Local representation of a deep parity and [formula omitted] potential

Abstract

We have found, using the IP inversion method, the l-independent potential which leads to the same angular distributions as the phenomenological parity and l-dependent “deep” potential of Gao and He, fitted to the 16O + 20Ne scattering for energies below 40 MeV. The real part of this potential is deeper over the whole range. The absorptive part is surface transparent having a small and energy-dependent radius reflecting the original l-dependent cut-off. We show that the parity odd-even staggering effect in S( l) is necessary only for the grazing partial waves in order to yield the Gao and He cross sections. We also show that the present potential leads to wave functions that are different from those of Gao and He. The implications for phenomenology are discussed.