Role of nuclear densities in nucleon elastic scattering

A framework based on a full-folding model of the nucleon optical potential is presented for studying nuclear densities of closed-shell nuclei using intermediate energy nucleon scattering. Using a density-matrix expansion for the mixed density, a simplified optical potential is obtained that retains the energy and momentum dependence of the effective interaction prescribed by the full-folding model. The interplay between the local density, nonlocality of the mixed-density and off-energy-shell degrees of freedom in the full-folding approach to nucleon scattering is made relatively transparent. The validity of the proposed framework is established for momentum transfers out to ∼2.5 ${\mathrm{fm}}^{\mathrm{-}1}$ in p${+}^{16}$O and p${+}^{40}$Ca scattering at energies between 200 and 400 MeV. The sensitivity of the scattering observables to nuclear densities is investigated.