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Resonances in three-body atomic systems by Lagrange-mesh methods

par Servais, Jean
Président du jury Vaeck, Nathalie
Promoteur Dohet-Eraly, Jérémy
Publication Non publié, 2024-09-20

Thèse de doctorat

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Résumé :

This work aims at describing accurately the resonance spectra of various three-body atomic systems. The studied systems range from standard atomic systems, such as the helium atom and the hydrogen ion, to more exotic ones, such as the positronium ion, the antiprotonic helium or the pionic helium atoms. The relevancy of the study of such systems is addressed.The wavefunction of the system is described in perimetric coordinates. The Lagrange-mesh method, a pseudovariational method practical for its simplicity and high accuracy, is used for evaluating the radial matrix elements. Two different approaches are developed in order to evaluate the resonance parameters (energy and width). On one hand, the complex scaling method, a bound-state-like approach, is combined to the Lagrange-mesh method in order to extract resonance parameters. On the other hand, a scattering approach, combining the Lagrange-mesh method and the Kohn variational method, is developed. This scattering approach not only leads to the resonance parameters, but also to scattering properties of the systems under study. We start the physical discussion with three bielectronic systems : He, Ps− and H− , for states witha low total angular momentum. First, resonance parameters are evaluated by using the complex scaling method on a Lagrange mesh. The results are more accurate than most of the results presented in literature, often by several orders of magnitude. Second, the case of H− is studied to illustrate the results obtained with the Kohn variational method on a Lagrange mesh,in a low-energy case. The obtained phase shifts are more accurate than most of the phase shifts reported in literature. It is demonstrated that applying this approach to obtain accurate values of the resonance parameters is appropriate as well. Next, we present a detailed and broad theoretical discussion of a pseudomolecular exotic system,antiprotonic helium. This system, which consists of a helium nucleus, an electron, and an antiproton, has been used in spectroscopic experiments to determine the antiproton mass, with the highest accuracy ever achieved. The general theoretical properties of this system are accurately determined by applying the two approaches developed in this work. The radiative transition widths, Auger widths, resonance energies as well as leading-order relativistic corrections are computed. In particular, the Auger widths are obtained for a wide range of the angular momentum, a study never conducted so far. We also apply the developed method to the case of pionic helium, a similar pseudomolecular exotic system. Overall, the method appears to be promising to study other exotic helium-like atoms.