The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics: Applications to collisional energy transfer

A generalized cumulant expansion method is developed for applying stochastic reductions to molecular collision processes. We begin by introducing an approximate partitioning of a collision system into two subsystems S _r and S_i which are assumed to be weakly correlated. Cumulant expansion methods are then used to simultaneously perform a stochastic reduction over S_i, and a projection of the diagonal elements of the reduced density matrix for S_r thereby leading to a Pauli master equation describing S_r. We then apply this general equation using an impulse approximation partitioning to problems in inelastic V-T and R-T scattering. For He+ H₂ vibrationally inelastic collisions, the stochastic theory predicts low order moments and some probabilities in very good agreement with exact quantum results. In applications to He+ H₂ rigid rotor scattering, integral cross sections and opacity functions within 10%-30% of exact results are obtained at most energies.