Compton scattering and electron-atom scattering in an elliptically polarized laser field of relativistic radiation power

Presently available laser sources can yield powers for which the ponderomotive energy of an electrons Up can be equal to or even larger than the rest energy mc2 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-induced Compton scattering and laser-assisted electron atom scattering in such fields, assuming that the laser beam has arbitrary elliptic polarization. We investigate in detail the angular and polarisation dependence of the differential cross-sections of the two laser-induced or laser-assisted nonlinear processes as a function of the order N of absorbed or emitted laser photons $\omega $. The present work is a generalization of our previous analysis of Compton scattering and electron-atom scattering in a linearly polarized laser field [Phys. Rev. A 65, 022712 and 033408 (2002)]