On predicting quantal cross sections by interpolation: Surprisal analysis of <i>j</i> <i>z</i>CCS and statistical <i>j</i> <i>z</i> results

Abstract

New methods for predicting the full matrix of integral cross sections are developed by combining the surprisal analysis of Bernstein and Levine with the jz-conserving coupled states method (jzCCS) of McGuire, Kouri, and Pack and with the statistical jz approximation (Sjz) of Kouri, Shimoni, and Heil. A variety of approaches is possible and only three are studied in the present work. These are (a) a surprisal fit of the j=0→j′ column of the jzCCS cross section matrix (thereby requiring only a solution of the λ=0 set of jzCCS equations), (b) a surprisal fit of the ?=0 Sjz cross section matrix (again requiring solution of the λ=0 set of jzCCS equations only), and (c) a surprisal fit of a ?≠0 Sjz submatrix (involving input cross sections for j,j′?? transitions only). The last approach requires the solution of the λ=? set of jzCCS equations only, which requires less computation effort than the effective potential method. We explore three different choices for the prior and two-parameter (i.e., linear) and three-parameter (i.e., parabolic) fits as applied to Ar–N2 collisions. The results are in general very encouraging and for one choice of prior give results which are within 20% of the exact jzCCS results.