On the classical and semiclassical limits in collision theory

The classical scattering observable is obtained as exp(i Delta) where Delta is the interaction. Elements of the scattering matrix in the semiclassical limit are the defined, using the correspondence procedure. as the Fourier components of the classical scattering observable. This procedure is equivalent to carrying out the exponential approximation to the lowest order in H. A soluble model of vibrational excitation is considered as an example.