Studies of inelastic molecular collisions using impact parameter methods. III. Line shape functions

Extension of impact parameter methods within an effective Hamiltonian framework is made to yield generalized cross sections or transition rates such as those encountered in spectral line broadening. An exact impact parameter expression is derived for the diagonal elements of the generalized cross sections. Approximations to the exact impact parameter expression are discussed, and it is shown that they involve two stages: (1) approximation of the S-matrix elements and (2) replacement of a sharply peaked nonlocal impact parameter kernel by a delta function. The special case of a high-energy exponential impact parameter form is used for illustration.