Variational Corrections to Decoupling Approximations in Molecular Collision Theory

A simple correction to the decoupling approximation is introduced in order to account for the possible occurrence of energy-conserving transitions. The correction, derived from a variational principle for effective potentials, uses only matrix elements and wavefunctions available from decoupling procedure computations to introduce a nonlocal, imaginary part, for the effective potential. The imaginary part is used to compute transition rates for energetically allowed transitions, which are neglected in the decoupling approximation. Explicit results (and error terms) are obtained in the two-state approximation.