Shape resonances and deep optical potentials: A mean-field description of scattering at low energies

Abstract A critical review is given of the features of 12 C + 12 C elastic scattering at low energies ( E cm ⩽ 37.5 MeV) which may be ascribed to a mean field, or optical potential, and how this field matches smoothly on to optical model descriptions of the scattering at higher energies ( E cm from 35 to 725 MeV). In particular we examine the proposed shape resonance band at low energy and show that it follows naturally from the use of a deep optical potential such as is required at higher energy. Furthermore we show that such a potential results in radial wavefunctions with sufficient numbers of nodes to satisfy the requirements of the Pauli principle under antisymmetrization. The reported reaction cross section data appear to be too small and inconsistent with the elastic cross sections measured in the same energy range; in addition, their oscillations with energy are too large in amplitude to be ascribed to spherical mean field effects. Some discussion is also given of the bound states implied by these potentials and their relation to a cluster model of 24 Mg.