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Représentation des états du continuum par des gaussiennes complexes : application aux processus d’ionisation atomiques et moléculaires

Abstract : This theoretical work lies at the border between molecular physics and quantum chemistry. It deals with a methodological and numerical development whose scope is to represent continuum wavefunctions by complex Gaussians. The ultimate goal is to apply these optimized Gaussians in the description of ionization processes involving molecules, where the multicenter integrals required to evaluate cross sections would be calculated analytically. For that purpose, we have developed an efficient numerical code to fit a set of arbitrary functions over finite radial distances, with either real or complex Gaussians. We have demonstrated the superiority of complex over real Gaussians in the representation of oscillating functions such as Coulomb functions or generalized Sturmian functions of positive energy. We have first validated the proposed approach to describe the ionization of the hydrogen atom by electron impact (in the first Born approximation) or photon impact (in the dipolar approximation). We have then applied the optimized complex Gaussians to describe molecular photoionization in a one-center approach. The results confirm the reliability of complex Gaussians in this kind of applications. Finally, we have considered the possibility of extending the approach to multicenter gaussian wavefunctions for the initial state. Similarly to the one-center case, we have shown that the multicenter integrals appearing in transition matrix elements can be performed analytically, also in the case of complex Gaussians.
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https://hal.univ-lorraine.fr/tel-03150935
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Submitted on : Wednesday, February 24, 2021 - 11:39:03 AM
Last modification on : Thursday, February 25, 2021 - 3:18:20 AM

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Abdallah Ammar. Représentation des états du continuum par des gaussiennes complexes : application aux processus d’ionisation atomiques et moléculaires. Physique Quantique [quant-ph]. Université de Lorraine, 2020. Français. ⟨NNT : 2020LORR0173⟩. ⟨tel-03150935⟩

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