à Pi_{1/2} nous a permis de résoudre ce désaccord, l'exciplexe RbHe ayant alors assez d'énergie pour désorber. Le deuxième aspect concerne une investigation purement théorique inspirée par les travaux récents de Gomez et Vilesov et al., où les tourbillons quantiques étaient visualisés en dopant les nanogouttes d'hélium avec des atomes d'argent, puis en les faisant atterrir en douceur (soft landing) sur un écran de carbone. Les images au microscope électronique montrent de longs filaments d'agrégats d'atomes d'argent qui s'étaient accumulés le long des coeurs des vortex. La formation de réseaux de tourbillons quantiques à l'intérieur de nanogoutelettes dopées par du xénon est également mise en évidence par diffraction de rayons X qui montrent des pics de Bragg caractéristiques d'agrégats de xénon piégés dans les coeurs des vortex. Nous avons d'abord étudié des collisions frontales entre un atome de xénon, héliophile, et une nanogoutte de 1000 héliums, et comparé les résultats à ceux d'une étude précédente sur le même processus avec le césium (Cs), qui est héliophobe. Dans le cas de Xe une «boule de neige» se forme autour de lui quand il entre dans la nanogoutte, et il lui faut beaucoup plus d'énergie qu'au Cs pour qu'il puisse en ressortir. Quand il le fait, il emporte des héliums avec lui, contrairement au Cs. Nous avons ensuite simulé des collisions entre Ar/Xe et des nanogouttes d'hélium superfluides pour différentes vitesses initiales et paramètres d'impact afin de déterminer leur section efficace de capture. Ces simulations ont ensuite été répétées pour des gouttelettes hébergeant un vortex quantique. On observe que l'impact des impuretés induit de grandes déformations de flexion et de torsion de la ligne de vortex, allant jusqu'à la génération d'ondes de Kelvin hélicoïdales qui se propagent le long du coeur du vortex. Ar/Xe est bien finalement capturé par le vortex, mais pas dans son coeur. Nous avons également découvert que l'existence d'un réseau de 6 lignes de vortex dont les noyaux sont remplis d'atomes d'Ar donne une rigidité accrue à la nanogoutte qui permet de stabiliser le système nano-goutte + vortex même à de faibles vitesses angulaires. Nos simulations impliquant des nanogouttes d'hélium comportant des tourbillons quantiques ouvrent la voie à d'autres investigations sur des nanogouttes hébergeant un ensemble de vortex, en collision avec de multiples impuretés. / In this thesis we investigate two aspects of the dynamics of atomic impurities interacting with superfluid helium (He) nanodroplets, namely the photo-excitation of alkalis on a nanodroplet and the doping process of nanodroplets hosting quantised vortices with noble gas atoms. For the theoretical investigations we use He density functional theory and its time-dependent version. The first aspect involves a joint experimental and theoretical collaboration that focusses on the photo-excitation of the alkali rubidium (Rb). Alkalis are a very interesting probe of He droplets since they reside in their surface region, where it has been argued that almost 100% Bose-Einstein condensation could be achieved due to a density that is lower than in bulk superfluid He. In our simulations we find that states excited to the 5p and 6p manifold desorb at very different timescales, separated by 2 orders of magnitude (~100 ps and ~1 ps for 5p and 6p respectively). This is in good agreement with experimental results where the desorption behaviour of photo-excited Rb atoms is determined using a femtosecond pump-probe scheme. However, in our simulations excitation to the 5pPi_{3/2}-state results in a surface-bound RbHe exciplex, contrary to the experimental case where the RbHe exciplex desorbs from the droplets surface. Introducing spin-relaxation from Pi_{3/2} to Pi_{1/2} into the simulations, the RbHe exciplex is able to desorb from the droplet's surface, which resolves this contradiction. The second aspect concerns a purely theoretical investigation that is inspired by recent work of Gomez and Vilesov et al., where quantised vortices were visualised by doping He nanodroplets