Multiphoton transitions in the coulomb continuous spectrum

Abstract

We report an exact perturbative calculation of two-photon free-free transition amplitudes in the Coulomb continuous spectrum. The corresponding cross sections are associated to an experimental situation in which, while scattered in the field of a nucleus, incoming electrons absorb (or emit) two photons of an external single-made laser field. Both the non relativistic and dipole approximations are assumed. Within this context the term exact means that we have used exact Coulomb wave function for describing the incoming and outgoing electron states. The infinite summation over the complete hydrogenic spectrum, contained into the second order amplitude, is implicitly performed by using a compact representation of the Coulomb Green' s function (1). Our results represent, in some sense, the two-photon generalization of Sommerfeld's celebrated formulae for the bremsstrahlung in a Coulomb potential (2).