Semiclassical Theory for Collisions Involving Complexes (Compound State Resonances) and for Bound State Systems

Abstract

Semiclassical theory for bound states is discussed and a method is described for calculating the eigenvalues for systems not permitting separation of variables. Trajectory data are supplemented by interpolation to connect open ends of quasi-periodic trajectories. The method is also applied to quasi-bound states. Previously, semiclassical S-matrix theory has focused on “direct” reactions. Processes involving complexes (compound state resonances) are treated in the present paper and an expression is derived for the S-matrix. Use is made of the above analysis of quasi-bound states and of trajectories connecting those states with open channels. The result deduced for the S-matrix has the expected factorization property, and expressions are given for computing the quantities involved. Some extensions and applications will be described in later papers. An implication for classical trajectory calculations of complexes is noted.