Coulombian asymptotic states

Abstract

We define and study Coulombian asymptotic states, denoted by ‖k∞〉, which are useful and important for stationary Coulombian scattering theory. Using these asymptotic states, we are able to derive from the off-shell T matrix the physical on-shell T matrix for Coulomb plus short-range potentials. This function is proportional to the physical scattering amplitude. A generalized Lippmann–Schwinger equation and related equations are derived. Many other applications of the asymptotic states exist. We show the precise connection of ‖k∞〉 with the time-dependent Coulomb scattering theory.