Heavy-ion scattering at intermediate and high energies

Abstract

We investigate the elastic scattering of two heavy ions. Elastic scattering gives us information on the heavy-ion optical potential and forms a basis for a further description of heavy-ion reactions using either the DWBA or the semi-classical approach to these processes. To extract the nuclear parameters from elastic scattering, one can use an exact phase-shift analysis, which at high energies is tedious and difficult (the Coulomb barrier sets the energy scale), or one can use various approximation schemes to compute the phase shifts. Here we investigate the validity of the WKB approximation and its high-energy eikonal limit (the “Glauber approximation”). The high-energy limit has the advantage that it is very simple and gives a useful picture of the scattering process in terms of straight-line eikonal trajectories. We also look at the systematic V / E corrections to the high-energy phase shift. The exact scattering amplitude is compared with the various approximations to it for an optical potential which fits 60 Ni( 16 O, 16 O) 60 Ni at low energies. The simple high-energy approximation is shown to provide an accurate description of the scattering process at energies and scattering angles of practical interest. We give some analytical expressions for the heavy-ion scattering amplitude in the high-energy approximation and also look at the model problem of heavy-ion scattering by a totally absorbing black sphere.