The calculation of rainbow scattering cross sections

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Abstract
A method is described for calculating low resolution differential cross sections near the rainbow angle. It is used to calculate a table of the positions of the principal maxima and minima in the rainbow structure for a 6–12 potential for different rainbow angles and different values of the de Boer parameter, Λ*, between 0·1 and 0·01. A comparison with similar results obtained using Ford and Wheeler's approximation shows that the latter is quite accurate for determining the energy parameter, ε, but is usually unsatisfactory for determining the distance parameter, σ. A method is given for determining both of these parameters more accurately from the values in the table and a further table is given with which it is possible to determine which region of the real potential is being fitted by the 6–12 potential. It is found that the rainbow structure in determined only by the attractive part of the potential close to the minimum and is independent of the shape of the potential inside the minimum.