Determination of matter radius and neutron skin of $^{58}$Ni from reaction cross section of proton+$^{58}$Ni scattering based on chiral $g$-matrix model

Abstract

Background: Using the chiral (Kyushu) g-matrix folding model with the densities calculated with Gogny-HFB (GHFB) with the angular momentum projection (AMP), we determined the central values of matter radius and neutron skin from the central values of reaction cross sections σR(EXP) of p+ 40,48 Ca and p+ 208 Pb scattering. As for p+ 58 Ni scattering, σR(EXP) are available as a function of incident energy Ein. Aim: Our aim is to determine matter radius rm and skin r skin for 58 Ni from the σR(EXP) of p+ 58 Ni scattering by using the Kyushu g-matrix folding model with the GHFB+AMP densities. Results: For p+ 58 Ni scattering, the Kyushu g-matrix folding model with the GHFB+AMP densities reproduces σR(EXP) in 8.8 ≤ Ein ≤ 81MeV. For Ein = 81MeV, we define the factor F as F = σR(EXP)/σR(AMP) = 0.9775. The F σR(AMP) be much the same as the center values of σR(EXP) in 8.8 ≤ Ein ≤ 81MeV. We then determine rm(EXP) from the center values of σR(EXP), using σR(EXP) = Cr 2 m (EXP) with C = r 2 m (AMP)/(F σR(AMP)). The rm(EXP) thus obtained are averaged over Ein. The averaged value is rm(EXP) = 3.697fm. Eventually, we obtain r skin (EXP) = 0.023fm from rm = 3.697fm and rp(EXP) = 3.685fm of electron scattering.