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

Abstract

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 40 Ca, 48 Ca and 208 Pb 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, ρ p v , is determined from the empirical charge density after unfolding the proton form factor. The other densities, ρ n v , ρ p s , ρ n s , 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 40 Ca 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 40 Ca, 3.314 > R n > 3.310 fm and −0.063 > S n > −0.067 fm; for 48 Ca, 3.459 > R n > 3.413 fm and 0.102 > S n > 0.056 fm; and for 208 Pb 5.550 > R n > 5.522 fm and 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 48 Ca and 208 Pb are generally not in agreement with the usual relativistic mean-field models.

Coulomb corrections for quasielastic scattering: eikonal approximation

“…The harmonic oscillator model overestimates the charge density in the center of the nucleus, but the impact of this mismatch is reduced due to the small volume of the central region. The rms radius of the neutron density distribution was taken from a recent study presented in [32]. The binding energies, which also enter in the calculation of the wave functions of the outgoing protons and in the phase space factors, were taken from [33].…”

Neutron skin thickness in the droplet model with surface width dependence: Indications of softness of the nuclear symmetry energy

“…The rms radius of neutron densities in nuclei has been measured with hadronic probes such as proton-nucleus elastic scattering [42][43][44][45] or inelastic scattering excitation of the giant dipole and spin-dipole resonances [46,47]. Antiprotonic atoms are helpful to probe the size of the neutron skin of nuclei from the fact that the nuclear periphery is very sensitive to antiprotons in the normally electronic shell.…”

Measurement of the Neutron Radius ofPb208through Parity Violation in Electron Scattering

“…DOI Nuclear charge densities have been accurately measured with electron scattering and have become our picture of the atomic nucleus, see for example [1]. In contrast, our knowledge of neutron densities comes primarily from hadron scattering experiments involving, for example, pions [2], protons [3][4][5], or antiprotons [6,7], the interpretation of which requires a model-dependent description of the nonperturbative strong interaction. Because of the fact that the weak charge of the neutron is much larger than that of the proton, the measurement of parity violation in electron scattering provides a model-independent probe of neutron densities that is free from most strong-interaction uncertainties [8].…”