Ingoing and outgoing waves in the non-relativistic theory of photoionization

A well-known formula for the differential cross section for photoionization contains a so-called 'final state' wave function which asymptotically behaves as a Coulomb-modified plane wave plus an ingoing Coulomb-modified radial wave. We explain the reason of appearance of that function on the ground of an analysis of an asymptotic form of a relevant outgoing Green's function. The reasoning is carried out without referring to an intuitive argumentation of Breit and Bethe [Phys. Rev. 93 (1954) 888].