Rotational energy sudden approximation in vibrationally inelastic collisions

In the rotational energy sudden approximation, certain relations exist among the differential and integral cross sections. These relations are expanded to encompass the vibrational degree of freedom. The extent to which these relations hold for exact cross sections gives an indication of the minimum error one might expect when the energy sudden approximation is used. An evaluation is made of the extent to which these relations are satisfied for He--H2 collisions. The He--H2 system is one, for which the conditions under which the energy sudden approximation is valid, are poorly satisfied. Thus, these calculations represent a worst case example for the energy sudden approximation and exhibit the greatest error one is likely to encounter in the use of the approximation. One may expect improvement in the accuracy of these relations whenever the validity conditions are better satisfied. Several features of the cross sections which the approximation cannot duplicate are pointed out