Reanalyses for $^{42-51}$Ca scattering on a $^{12}$C target at $280$ MeV/nucleon based on chiral $g$ folding mode with Gogny-D1S Hartree-Fock-Bogoliubov densities

Abstract

In our previous paper, we predicted neutron skin r skin and proton, neutron, matter radii, rp, rn, rm for 62,64 Ca after determining the neutron dripline, using the Gogny-D1S Hartree-Fock-Bogoliubov (GHFB) with and without the angular momentum projection (AMP). Using the chiral g-matrix folding model, we predicted reaction cross section σR for 62,64 Ca scattering on a 12 C target at 280 MeV/nucleon, since Tanaka el al. measured interaction cross sections σI(≈ σR) for 42−51 Ca in RIKEN. After our prediction, they determine rm(RIKEN), r skin (RIKEN), rn(RIKEN). In this paper, we reanalyses the σI, since they assumed the Wood-Saxon densities for 42−51 Ca. The σR calculated with the folding model with GHFB and GHFB+AMP densities almost reproduce the σI. We then scale proton and neutron densities so that rp and rn may agree with the central values of rp(exp) and rn(RIKEN), respectively. The σR calculated with the scaled densities do not reproduce the central values of σI perfectly. We then determine the rm that agree with the central values of σI, using the chiral g-matrix folding model. The fitted rm do not reproduce the central values of rm(RIKEN) perfectly, but are in one σ level. Finally, we show the r skin , rn determined from the fitted rm are close to the original ones except for r 48 skin . The fitted r 48 skin is 0.105 fm, while the central value of r 48 m (RIKEN) is 0.146 fm. When we fit rm to the upper bound of σI, the fitted r 48 skin is 0.164 fm and near the central vale 0.17 fm of the high-resolution E1 polarizability experiment.

Neutron skin thickness of ${}^{208}$Pb determined from reaction cross section for proton scattering

“…r 48 skin (E1pE) = 0.17 ± 0.03 +0.025 −0.021 = 0.14 − 0.20 fm (6) for 48 Ca [5]. In our previous work, we determined r 48 skin = 0.164 fm as a central value [6].…”

“…for the numerical values. In our previous work [6], we reanalyzed the σ I with the chiral g-matrix folding model with the densities calculated with Gongy D1S HFB (GHFB) with the angular momentum projection (AMP), and determined r skin (AMP), r m (AMP), r n (AMP) for 42−51 Ca. One of the results is r 48 skin = 0.164 fm as a central value.…”