arXiv:physics/9808046·v1·Atomic Physics
Asymptotic channels and gauge transformations of the time-dependent Dirac equation for extremely relativistic heavy-ion collisions
J. C. Wells (1 and 2)🇺🇸 · B. Segev (2)🇺🇸 · J. Eichler (3) ((1) Center for Computational Sciences, Oak Ridge National Laboratory; (2) Institute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics; (3) Bereich Theoretische Physik, Hahn-Meitner-Institut Berlin; and Fachbereich Physik, Freie Universitat Berlin)🇩🇪
Abstract
We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.
Comments: 12 pages, RevTeX, 2 figures, submitted to PRA