Validity of the relativistic impulse approximation for elastic proton-nucleus scattering at energies lower than 200 MeV

Abstract

We present the first study to examine the validity of the relativistic impulse approximation (RIA) for describing elastic proton-nucleus scattering at incident laboratory kinetic energies lower than 200 MeV. For simplicity we choose a 208 Pb target, which is a spin-saturated spherical nucleus for which reliable nuclear structure models exist. Microscopic scalar and vector optical potentials are generated by folding invariant scalar and vector scattering nucleon-nucleon (NN) amplitudes, based on our recently developed relativistic meson-exchange model, with Lorentz scalar and vector densities resulting from the accurately calibrated PK1 relativistic mean field model of nuclear structure. It is seen that phenomenological Pauli blocking (PB) effects and density-dependent corrections to σN and ωN meson-nucleon coupling constants modify the RIA microscopic scalar and vector optical potentials so as to provide a consistent and quantitative description of all elastic scattering observables, namely total reaction cross sections, differential cross sections, analyzing powers and spin rotation functions. In particular, the effect of PB becomes more significant at energies lower than 200 MeV, whereas phenomenological density-dependent corrections to the NN interaction also play an increasingly important role at energies lower than 100 MeV.

Global relativistic folding optical potential and the relativistic Green's function model

“…Two basic ingredients underlie the realization of these folding potentials, namely, a suitable representation for the NN interaction and an appropriate relativistic model of nuclear densities. We have extracted the vector proton density distribution from the charge distribution measured by electron scattering and we have fitted the vector neutron density to give the best χ 2 using the on-shell NN parametrization at 200 MeV, namely, the parametrization of Li et al [29,30]. The corresponding scalar densities are obtained using the method given in Sec.…”

“…Using the proton and neutron densities and all the already mentioned available NN parametrizations [24,25,27,29,30], we compared which one gives the best χ 2 results against the proton scattering data at a proton energy of 200 MeV, where all parametrizations have parameters, that is, where all of them overlap. The best results were obtained using the Li et al parametrization [29,30]. Thus we use as input the Li et al parametrization at 200 MeV and the proton density from the experimental charge distribution and start a fitting procedure of the neutron density to the data at 200 MeV.…”

“…We have used the following fitting procedure of NN parameters at different energies (for which exist experimental data). As a starting point, for the energy range 20-500 MeV, we used the Li et al [29,30] parametrization at 200 MeV. In the range between 20 and 200 MeV, where there is the largest number of experimental data, we used more intermediate energy points in the fitting procedure.…”

“…To determine the neutron densities, first we have compared three on-shell NN parametrizations at 200 MeV, namely, Li et al [29,30], Maxwell [27], and the original HLF model [24,25], assuming ρ n V (r) = ρ p V (r). Using the proton and neutron densities and all the already mentioned available NN parametrizations [24,25,27,29,30], we compared which one gives the best χ 2 results against the proton scattering data at a proton energy of 200 MeV, where all parametrizations have parameters, that is, where all of them overlap.…”

“…Maxwell has developed energy-dependent parametrizations of the NN scattering amplitudes for two energy ranges, namely, 200-500 MeV [27] and 500-800 MeV [28]. Li et al [29,30] have generated an energy-dependent Lorentz covariant parametrization of the on-shell NN scattering amplitudes for laboratory kinetic energies between 50 and 200 MeV. At these low energies, multiple scattering effects [31], medium modifications of the NN interaction [32], and Pauli blocking [25,33] contributions are important.…”