Validity of local density prescriptions for microscopic calculations of proton nucleus elastic scattering

The validity of the local density approximation as applied to the construction of the nucleon-nucleus optical potential is studied. A Wentzel-Kramers-Brillouin (WKB) local equivalent potential to the second-order term of the Kerman, McManus, and Thaler (KMT) multiple scattering expansion of the nucleon nucleus optical potential is derived. Assuming that the nucleon-nucleon transition amplitude is on the energy shell, we compare the microscopic KMT optical potential with the approximate potential deduced from the nuclear matter limit by use of the local density approximation. Calculations are presented for the nucleon-16O system at 135 and 200 MeV incident energies. It is shown that the use of the local density prescription leads to surface peaking of the optical potential. This effect is absent from the second-order term of the optical potential derived microscopically from the KMT approach