Speaker
Description
The Lagrange-mesh method in perimetric coordinates is an efficient and rather simple method to study three-body Coulomb systems such as He, H$^−$, Ps$^−$, or H$^+_2$ [1], as well as quasibound states of exotic Coulomb atoms such as He$^+\bar{p}$, $\bar{p}$H, and He$^+\pi^-$ [2-4]. Recently, two extensions of the method have been developed to properly describe resonant states [3-7]: one based on the complex scaling method and the other on the Kohn variational principle. In the latter case, scattering can also be studied. In this contribution, these methods will be applied to study the S-wave resonance states of the hydrogen ion. In addition to the resonance parameters, the S-wave H+e$^−$ elastic phase shifts, obtained with the Lagrange-mesh method combined to the Kohn variational principle, will be also presented.
[1] M. Hesse and D. Baye, J. Phys. B 32 (1999) 5605; J. Phys. B 34 (2001) 1425; J. Phys. B 36 (2003) 139.
[2] D. Baye and J. Dohet-Eraly, Phys. Rev. A 101 (2020) 022507.
[3] D. Baye, J. Dohet-Eraly, and P. Schoofs, Phys. Rev. A 99 (2019) 022508.
[4] D. Baye and J. Dohet-Eraly, Phys. Rev. A 103 (2021) 022823.
[5] J. Dohet-Eraly and J. Servais, J. Phys. B 55 (2022) 245001.
[6] J. Servais and J. Dohet-Eraly, J. Phys. B 56 (2023) 075001.
[7] J. Servais and J. Dohet-Eraly, arXiv:2404.04191.
