Skin values of 208Pb and 48Ca determined from reaction cross sections

Abstract

Background:The PREX and the CREX group reported skin values, rskin208(PREX2)=0.283±0.071fm and rskin48(CREX)=0.121±0.026(exp)±0.024(model) fm, respectively. Using the Love–Franey (LF) t-matrix folding model with the neutron and proton densities scaled to the neutron radius rn208(PREX2) and the proton radius of the electron scattering, we found that the reaction cross sections σR reproduce the data for p+ 208Pb scattering at Elab=534.1,549,806MeV. Zenihiro et al. deduce neutron radii rn48,40(exp) from the angular distributions of the cross sections and analyzing powers of proton elastic scattering, whereas we determine matter radius rm40(exp)=3.361±0.075 fm from measured σR for 4He+ 40Ca scattering. Aim:Our first aim is to determine rskin208 from measured σR of p+208Pb scattering at Elab=534.1,549,806MeV by using the Love–Franey (LF) t-matrix folding model. Our second aim is to determine rskin48 from the rm40(exp) and the difference Δ≡rm48(exp)−rm40(exp) that is evaluated from the rn48,40(exp) and the rp48,40(exp) calculated with the isotope shift method based on the electron scattering. Method and results:For the first aim, we use the Love–Franey t-matrix model with the densities scaled from the D1S-GHFB+AMP neutron density, where D1S-GHFB+AMP stands for D1S Gogny HFB (GHFB) with the angular momentum projection (AMP). The D1M-GHFB+AMP is also used to estimate a theoretical error. The resulting skin values are rskin208=0.324±0.047 fm for D1S and rskin208(exp)=0.333±0.047 fm for D1M. The difference Δ=0.109 fm and rm40(exp)=3.361±0.075 fm yield rm48=3.470±0.075 fm, leading to rskin48=0.144±0.075 fm. Conclusion:We conclude that rskin208(exp)=0.324±(0.047)exp±(0.009)thfm for p scattering at Elab=534.1,549,806MeV. Our skin value rskin48=0.144±0.083=0.061∼0.227 fm is consistent with rskin48(CREX)=0.071∼0.171 fm.