Two-photon free-free transitions in a Coulomb potential

We report a perturbative calculation of the cross sections for two-photon free-free transitions (absorption and emission) in a Coulomb potential within the nonrelativistic, dipole approximation. The matrix element was integrated analytically by the Greens-function method, and then computed numerically with great accuracy. Limiting cases are discussed (Born approximation, low and high photon-electron energy ratios). Results are presented for two-photon absorption, in the case when the initial electron momentum is perpendicular to the photon polarization vector.