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 (DP) approach based on the Relativistic Impulse Approximation (RIA). Data sets for Ca40, Ca48 and Pb208 in the energy range from 500 MeV to 1040 MeV are considered. The global fits are successful in reproducing the data and in predicting data sets not included in the analysis. Using this global approach, energy independent neutron densities are obtained. The vector point proton density distribution is determined from the empirical charge density after unfolding the proton form factor. The other densities are parametrized. This work provides energy independent values for the RMS neutron radius, R_n and the neutron skin thickness, S_n, in contrast to the energy dependent values obtained by previous studies. In addition, the results presented in paper show that the expected rms neutron radius and skin thickness for Ca40 is accurately reproduced. The values of R_n and S_n obtained from the global fits that we consider to be the most reliable are given as follows: for Ca40 R_n is 3.314 > R_n > 3.310 fm and S_n is -0.063 > S_n > -0.067 fm; for Ca48 R_n is 3.459 > R_n > 3.413 fm and S_n is 0.102 > S_n > 0.056 fm; and for Pb208 R_n is 5.550 > R_n > 5.522 and S_n is 0.111 > S_n > 0.083 fm. 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 Ca48 and Pb208 are generally not in agreement with the usual relativistic mean-field models.