Energy dependence and surface contribution of the folding-model optical potential for nucleon-nucleus scattering at energies up to 1 GeV/nucleon

An energy-dependent microscopic optical model potential (OP) is presented to analyze the elastic scattering of protons with incident energies up to 1000 MeV/nucleon on Be-9 nucleus. This microscopic optical model is built from the single-folding optical model. The density- and isospin-dependent M3Y-Paris nucleon-nucleon (NN) interaction is used for the real and spin-orbit parts and the NN-scattering amplitude of the high-energy approximation for the imaginary one. The microscopic complex spin-orbit OP is taken within Breiva-Rook approximation. The partial-wave expansion analysis with this optical model potential fails to reproduce the differential cross-section data at energies larger than 100 MeV/nucleon, a good improvement is obtained by including the surface contribution to the imaginary OP where most of the basic scattering observables are reproduced well at the considered wide energy range. The volume integrals are found to be have interesting energy dependencies and their parametrizations can be used to build an energy-dependent microscopic OP that is used to reproduce the observables at a wide energy range. This study shows that the partial-wave expansion analysis using the folding optical model can be used to analyze the scattering data at high energies as well as at low energies.