Quasistatic-field approximation to laser-assisted particle scattering

Abstract

An $S$-matrix treatment is given for potential scattering in the presence of a laser radiation field for the case when the collision time is much smaller than the radiation-field period. The resulting Born series has the same analytic structure as the field-free one, but with the free-particle energies and momenta renormalized to incorporate the effect of the field. Different expressions are derived for the transition probability giving the field-free result as a limit and the first laser field-dependent corrections to it. The present treatment clearly implies two distinct time scales: that of the variation of the radiation field, and that of the characteristic time of the quantum system involved in the scattering process. With respect to the first time scale, the collision event is assumed to take place instantaneously; on the contrary, the collision time must be sufficiently large with respect to the second time scale to neglect the effect of the switching on of the interaction. The proper limiting passages are stated to obtain from the Kroll and Watson low-frequency result one of the results derived within the present quasistatic-field approximation.