Solution of the two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction

Abstract

A nonperturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion of this potential, we express eigenfunctions of the two-center Hamiltonian in terms of well-known solutions of the ``monopole'' problem that employ solely the spherically symmetric part of the interaction. When combined with the coupled-channel method, such a wave-function--expansion technique allows for an accurate description of the electron dynamics in the field of moving ions for a wide range of internuclear distances. To illustrate the applicability of the proposed approach, the probabilities of the $K$- as well as $L$-shell ionization of hydrogen-like ions in the course of nuclear $\ensuremath{\alpha}$ decay and slow ion-ion collisions have been calculated.