SEMICLASSICAL, NON PERTURBATIVE APPROACH TO COLLISION-INDUCED TRANSITIONS BETWEEN ROTATIONAL LEVELS

Abstract

Using the effective potential formulated by $Rabitz,^{1}$ a nonperturbative and semi classical approach is used to calculate the time dependent operator for the internal rotational states of OCS-OCS and $N_{2}$-Ar collisions. In the case of OCS-OCS collisions, a straight Line path approximation with constant velocity is used, but in the case of $N_{2}$-Ar collisions, the trajectories of the molecule are calculated by taking the expectation value of the rotational energy and the expectation value of the isotropic parts of the interaction potential at each step. These calculated transition probabilities are compared with the values calculated from second-order time dependent perturbation $theory^{2}$ in the case of OCS-OCS collisions and with the values calculated from the sudden $approximation^{3}$ in the case of $N_{2}$-Ar collisions. The calculations suggest that a nonperturbative approach is necessary, especially for strong and intermediate collisions. In the case of $N_{2}$-Ar collisions, if the coupling between rotational and translational degrees of freedom is neglected, the transition probabilities change significantly for strong collisions although there are no significant changes in the corresponding trajectories.