Neutron densities from a global analysis of medium-energy proton-nucleus elastic scattering

A new method for extracting neutron densities from intermediate-energy elastic proton-nucleus scattering observables uses a global Dirac phenomenological approach based on the relativistic impulse approximation. Datasets for ⁴⁰Ca, ⁴⁸Ca, and ²⁰⁸Pb in the energy range from 500 MeV to 1040 MeV are considered. The global fits are successful in reproducing the data and in predicting datasets not included in the analysis. Using this global approach, energy-independent neutron densities are obtained. The vector point proton density distribution ρᵥᵖ is determined from the empirical charge density after unfolding the proton form factor. The other densities, ρᵥⁿ, ρₛᵖ, ρₛⁿ, are parametrized. This work provides energy-independent values for the rms neutron radius Rₙ and the neutron skin thickness Sₙ, in contrast to the energy-dependent values obtained by previous studies. In addition, the results presented in this paper show that the expected rms neutron radius and the skin thickness for ⁴⁰Ca are accurately reproduced. The values of Rₙ and Sₙ obtained from the global fits that we consider to be the most reliable are given as follows: for ⁴⁰Ca, 3.314>Rₙ>3.310fm and -0.063>Sₙ >-0.067fm; for ⁴⁸Ca, 3.459>Rₙ>3.413fm and 0.102>Sₙ>0.056fm; and for ²⁰⁸Pb, 5.550>Rₙ>5.522fm and 0.111>Sₙ>0.083fm. These values are in reasonable agreement with nonrelativistic Skyrme-Hartree-Fock models and with relativistic Hartree-Bogoliubov models with density-dependent meson-nucleon couplings. The results from the global fits for ⁴⁸Ca and ²⁰⁸Pb are generally not in agreement with the usual relativistic mean-field models.