Phenomenological Analysis of Reactive Scattering

Abstract

An analysis of the angular distribution of elastic scattering concomitant with chemical reaction by means of an “opacity function” (reaction probability) is discussed. Computational results (i.e., differential elastic scattering cross sections) based on a partial wave expansion are presented for a model problem with various reasonable assumed forms of the opacity function $p_l$ . The semiclassical “inversion” procedure of Ross and Greene is tested and found to be of quite usable accuracy, except when $\mathrm{pl}$ has an abrupt “cutoff.” Such a sharp‐edged opacity function is in any case an oversimplification, whose use can, moreover, lead to erroneous conclusions regarding the range of impact parameters $b$ contributing to reaction. Proper account should be taken of the “diffuse” shape of $p_l$ or $\mathrm{P(b)}$ in the region of its decline. In the absence of a detailed understanding of the microscopic dynamics of the reaction, when the optical model is most advantageously employed, the phenomenological analysis of experimental scattering data in terms of an energy‐dependent opacity function appears to be the optimum means of characterization of the reacting system.