Isovector effects in nucleon inelastic scattering in a density-dependent folding model

Abstract

Differential cross section data for inelastic proton and neutron scattering to the first ${2}^{+}$ states in $^{54}\mathrm{Fe}$ and $^{56}\mathrm{Fe}$ at several energies in the 11-26 MeV range have been analyzed using a microscopic distorted-wave Born approximation model. The entrance- and exit-channel optical potentials and the transition form factors were calculated consistently in a folding model using a density-dependent interaction obtained from nuclear matter calculations based upon a free nucleon-nucleon interaction. These microscopic calculations yield reasonable agreement with the data. The model was used to determine the ratio of neutron and proton transition matrix elements $\frac{{M}_{\mathrm{n}}}{{M}_{\mathrm{p}}}$ for these excitations.