M dependence in rotationally inelastic collisions in cell experiments: Implications of an irreducible tensor expansion for molecules in 1Σ electronic states

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Abstract
The tensorial coupling of initial and final angular momenta, commonly used in atomic collisions and attributed to Grawert, is here applied to M dependent collisions of molecules in 1Σ electronic states under conditions where the relative velocity vectors of the collision partners are uniformly distributed with respect to a laboratory fixed z axis. The integral inelastic cross sections are given by sums over tensor opacities, weighted by squares of vector coupling coefficients. The resulting expressions differ from those obtained within the tensorial treatment usually applied to molecular collisions. One can rigorously show that strict M conservation will not occur and, furthermore, that the complete matrix of M → M′ cross sections can be related to the smaller set of tensor opacities. In the energy sudden limit the JM → J′M′ cross sections can be related to the degeneracy‐averaged J″ → 0 cross sections. Accurate close‐coupling cross sections for the He–CO system due to Green are used to obtain the relevant tensor opacities and to demonstrate how degeneracy averaged J″ → 0 cross sections can be extracted from the fully resolved JM → J′M′ cross sections. Finally, the sudden scaling relation is used to analyze rotational relaxation in the Na2(A 1Σ+u)+He system. We show that θ conservation, where θ=cos−1(J ⋅ ẑ), is a more appropriate dynamical model than M conservation.