Laser assisted excitation in electron-hydrogen-like ion collisions

An approach is developed for the study of the excitation of a ground-state hydrogenic ion under the simultaneous action of fast electron impact and a single mode, linearly polarized laser field in the framework of the Coulomb-Born approximation. The projectile-laser interaction is considered to all orders while the laser-ion interaction is considered to first order only. An elegant method is developed to construct the dressed excited states of a hydrogen-like ion target using the first-order perturbation theory in the parabolic coordinate representation which is the correct prescription for such laser assisted excitation processes. By virtue of this, the problem arising due to the L degeneracy of the excited states of a hydrogenic ion is overcome successfully. The differential (DCS) as well as total (TCS) cross sections are studied for the excitation to n = 2 level accompanied by the transfer of L photons with the field direction parallel to the incident momentum ((epsilon) over right arrow parallel to(k) over right arrow (i)). The variations of the cross sections with respect to the target charge number Z are also studied. The overall effect of the laser field is to suppress the field free cross sections. Some numerical results are also presented for the excitation of He+ ion to individual Stark manifolds for the n = 2 level.