Two-photon transition in a colliding particle system

The first analysis is made of stimulated Raman scattering and two-photon absorption (emission) processes resulting in a change in the states of two colliding particles. These processes are caused the by interaction between dipole moments induced as a result of polarization of the particles by the radiation. Equations are derived to describe multiphoton transitions during a collision between two particles in a radiation field. Using the approximation of rectilinear trajectories, expressions are derived and analyzed for the cross section of collisional two-photon transitions in weak and strong fields. It is shown that in fields of $\mathcal E\approx10^3$ cgs esu, the cross section of these transitions may reach $10^{-4}$ cm$^2$.