Collisional scaling within a multichannel square representation

Abstract

A new approach is examined for the state-to-state scaling of collision problems. It derives from multichannel scattering at a square interaction and is referred to as mutlichannel square (MS) scaling. Since it retains the full internal energy spectrum while approximating the radial coupling elements, it may be viewed as complementing the conventional energy sudden (ES) scaling. Some general comments are made with regard to the structure of the MS relations and we show how several attractive features of ES scaling can be matched by the new scaling. Application is made to the analysis of rotationally inelastic integral cross sections for the scattering of He from p-H2. We compare MS scaled results with both ES and modified ES results. It is found that for the range of total energies examined, the MS scaling yields results which are in good agreement with exact ones and are dramatically improved over the basic ES ones. The modified ES procedure depends upon incorporating off-energy shell effects into the ES scaling and like the MS scheme is here set up to contain a single free parameter. We find that the MS results are roughly twice as accurate as the modified ES ones. A number of avenues for further development and application of the MS scaling are discussed.