Analysis of resonances in Møller scattering in a laser field of relativistic radiation power

Presently available laser sources can yield powers for which the ponderomotive energy ${U}_{p}$ of an electron can be equal to or even larger than the rest energy ${\mathrm{mc}}^{2}$ of an electron. Therefore it has become of interest to consider fundamental radiation-induced or assisted processes in such powerful laser fields. In the present work we consider laser-assisted electron-electron scattering in such a field, assuming that the laser beam has linear polarization. We investigate in detail the angular and polarization dependence of the differential cross sections of the laser-assisted nonlinear processes as a function of the order N of absorbed or emitted laser photons $\ensuremath{\omega}.$ The present work is a continuation of our previous analysis of Compton scattering and of Mott scattering in a linearly polarized laser field [Phys. Rev. A 65, 022712 (2002); 65, 033408 (2002)].