Procedure for averaging differential cross-sections over the experimental angular resolution
Differential cross-sections for collisions of molecules in the thermal energy range normally oscillate rapidly with angle, the oscillations becoming more rapid with increasing relative kinetic energy. The angular resolution in crossed molecular beam experiments is generally insufficient to resolve these rapid oscillations. A method is proposed for averaging differential cross-sections over small angular ranges without actually evaluating them at many angles. The method permits the calculation of averaged cross-sections, which are much more directly comparable with the experimentally determined ones than those evaluated without averaging. Illustrative calculations are presented for three examples : one for elastic scattering (Ar + Kr) and two for rotationally inelastic scattering (Ar + CsF and Ne + N2). When the differential cross-section oscillates rapidly, as it does in the first two cases, it requires less computational effort to plot the relatively smoothly varying averaged differential cross-section t...