Exact photoionization and radiative recombination cross section in a Coulomb potential

Abstract

In this work, we analytically evaluate the exact matrix element for a non-relativistic Continuum-Bound radiative transition in a Coulomb potential. We apply this result to the photoionization (and radiative recombination) process, and calculate the total cross sections giving an analytical expression for the transition from the ground state. To our best knowledge the exact solution to this problem has never been addressed even though the analytical calculation is quite simple, and the final result is not more complicated than any of its approximations. We compare our result with the well-known plane wave and Coulombian dipolar approximations, in a wide range of energies.