Microscopic Optical Potential from Brueckner-Hartree-Fock Theory

Abstract

Modern Brueckner-Hartree-Fock (BHF) calculations are very successful in describing various properties of symmetric and asymmetric nuclear matter. Within BHF theory a microscopic optical potential (MOP) for nucleon-nucleus scattering is developed. First, we parametrize the energy and density dependence of complex optical potentials in nuclear matter based on BHF calculations and then we construct the MOP for finite nuclei with the local density approximation extended to include the finite-range effects. The density distribution and the spin-orbit contribution are calculated from the Hartree-Fock (HF) approximation with LNS5 Skyrme interaction, the latter being constrained by the BHF results. The central real and imaginary potentials turn out to be quantitatively consistent with the phenomenological global Koning-Delaroche (KD) potentials. The performance of MOP is evaluated by considering neutron/proton scattering on $^{40,48}$Ca. The elastic scattering differential cross sections, analyzing powers and total/reaction cross sections are analyzed in the energy below 200 MeV. A good agreement between the theoretical results and the measurements is achieved. Since our results are presented in the analytic forms, they can thus be used easily in the analysis of the experimental data of the nucleon scattering on exotic nuclei.

Figures (8)

• Figure 1: (Color online) The solid dots represent the dependence on the density of the quantities $|{V_0(\rho,E)}|/\rho$ (a) and ${|W_0(\rho,E)|/\rho}$ (b) for energies $E$=10, 40, 70, 100, 130, 160, and 200 MeV by BHF calculations. The Solid lines correspond to the parametrizations.
• Figure 2: (Color online) The solid dots represent the dependence on the density of the quantities $|V_1(\rho,E)|/\rho$ (a) and $|W_1(\rho,E)|/\rho$ (b) for energies $E$=10, 40, 70, 100, 130, 160, and 200 MeV by BHF theory. The Solid lines correspond to the parametrizations.
• Figure 3: (Color online) The splitting of effective k-mass $m^*_{k,\tau}/m$ of neutron and proton. The symbols and the lines are the results of BHF and fitting at $\beta$=0.0, 0.2, and 0.4, respectively.
• Figure 4: (Color online) The real (left) and imaginary (middle) central parts as well as spin-orbit part (right) of MOP as function of the radial coordinate for n/p+ $^{40,48}\mathrm{Ca}$ with the $E$ ranging from 10 to 160 MeV. Solid and dashed curves represent the results from MOP and KD potentials, respectively.
• Figure 5: (Color online) The predicted differential cross sections $d\sigma/d\Omega$ for n + $^{40,48}\mathrm{Ca}$ elastic scattering with different projectile energies by MOP (solid lines) and KD potentials (dashed lines), respectively. The corresponding experimental data (dots) are also plotted. The experimental data are taken from Ref. exfor.