On predicting quantal cross sections by interpolation: Surprisal analysis of j zCCS and statistical j z results

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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.