with silver atoms, subsequently "soft landing" them on a carbon screen. Electron-microscope images show long filaments of silver atom clusters that accumulated along the vortex cores. Also the formation of quantum-vortex lattices inside nanodroplets is evidenced by using X-ray diffractive imaging to visualise the characteristic Bragg patterns from xenon (Xe) clusters trapped inside the vortex cores. First, head-on collisions between heliophilic Xe and a He nanodroplet made of 1000 He atoms are studied. The results are then compared with the results of a previous study of an equivalent kinematic case with cesium (Cs), which is heliophobic. Xe acquires a "snowball" of He around itself when it traverses the droplet and much more kinetic energy is required before Xe is able to pierce the droplet completely. When it does, it takes away some He with it, contrary to the Cs case. Next, collisions between argon (Ar)/Xe and pristine superfluid He nanodroplets are performed for various initial velocities and impact parameters to determine the effective cross-section for capture. Finally, the simulations are then repeated for droplets hosting a single quantised vortex line. It is observed that the impact of the impurities induces large bending and twisting excitations of the vortex line, including the generation of helical Kelvin waves propagating along the vortex core. We conclude that Ar/Xe is captured by the quantised vortex line, although not in its core. Also we find that a He droplet, hosting a 6-vortex line array whose cores are filled with Ar atoms, results in added rigidity to the system which stabilises the droplets at low angular velocities. Our simulations involving droplets hosting quantum vortices open the way to further investigations on droplets hosting an array of vortices, involving multiple impurities.

Neste trabalho estudamos o processo de foto-ionização associativa(PAI) em uma amostra fria de átomos de sódio com o objetivo entender os efeitos dos estados repulsivos e dimensão da colisão. Realizamos experimentos de PAI com duas cores em uma armadilha magneto-óptica adicionando um feixe de prova com intensidade, frequências e polarização ajustáveis. O formato dos átomos aprisionados também foi uma das variáveis no estudo da PAI. Para os átomos em formação esférica, observamos uma mudança marcante no comportamento da constante de taxa de formação da foto-ionização associativa(K) para um determinado domínio de frequências, e essa mudança no comportamento pode ser atribuída a participação de estados moleculares repulsivos na PAI e a formação de um possível cruzamento evitado entre os níveis moleculares. No atomotron ,armadilha atômica em forma de anel, variamos a polarização do laser de prova e constatamos que a razão entre K das polarizações paralela e perpendicular ao movimento dos átomos é igual a 4. Uma comparação entre K do atomotron e o da armadilha esférica em função da intensidade do feixe de prova, nos mostrou uma diferença no comportamento e no valor da constante de taxa. / Photoassociative ionization (PAI) in a cold sample of sodium atoms was the main subject of our studies as a way to understand the effects of repulsive states and collision dimensions. Two-color PAI experiment were preformed in a magneto-optical trap (MOT) trough the addition of a probe laser beam, the intensity, polarization and frequency of that probe laser were tunable. The shape of the trapped atoms also could be changed. In a spherical shape MOT, we observed a marked change in the PAI rate constant (K) for a definite frequency range, and that change can be attributed to the influence of repulsive molecular states and the a possible formation of an avoided crossing between molecular levels. In atomotron, ring shaped mot, we changed the polarization of the probe beam, and saw that the ratio between K for a polarization parallel to the atoms motion and a perpendicular one is 4. Comparing the K as a function of the intensity between a spherical shaped mot and atomotron showed us a difference in the behavior and the value of the rate constant.

