High-intensity multiphoton free-free transitions

Based on a fundamental and simple treatment, selected calculations are performed of differential and total cross sections of multiphoton free-free transitions. The emphasis is on high values of the radiation field intensity such that the amplitude $v_0$ of the classical electron oscillatory velocity is equal or larger than the incoming velocity $v_i$. A variety of new information is obtained which gives a useful insight into various aspects of both the current theory and the physics of multiphoton free-free transitions. The calculations concern the following: (i) total cross sections in parallel and perpendicular geometry for both multiphoton emissions and absorptions, (ii) the breakdown of a known sum rule, (iii) the comparison of exactly calculated total cross sections with those based on widely used simplifications, and (iv) the investigation of the role of the range of scattering potential. Under particular conditions, the classical aspects of the elementary process (the interaction with the field) are found to affect the collision event and its characteristic parameters in a very peculiar way. The most interesting and new results are obtained when $v_0$≥$v_i$ and ${\mathrm{v}}_0$∥${\mathrm{v}}_i$.