A theoretical investigation on vibrational energy transfers in near-resonant molecular collisions

In order to improve the Sharma-Brau theory on vibrational energy transfers in near-resonant molecular collisions a theoretical analysis has been developed. The analysis concerns, first of all, the relationships among the calculation methods for three-dimensional collision models proposed by Takayanagi, Cottrell and Ream, and Shin. We are led to the choice of the Cottrell and Ream equation to overcome the constant velocity and the rectilinear trajectory approximations intrinsic to the Sharma-Brau theory. These approximations are partially responsible for the failure of the S.B. theory at very low temperature (T ≈ 100 °K), since they lead to inaccurate calculation of the effective collision time τ. In order to obtain an improved expression for τ, a first order calculation method is proposed concerning the classical trajectory near the maximum approach distance between molecules. In order to improve the agreement between classical and JWKB expressions of the transfer probabilities a “velocity symmetrization rule” different from the usual ones is proposed. Some calculations are also being developed to evaluate the contribution to the transfer probability due to “satellite” molecular orbits.