La compréhension des processus électroniques engendrés au cours des collisions atomiques ou moléculaires est essentielle au niveau fondamental mais aussi en raison des besoins d’informations quantitatives sur ces processus de plusieurs domaines d’application, notamment la physique médicale et la physique des plasmas. Notre objectif est de fournir une meilleure description de ces processus. Dans le cadre de la thèse, nous avons modélisé les processus électroniques ayant lieu au cours des collisions entre des ions nus et l’atome d’hélium, Aq+-He (2≤q≤10). Cette étude est effectuée dans la gamme des énergies intermédiaires (0.25-625 keV/u) en adoptant le modèle semi-classique non perturbatif de close coupling. Un intérêt particulier est porté sur l’étude des processus de simple et de double capture vu leur grande importance dans cette gamme des vitesses. Plus précisément, nous avons analysé la double capture en détail, en séparant celle peuplant les états liés à celle qui concerne les états auto-ionisants. Cette dernière est particulièrement complexe à modéliser car elle nécessite une bonne description des états doublement excités (au-delà des deux premiers seuils d’ionisation dans notre cas), difficile à implémenter dans une approche dépendante du temps non perturbative comme la nôtre. En analysant les sections efficaces de ces deux processus pour l’ensemble des systèmes étudiés, et en les comparant systématiquement aux données expérimentales et théoriques existantes, nous avons pu extraire un comportement général reliant les processus électroniques les plus favorables à la charge et à la vitesse du projectile considérée. / The understanding of the electronic processes occurring during atomic and molecular collisions concerns the fundamental level but also the needs for quantitative information on these processes, requested by several fields of application, in particular medical physics and plasma physics. Our goal is to provide a better description of these processes. In the framework of the thesis, we have modelled the electronic processes taking place during the collisions between bare ions and the helium atom, Aq +-He (2≤q≤10). This study is carried out in the range of intermediate energies (0.25-625 keV/u), adopting the semi-classical non-perturbative close coupling approach. A particular interest is paid to the single and double capture processes because of their great importance in this energy range. More precisely, we have analysed the double capture processes, splitting the contributions of double capture to bound states and to auto-ionizing states. This latter is particularly complex to describe since it requires a good description of doubly-excited states (beyond the two first thresholds in our study), difficult to implement in time-dependent coupled-channel approaches as ours. By analysing the cross sections of these two processes for all the systems studied and comparing them to available experimental and theoretical data, we were able to extract a general behaviour linking the most favourable electronic processes to the projectile charge and velocity.

<p>    </p> <p><em>P</em>-wave Efimov physics for three equal mass fermions with different symmetries has been modeled using two-body interactions of Lennard-Jones potentials between each pair of Fermi atoms, and is predicted to modify the long range three-body interaction potential energies, but without producing a real Efimov effect. Our analysis treats the following trimer angular momenta and parities, L^Π = 0⁺,1⁺,1⁻ and 2⁻, for either three spin-up fermions (↑↑↑), or two spin-up and one spin-down fermion (↑↓↑). Our results for the long range behavior in some of those cases agree with previous work by Werner and Castin and by Blume <em>et al.</em>, namely in cases where the s-wave scattering length goes to infinity. This thesis extends those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and considers additional unitarity scenarios where the p-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized. For the equal mass fermionic trimers with two different spin components near the unitary limit are shown to possess a universal van der Waals bound or resonance state near s-wave unitarity, when p-wave interactions are included between the particles with equal spin. Our treatment uses a single-channel Lennard-Jones interaction with long range two-body van der Waals potentials. While it is well-known that there is no true Efimov effect that would produce an infinite number of bound states in the unitary limit for these fermionic systems, we demonstrate that another type of universality emerges for the symmetry L^Π = 1⁻. The universality is a remnant of Efimov physics that exists in this system at p-wave unitarity, and it leads to modified threshold and scaling laws in that limit. Application of our model to the system of three lithium atoms studied experimentally by Du, Zhang, and Thomas [Phys. Rev. Lett. <strong>102</strong>, 250402 (2009)] yields a detailed interpretation of their measured three-body recombination loss rates. </p>

On s'intéresse à la dynamique électronique de systèmes atomiques soumis à une impulsion laser brève et intense ou à l'impact d'un ion positivement chargé. On procède alors à une comparaison détaillée des descriptions classique et quantique de ces interactions. Sur la base de cette comparaison, on développe une méthode auto-cohérente de trajectoires quantiques, basée sur l'approche hydrodynamique de Bohm. Cette méthode permet d'obtenir des observables très précises tout en conservant le caractère illustratif des méthodes de trajectoires classiques. / We are interested in the electronic dynamic of atomic system under influence of a short and intense laser pulse or induced by impact of positively charged ion. We then proceeds in a deeper comparative study of classical and quantal description of these interactions. On the basis of this study, we developped a self-consistent quantum trajectory method, based on the hydrodynamical formulation of Bohm. This method allow to obtain very precise observable while retaining the illustrative character of classical trajectory method.