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

TL;DR

This paper introduces a non-perturbative, multipole expansion-based method for solving the two-center time-dependent Dirac equation, enabling accurate modeling of electron dynamics in moving ion fields for various internuclear distances.

Contribution

It presents a novel wavefunction-expansion technique combining multipole expansion with the coupled-channel method for the Dirac equation in two-center problems.

Findings

Accurate calculation of K- and L-shell ionization probabilities during nuclear alpha-decay.

Method effectively describes electron dynamics in slow ion-ion collisions.

Applicable across a wide range of internuclear distances.

Abstract

A non-perturbative 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 employs solely the spherically-symmetric part of the interaction. When combined with the coupled-channel method, such a wavefunction-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 alpha-decay and slow ion-ion collisions have been calculated.