Skin values of ²⁰⁸Pb and ⁴⁸Ca determined from reaction cross sections (published in Results in Physics)

2022/11/10 by Wakasa, Tomotsugu, Tagami, Shingo, Yahiro, Masanobu
#FOS: Physical sciences #Nuclear Experiment (nucl-ex) #Nuclear Theory (nucl-th)

paper · doi:10.48550/arxiv.2211.05312

Abstract

The PREX and the CREX group reported their skin values. Using the Love-Franey (LF) t-matrix folding model with the neutron and proton densities scaled to the neutron radius r_{\rm n}²⁰⁸(\rm PREX2) and the proton radius of the electron scattering, we found that the model reproduces σ_R for p+ ²⁰⁸Pb scattering at E_{\rm lab} = 534.1, 549, 806MeV. Zenihiro \it el al. deduce neutron radii r_{\rm n}^48,40(\rm exp) from proton elastic scattering, whereas we determine r_{\rm m}^{\rm 40}(\rm exp)=3.361 ± 0.075fm from measured σ_R for ⁴He+ ⁴⁰Ca scattering. Our first aim is to determine r_{\rm skin}^{\rm 208} from measured σ_R of p+²⁰⁸Pb scattering at E_{\rm lab} = 534.1, 549, 806MeV by using the LF t-matrix folding model. Our second aim is to determine r_{\rm skin}^{\rm 48} from the r_{\rm m}^{\rm 40}(\rm exp) and Δ≡ r_{\rm m}^{\rm 48}(\rm exp)-r_{\rm m}^{\rm 40}(\rm exp) that is evaluated from the r_{\rm n}^48,40(\rm exp) and the r_{\rm p}^48,40(\rm exp) calculated with the isotope shift method based on the electron scattering. For the first aim, we use the LF t-matrix model with the densities scaled from the D1S-GHFB+AMP neutron density. The D1M-GHFB+AMP is used to estimate a theoretical error. The resulting skin values are r_{\rm skin}^{\rm 208}= 0.324 ± 0.047fm for D1S and r_{\rm skin}^{\rm 208}(\rm exp)=0.333 ± 0.047 fm for D1M. The Δ=0.109fm and r_{\rm m}^{\rm 40}(\rm exp)=3.361 ± 0.075fm yield r_{\rm m}^{\rm 48}=3.470 ± 0.075fm, leading to r_{\rm skin}^{\rm 48}=0.144 ± 0.075fm. We conclude that r_{\rm skin}²⁰⁸(\rm exp)=0.324 ± (0.047)_{\rm exp} ± (0.009)_{\rm th}~\rm fm for p scattering at E_{\rm lab} = 534.1, 549, 806MeV. Our skin values are consistent with the PREX2 and CREX values.

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