Angular entropy: The information content of molecular scattering angular distributions

Abstract

The concept of the angular entropy arises from consideration of the information content of a scattering pattern, i.e., an angular distribution of collision products. It is shown that information theory (I.T.) provides the framework for evaluation and interpretation of the entropy (and entropy deficiency) of an angular distribution of reactive, inelastic, or elastic scattering. The differential cross section σ (ϑ) is converted to a normalized probability density function (pdf), P (u) [u= (1/2)(1−cosϑ)], from which the angular surprisal is obtained as −lnP (u). The average over u of the surprisal yields the angular entropy deficiency. (A histogrammic approximation to the continuous pdf can provide a simple estimate of ΔS). Examples are presented of reactive and inelastic molecular scattering patterns and of various prototype angular distributions giving insight into the angular entropy. The I.T. method is also applied to elastic scattering of atoms and molecules. It inherently demands the elimination of the well-known ’’classical divergencies’’ (the forward infinity and rainbow spike). These problems disappear when quantal (or semiclassical) differential cross sections are used. Nevertheless, the forward cone makes the dominant contribution to the angular entropy deficiency for elastic scattering at moderate energies. The rainbow structure introduces some entropy deficiency, but the quantal interferences in σ (ϑ) contain little information (in the strict I.T. sense). However, nuclear symmetry effects are found to be significant.