Tensorial factorization and rotationally inelastic collisions

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Abstract
Since the transition‐ or T‐operator is a scalar it can be expanded as a sum of products of operators which transform as spherical tensors. Consequently the T matrix for rotationally inelastic atom–molecule collisions can be factored into products of reduced matrix elements in the internal (rotational) and relative (orbital) degrees of freedom. This basic factorization, which is independent of specific dynamical approximations, leads to generalized cross section scaling relations. In the sudden limit these reduce to the expressions derived earlier by Goldflam, Kouri, and Green [J. Chem. Phys. 67, 5661 (1977)]. From previously computed T matrices one can extract partial opacities corresponding to the various tensor orders which contribute. This is done for the case of Ar–N2 collisions. The spherical tensor factorization is extended to the more complex case of collisions between two diatomic molecules. Recent energy‐gap models are discussed in light of the tensorial analysis developed here.