Neutron skin in ⁴⁸Ca determined from p+⁴⁸Ca and ⁴⁸Ca+¹²C scattering

Background: In our previous paper, we determined r_skin²⁰⁸(exp)=0.278±0.035 fm from measured reaction cross sections σ_R for p+²⁰⁸Pb scattering, using the Kyushu (chiral) g-matrix folding model with the densities calculated with the Gogny-D1S Hartree–Fock–Bogoliubov (D1S-GHFB) with the angular momentum projection (AMP). The value agrees with that of PREX2. Reaction cross sections σ_R are available for p+⁴⁸Ca scattering, whereas interaction cross sections σ_I(≈σ_R) are available for ⁴⁸Ca + ¹²C scattering. As for ⁴⁸Ca, the high-resolution E1 polarizability experiment (E1pE) yields r_skin⁴⁸(E1pE)=0.14∼0.20fm. Purpose: We determine r_skin⁴⁸(exp) from the data on σ_R for p+⁴⁸Ca scattering and from the data on σ_I for ⁴⁸Ca+¹²C scattering. Methods: We use the Kyushu g-matrix folding model with the densities calculated with the D1M-GHFB+AMP densities. The D1M-GHFB+AMP proton and neutron densities are scaled so as to reproduce the data under the condition that the radius r_p of the scaled proton density equals the data r_p(exp) determined from the electron scattering. We deduce skin values r_skin=r_n(exp)−r_p(exp) from the resulting r_n(exp) and the r_p(exp) determined from electron scattering. The same procedure is taken for D1S-GHFB+AMP. Results: We regard r_skin⁴⁸(E1pE) as a reference skin value. Using the reference skin value and taking D1M-GHFB+AMP, we determine r_skin⁴⁸(exp)=0.158±0.025 fm for p+⁴⁸Ca scattering and 0.160±0.058 fm for ⁴⁸Ca + ¹²C scattering. Conclusion: We take the weighted mean and its error for the two skin values. The result is r_skin⁴⁸(exp)=0.158±(0.023)_exp±(0.012)_thfm.