Sensitivity analysis of differential cross sections to the intermolecular potential

This paper considers the sensitivity of both final state summed and state to state differential cross sections to the variation of parameters within a model intermolecular potential. In order to simplify the calculation of the cross sections and first order sensitivity coefficients (i.e., the partial derivative of cross sections with respect to potential parameters) attention is restricted to the scattering of an atom and rigid rotor. Furthermore, the collision dynamics are approximated by using the infinite order sudden (IOS) approximation. Particular emphasis is given to an examination of the sensitivity of angular features of the cross sections to potential parameter variations. This is facilitated by fitting the cross sections to functional forms which contain several adjustable parameters, each of which controls a particular feature. First order sensitivity coefficients are then used to derive quantitities which measure the sensitivity of a "feature parameter" with respect to the variation of a potential parameter. The first order sensitivities are also used to obtain so called derived sensitivity coefficients and, in particular, those which describe how the potential parameters are interrelated for a given set of cross section measurements. The behavior of these coefficients is examined as the angular range of the measurements is varied and as account is taken of the finite angular resolving power of molecular beam detectors. The results are used to determine the degree to which a set of differential cross section measurements is able to define various parameters of the assumed potential.