The influence of the real nuclear potential on the heavy-ion elastic cross section

Abstract

Using a simple but reasonably realistic form for the long-range part of the real nucleus-nucleus potential some simple approximations are derived for the nuclear parts of the WKB phase shift and classical deflection function for the elastic scattering of two heavy ions. The formulae are presented in the form of universal functions which allow a rapid evaluation of the approximate “rainbow” angle and angular momentum. The numerical simplicity of this form of the nuclear phase allows a rapid determination of the corresponding cross section using the partial wave expansion. The cross sections show a shift of the quarter-point to forward angles with respect to the corresponding cross section in which to real nuclear potential is ignored. This suggests that critical angular momenta evaluated from the usual quater-point recipe will generally be an overestimate. It is shown that for very heavy ions the nuclear potential may give a large enhancement of the peak in the elastic cross section and indirect evidence for this effect is cite. For lighter ions the oscillatory structure of the cross sections appears to be dominated by absorption rather than by the real potential.