Production and relaxation cross sections for the shear viscosity Senftleben–Beenakker effect. I. Formal expressions and their coupled-states and infinite-order–sudden approximations for atom–diatom systems

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Abstract
Starting from kinetic theory collision integrals obtained from a generalized Boltzmann equation for a linear molecule in a bath of atomic perturbers and using Liouville (vector) space algebra, general expressions are derived for the three cross sections determining the shear viscosity Senftleben–Beenakker effects. These expressions are presented in terms of S‐matrix elements in the total‐J representation since this representation is especially useful for dynamical calculation and approximation procedures. Coupled‐states and infinite‐order–sudden dynamical approximations are then introduced and expressions obtained for the three cross sections in initial‐l, final‐l, and average‐l labeling schemes. All cross sections simplify greatly when initial or final‐l labeling is employed but little or not at all when average‐l labeling is used. Nonetheless, even when the latter choice is made, less work will be involved than would be required for the corresponding full close‐coupled or coupled‐states calculation.