Semiclassical inversion of rainbow scattering data

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Abstract
A critical evaluation is carried out of a standard method used to fit monoenergetic rainbow differential cross section data. It is demonstrated in one particular case that potentials with well depth values, ε, differing by a factor of two and distance parameter values, r e, differing by a factor of six both reproduce the same Na-Hg experimental rainbow scattering data. An analysis is given which explains how this result is possible and which indicates that one cannot rely very heavily on potentials fitted solely to the angular positions of the main rainbow oscillations, taken at a single energy. Somewhat more reliable, though still by no means unique, results can be obtained if fine oscillations like those which Barwig, Buck, Hundhausen and Pauly observed superimposed on the rainbow cross sections of Na-Xe, are used in the determination. A detailed analysis is given of the structure of these fine oscillations.

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