  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.

Atomic Physics