On accurate quantum mechanical approximations for molecular relaxation phenomena. Averaged j z-conserving coupled states approximation

Abstract

A rigorous formal theory of relaxation phenomena within the framework of the averaged jz-conserving coupled states (jzCCS) (Ajz) approximation is developed. Using the expressions obtained in this paper, the Ajz approximation is shown to yield pressure broadening cross sections which are in exact agreement with full close coupling results for a He+HCl model system. Previous jzCCS approximations to pressure broadening cross sections, which were in complete disagreement with close coupling for all systems studied, are shown to be the result of incorrect labeling of jzCCS T-matrices by total angular momentum J rather than by the effective orbital angular momentum ?. The correctly labeled results are not only found to be highly accurate but also considerably simpler than the expressions resulting from incorrectly labeled jzCCS T-matrices. Expressions are also derived for NMR spin–lattice relaxation cross sections within the Ajz approximation. Because the decoupled dynamical equations may be solved much more easily than the full exact CC ones, it is now feasible for the Ajz pressure broadening and spin–lattice relaxation cross sections to be computed in an iterative procedure. This will enable one to use such experimental data as a tool for determining molecular interactions.