ON-SHELL AND OFF-SHELL LOW-FREQUENCY APPROXIMATIONS FOR POTENTIAL SCATTERING IN A STRONG LASER FIELD - OPTICAL THEOREM AND SUM-RULE

We present analytical and numerical results for the T matrix and cross sections (differential and total) for scattering in a strong low-freq uency laser field. Presented results, based on recently derived expres sions for the off- and on-shell low-frequency T matrices are beyond th e first Born approximation results of Daniele ef al for scattering on the Yukawa potential in a laser field. An analytical expression for th e total cross section is obtained using the [1, 1] Pade approximant to the off-shell low-frequency T matrix. This result explicitly shows de parture from the sum rule and it is analysed as function of the laser field intensity and polarization angle. If the laser field is so stron g that the laser field induced scattering particle impulse eA(0) is co mparable with the initial impulse pi this departure has a maximum. For an ultra-strong laser field (eA(0)>>p(i)) 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 d eparture from the sum rule is larger for long-range potentials (when t he interplay between the potential and the intense radiation field is important). The departure is strong for small values of the polarizati on angle (Theta(i)<20 degrees) and weak for 45 degrees<Theta(i)<135 de grees.