On-shell and off-shell low-frequency approximations for potential scattering in a strong laser field-optical theorem and sum rule

Abstract

We present analytical and numerical results for the T matrix and cross sections (differential and total) for scattering in a strong low-frequency laser field. Presented results, based on recently derived expressions for the off- and on-shell low-frequency T matrices are beyond the first Born approximation results of Daniele et al. (1986) for scattering on the Yukawa potential in a laser field. An analytical expression for the total cross section is obtained using the (1,1) Pade approximant to the off-shell low-frequency T matrix. This result explicitly shows departure from the sum rule and it is analysed as function of the laser field intensity and polarization angle. If the laser field is so strong that the laser field induced scattering particle impulse eA0 is comparable with the initial impulse pi this departure has a maximum. For an ultra-strong laser field (eA0>>pi) the total cross section is small in comparison with the field-free section, i.e. the influence of the scattering potential is weak. The results for different values of the screening radius are also presented and it is observed that the departure from the sum rule is larger for long-range potentials (when the interplay between the potential and the intense radiation field is important). The departure is strong for small values of the polarization angle ( Theta i<20 degrees ) and weak for 45 degrees < Theta i<135.