Calculations of laser-assisted electron–hydrogen-atom elastic scattering with consideration of higher-order terms of laser-modified wave functions

Abstract

We study the problem of laser-assisted electron--hydrogen-atom elastic scattering in the general case when the electromagnetic field is elliptically polarized, and obtain the results for plane-polarized and circularly polarized electromagnetic fields as special cases. We extend the work of F. W. Byron and C. J. Joachain (J. Phys. B 17, L295 (1984)) by considering all higher-order terms of the laser-modified atomic wave function, which have increasingly important effects on the scattering amplitude for small momentum transfer when the number of photons emitted or absorbed increases. We set up recurrence relations for determining all higher-order coefficients in the spectral expansion of the laser-dressed wave function and also determine all higher-order terms in the energy shift and the time-dependent phase. Our general expression for the laser-assisted first-Born-approximation scattering amplitude for l-photon transfer is cast into a form which gives the probability for the case in which l/sup a/ photons are absorbed or emitted by the bound atomic electron and the remaining (l-l/sup a/) photons by the free projectile electron. We discuss the dependence of the scattering amplitude on the polarization of the electromagnetic field. Exchange effects in the presence of the laser are also taken into account in a simple though approximatemore » manner. We further discuss the problem of replacing the above-mentioned first-Born-approximation scattering amplitude by some higher-order scattering amplitude in the presence of the time-dependent laser field.« less