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

Abstract

Background: Reaction cross sections σR are available as a function of incident energy Ein for p scattering on a 208 Pb target. Very lately, we reanalyzed interaction cross sections σI (≈ σR)) for 42−51 Ca+ 12 C scattering at Ein = 280 MeV per nucleon, using the chiral (Kyushu) g-matrix folding model with the densities calculated with Gongny-HFB (GHFB) with and without the angular momentum projection (AMP). We determined neutron skin r skin and proton, neutron, matter radii, rp, rn, rm for the σI, using the Kyushu g-matrix folding model. One of the results is r 48 skin = 0.164 fm for 48 Ca. Aim: We determine r 208 skin from the central values of measured σR for p+ 208 Pb scattering, using the Kyushu g-matrix folding model with the GHFB+AMP densities. Results: The Kyushu g-matrix folding model with the GHFB+AMP densities reproduces σR in 40 ≤ Ein ≤ 180 MeV in one-σ level. The rm(AMP) calculated with GHFB+AMP slightly overestimates the lower bound 5.54 fm of rm(PREX) by 0.3%. We then identify the σR(AMP) with the lower bound of σR(PREX). The rp(PREX) and rn(PREX) in PREX are most reliable. The rp(AMP) and rn(AMP) slightly underestimate the central value rp(PREX) =5.45 fm by 0.1% and the central value rn(PREX) =5.78 fm by 3.6%, respectively. The small deviation allows us to scale the GHFB+AMP densities to the central values of rp(PREX) and rn(PREX). The Kyushu g-matrix folding model with the scaled densities almost reproduces the central values of σR when Ein = 40 − 81 MeV, so that both the σR(AMP) and σR(PREX) are in one σ of σR there. In Ein = 40 − 81 MeV, we determine the rm from the central values of σR and take the average for the rm. The averaged value is rm = 5.61 fm, leading to r 208 skin = 0.25 fm.

Reaction cross section of proton scattering consistent with PREX-II

“…The R P V skin value is considerably larger than the other experimental values which are significantly model dependent [11][12][13][14]. The nonlocal dispersive-optical-model (DOM) analysis of 208 Pb deduces r DOM skin = 0.25 ± 0.05 fm [15], The chiral (Kyushu) g-matrix folding model determines r 208 skin = 0.27 ± 0.03 fm from reaction cross section σ R in 30 ≤ E in ≤ 100 MeV [16]. These values are consistent with R P V skin .…”

Neutron skin of 48Ca deduced from interaction cross section

“…this suggests rather soft slope parameters around 27 MeV, in contrast to the 208 Pb results of PREX II and Refs. 2,3…”

“…A new method that relies more directly on another experimental observable, the reaction cross section σ R , was proposed in Refs. 2,3 From the experimental perspective, this is a method to extract R skin from σ R based on a reaction model with a microscopic optical potential. At the same time, from a theoretical perspective, this improves the calculated R skin given by mean-field models with energy-density functionals whose parameters might not yet be fully constrained.…”

Neutron skin $r_{\rm skin}^{48}$ determined from reaction cross section of proton+$^{48}$Ca scattering

“…In the previous work [8], we determined the neutron skin r 208 skin = 0.25 fm from the central values of σ R (EXP) of p+ 208 Pb scattering in E in = 40 − 81 MeV, using the chiral (Kyushu) g-matrix folding model with the densities calculated with Gongny-HFB (GHFB) with the angular momentum projection (AMP), The g-matrix folding model is a standard way of obtaining microscopic optical potential for proton scattering and nucleus-nucleus scattering [9][10][11][12][13][14][15][16][17][18]. Applying the folding model with the Melbourne g-matrix [12] for interaction cross sections σ I for Ne isotopes and σ R for Mg isotopes, we found that 31 Ne is a deformed halo nucleus [19], and deduced the matter radii r m for Ne isotopes [20] and for Mg isotopes [21].…”