Electron-atomic-hydrogen elastic scattering in the presence of a laser

Laser-assisted electron-atomic-hydrogen elastic scattering is studied in the first Born approximation. The initial and filial states of projectile electron are described by the Volkov wavefunctions: the dressed state of target described by a time-dependent perturbative wavefunction in soft photon approximation. The laser modified cross-sections are calculated in two distinct geometries for laser polarization either parallel or perpendicular to the incident direction of electron. The numerical results shows that the multiphoton cross-sections oscillate by a few orders over the whole scattering angular region. The results for a parallel geometry oscillate more frequently in the intermediate angles: while the results for a perpendicular geometry oscillate more frequently in the forward and backward angles. At large scattering angles. the sum rule of Kroll and Watson is noticeably violated. The laser modification on summed total cross-section increases with field strength. but decreases with field frequency and polarization deviation from the incident direction.