Multiphoton (e, 2e) process of hydrogen atom in strong laser field

The dynamics of the electron impact multiphoton ionization of a hydrogen atom in the presence of an intense laser field (e, n γ e) has been studied theoretically for laser polarization parallel (||^l\vert \vert^{l}) and perpendicular (⊥^r) to the incident momentum, with a view to comparing (qualitatively) the results with the recent kinematically complete experiments of H?hr et al. Phys. Rev. Lett. 94, 153201 (2005)] for the He target. Significant laser modifications are noted in the present doubly (DDCS) and the fully differential multiphoton cross sections (TDCS) for both the geometries (||^l\vert \vert^{l} and ⊥^r). For most of the explored kinematics (chosen in accordance with the experiment), the present binary peak intensity of the laser-assisted multiphoton TDCS is significantly enhanced with respect to the field free ones, in qualitative agreement with the experiment. Importance of the multiphoton effects is also studied. The multiphoton cross sections in the zeroth order approximation of the ejected electron wavefunction (CV) obeys the Kroll Watson sum rule while it does not hold good in the corresponding first order approximation (MCV).