The impact operator in semiclassical theory

Let us consider first quantum J-diffusion. It is carried out by purely non-adiabatic collisions realized for anc C 1 where a is the average rotational frequency. A semiclassical analogue of the infinite-order sudden 

The important relation resulting from S-matrix unitarity 

Interference in the Q-branch and population relaxation are ruled by the operator 

8) formulates the same particle conservation law that was expected to hold for any f(0) in Eq. (4.65). The meaning of Eq. (5.9) becomes clear if one looks for rotational energy relaxation, which obeys the equation 

The energy is expected to relax from any initial state ((p(0) to equilibrium, but an entirely different result emerges if we employ in Eq. (5.12) an impact operator with properties (5.8) and (5.9). Considering the initial matrix as a normalized one (((p(0) /)) = 1), we obtain 

---