SHAPE RESONANCES AND DEEP OPTICAL POTENTIALS - A MEAN-FIELD DESCRIPTION OF C-12-12 SCATTERING AT LOW ENERGIES(C)

A critical review is given of the features of C-12 + C-12 elastic scat tering at low energies (E-cm less than or equal to 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 a t 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 follo ws naturally from the use of a deep optical potential such as is requi red at higher energy. Furthermore we show that such a potential result s :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 incon sistent with the elastic cross sections measured in the same energy ra nge; in addition, their oscillations with energy are too large in ampl itude to be ascribed to spherical mean field effects, Some discussion is also given of the bound states implied by these potentials and thei r relation to a cluster model of Mg-24. (C) 1998 Published by Elsevier Science B.V.