On an M-conserving approximation in time-dependent theories of rotational excitation in atom-molecule collisions

A new approximation is derived in which the rotor azimuthal quantum number is assumed to be conserved. It is applicable to any method based on a classical-path approximation for the relative motion. Studies are made of its use in quantal first-order time-dependent perturbation theory, the sudden approximation and the strong-coupling correspondence principle for transition probabilities between levels. These results show that the new approximation is generally more accurate and more reliable than the body-fixed approximation. Comparisons with close-coupling calculations for Ar-TlF coIlisions are presented.