Numerical treatment of the time-dependent Dirac equation in momentum space for atomic processes in relativistic heavy-ion collisions

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Abstract
A numerical method for the solution of the time-dependent Dirac equation to describe atomic processes in relativistic heavy-ion collisions is presented. Different from previous approaches found in the literature, we are working entirely in momentum space to propagate the electron wave function in time. Due to the localization of the electron in momentum space the wave function can be confined to a finite discretization volume without the stringent violation of the boundary conditions which is encountered in configuration-space methods. From the final state, we can extract probabilities on inner-shell ionization, excitation, electron transfer, and bound-free pair production. Results are presented in the energy range from 0.24 to 10 GeV/nucleon. At 0.24 GeV/nucleon we demonstrate that our formalism incorporates both the ionization and the transfer channel, which are equally important at this energy. At higher energies from 0.93 to 10 GeV/nucleon we focus on ionization and bound-free pair production. We find that the enhancement of bound-free pair production as compared to perturbation theory is much smaller than reported previously by others. © 1996 The American Physical Society.