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This paper considers the response of various types of elastic collision cross sections to functional variations in the intermolecular potential. The following cross sections are considered differential, total, effective diffusion, and effective viscosity. A very simple expression results for the diffusion and viscosity cross sections at high energy relating the variations to the classical deflection function. Attention is first given to the forward sensitivity densities δσ(E)/δV(R) [i.e., the functional derivative of cross sections σ(E) with respect to the potential surface V(R)]. In addition inverse sensitivity densities δV(R)/δσ(E) are obtained. These inverse sensitivity densities are of interest since they are the exact solution to the infinitesimal inverse scattering problem. Although the inverse densities do not in themselves form an inversion algorithm, they do give a quantitative measure of the importance of performing particular measurements for the ultimate purpose of inversion. In addition, the ...

A general technique is described for gaining insight into inversion processes. Upon solving the equation of motion associated with a given physical model, specialized inverse coefficients are calculated to address questions on inverse modeling. The number of accessible independent inverse coefficients is shown to be directly related to the number of independent pieces of modeling data taken as available. Although the inverse coefficients do not in themselves form an inversion algorithm, they do give a quantitative measure of the importance of performing certain additional measurements for the ultimate purpose of inversion. The concepts are illustrated by some simple dynamical models. The calculations show that the normal forward sensitivities and the new inverse coefficients generally exhibit disparate behavior in accord with the differing physical quantities being addressed.

This paper considers the response of various rotational energy transfer processes to functional variations about an assumed model intermolecular potential. Attention is focused on the scattering of an atom and a linear rigid rotor. The collision dynamics are approximated by employing both the infinite order sudden (IOS) and exponential distorted wave (EDW) methods to describe Ar–N2 and He–H2, respectively. The following cross sections are considered: state‐to‐state differential and integral, final state summed differential and integral, and effective diffusion and viscosity cross sections. Attention is first given to the forward sensitivity densities δ0/δV(R,r) where 0 denotes any of the aforementioned cross sections, R is the intermolecular distance, and r is the internal coordinates. These forward sensitivity densities (functional derivatives) offer a quantitative measure of the importance of different regions of the potential surface to a chosen cross section. Via knowledge of the forward sensitivities...