Coulomb propagator in the WKB approximation

Employing the WKB approximation, we derive an analytical expression for the two-body Coulomb propagator in terms of the asymptotic momentum pas, coordinates r and r' and the difference of time τ. The momentum pas is a solution of the stationary phase equation. The problem of solving it is reduced to seeking the roots of some one-dimensional equation. The WKB Coulomb propagator is applied to calculate the continuum state of an atomic electron, subject to a sequence of δ -function impulses. The derived continuum state includes the effects of electron rescatterings into the continuum that may play an important role in various processes of atomic fragmentation. (author)