Theory of electron-hydrogen-atom collisions in the presence of a laser field

Expressions for the scattering amplitude of multiphoton processes occurring during the collision of electrons with a hydrogen atom in the presence of an electromagnetic field have been obtained in several approximations: the momentum translation, the space translation, and the Keldysh approximation for the bound-electron wave function. We also propose a perturbation approach based on the space-translation approximation to treat the hydrogen-atom bound states. Our results show that it is of fundamental importance to consider the modifications of bound states due to the presence of the field.