Integral representation of the Coulomb Green function derived from the Sturmian expansion

We recast the Sturmian expansion of the one-particle Coulomb Green function as an integral which, through an appropriate choice of contour, is applicable anywhere on the Riemann energy surface (excluding the neighborhood of the negative real axis on the physical energy sheet, a region to which the series representation is ideally suited). As a numerical test we have used this integral representation, in conjunction with a two-particle convolution of one-particle Coulomb Green functions, to calculate the cross sections for both partial and complete breakup of the negative hydrogen ion by one-photon absorption.