The quantum impulse approximation theory has been extended to the inelastic collision. The total inelastic cross sections for the degenerated states with different angular momenta was calculated. It was proved that summing over the transitions from nl to n' and from nl to n'l' would give us the total cross section of transition from n to n'. Rate coefficients were calculated for the common gases in the atmosphere being the third particle. The resonant effect of the rate coefficients had been observed. Recombination coefficients were then calculated in terms of rate coefficients. Previous calculations were carried out in compare with the net rate flow through certain excited levels, which were found to be more stable and reflected a clearer picture of the whole process. Results have been compared with the elastic collision. A dramatic decreasing of rates when temperature increased was also observed. More thermal energy increases the probability of electrons for being re-ionized. Similar calculations had been carried out for the upper atmosphere gases, such as N₂, O₂, CO, CO₂, and H₂O. The recombination coefficients for electron combining with metallic ion Na+ were also calculated.

This thesis discusses the development and application of theoretical and computational methods to study three-body processes. The main focus is on the calculation of three-body resonances and bound states. This broadly includes the study of Efimov states and resonances, three-body shape resonances, three-body Feshbach resonances, three-body pre-dissociated states in systems with a conical intersection, and the calculation of three-body recombination rate coefficients. The method was applied to a number of systems. A chapter of the thesis is dedicated to the related study of deriving correlation diagrams for three-body states before and after a three-body collision. More specifically, the thesis discusses the calculation of the H+H+H three-body recombination rate coefficient using the developed method. Additionally, we discuss a conceptually simple and effective diabatization procedure for the calculation of pre-dissociated vibrational states for a system with a conical intersection. We apply the method to H_3, where the quantum molecular dynamics are notoriously difficult and where non-adiabatic couplings are important, and a correct description of the geometric phase associated with the diabatic representation is crucial for an accurate representation of these couplings. With our approach, we were also able to calculate Efimov-type resonances. The calculations of bound states and resonances were performed by formulating the problem in hyperspherical coordinates, and obtaining three-body eigenstates and eigen-energies by applying the hyperspherical adiabatic separation and the slow variable discretization. We employed the complex absorbing potential to calculate resonance energies and lifetimes, and introduce an uniquely defined diabatization procedure to treat X_3 molecules with a conical intersection. The proposed approach is general enough to be applied to problems in nuclear, atomic, molecular and astrophysics.

Doctor of Philosophy / Department of Physics / Brett D. Esry / The Efimov effect plays a central role in few-body systems at ultracold temperature and has thus accelerated a lot of studies on its manifestation in the collisional stability of the quantum degenerate gases. Near broad Feshbach resonances, Efimov physics has been studied both theoretically and experimentally through the zero-energy scattering observables. We have extended the theoretical studies of Efimov physics to a much broader extent. In particular, we have investigated the three-body Efimov physics near narrow Feshbach resonances and have also identified the Efimov features beyond the zero temperature limit. We have found, near a narrow Feshbach resonance, the non-trivial contribution from both of the resonance width and the short-range physics to the three-body recombination and vibrational dimer relaxation. Remarkably, the collisional stability of the Feshbach molecules are found to be opposite to that near the broad resonances: an increased stability for molecules made by bosons and a decreased stability for those made by fermions. The universal physics observed near the narrow Feshbach resonances is further found not to be limited to the zero temperature observables. We have found that the general features of Efimov physics and those pertaining to a narrow resonance are manifested in different energy ranges above zero temperature. This opens the opportunity to observe Efimov physics by changing the collisional energy while keeping the atomic interaction fixed. The landscape of the universal Efimov physics is thus delineated in both of the interaction and the energy domain. We have also investigated Efimov physics in heteronuclear four-body systems where the complexity can be reduced by approximations. In particular, we have proposed ways for controllable production of the Efimov tri-atomic molecules by three-body or four-body recombinations involving four atoms. We have also confirmed the existence of four-body Efimov effect in a system of three heavy particles and one light particle, which has resolved a decade-long controversy on this topic. Finally, we have studied the collisional properties of four identical bosons in 1D, which is important to the experiments on the quantum gases confined in the 1D optical lattices.

On trouve des manifestations de la physique quantique au niveau thermodynamique dansde nombreux systèmes. Un exemple marquant est la superfluidité, découverte au début du20ème siècle, que l’on retrouve de l’hélium aux étoiles à neutrons. Les gaz dilués ultrafroidsoffrent une polyvalence unique pour étudier des systèmes quantiquesmacroscopiques, pouvant directement tester les théories grâce à un environnementcontrôlé. Dans cette thèse, nous présentons plusieurs études expérimentales de gaz froidsde lithium. Le lithium fournit la possibilité de réaliser des ensembles de bosons et defermions, avec des interactions contrôlables entre les constituants. Nous présentons lestechniques utilisées pour préparer et étudier des gaz dégénérés de lithium, et uneamélioration possible des méthodes existantes. Nous décrivons premièrement une étudede la recombinaison à trois bosons avec une interaction à deux corps résonante. Comparésquantitativement à la théorie, ces résultats fournissent une référence pour les étudesfutures du gaz de Bose unitaire. Pour finir, nous présentons la première observationexpérimentale d’un mélange de superfluides de Bose et de Fermi. Nous démontrons queles deux composants sont superfluides et que leur écoulement relatif vérifie les propriétésdes écoulement superfluides, avec une absence de viscosité en dessous d’une vitessecritique puis la présence de dissipation au-delà. En utilisant des excitations collectives dece mélange, nous mesurons l’interaction entre les deux superfluides, en accord avec unmodèle théorique. / Manifestations of Quantum Physics at the thermodynamical level are found in a broadrange of physical systems. A famous example is superfluidity, discovered at the beginningof the 20th century and found in many different situations, from liquid helium to neutronstars. Dilute ultracold gases offer a unique versatility to engineer quantum many-bodysystems, which can be directly compared with theory thanks to the controllability of theirenvironment. In this thesis we present several experimental investigations led on ultracoldlithium gases. Lithium provides the possibility to study ensembles of bosons andfermions, with controllable interactions between the constituents. We present experimentaltechniques for preparation and studies of degenerate gases of lithium, with prospects forimprovement of the existing methods. We first report on an investigation of three-bodyrecombination of bosons under a resonant two-body interaction. This study, quantitativelycompared with theory constitutes a benchmark for further studies of the unitary Bose gas.Finally, we present the first experimental realization of a mixture of a Bose superfluid witha Fermi superfluid. We demon- strate that both components are in the superfluid regime,and that the counter-flow motion between them possesses the characteristics of superfluidflow, with the absence of viscosity below a critical velocity, and an onset of friction above.Using collective oscillations of the mixture, we measure the coupling between the twosuperfluids in close agreement with a theoretical model.