Reaction cross section of proton scattering consistent with PREX-II

Background: The neutron skin thickness $R_{rm skin}^{rm PV}$ of PREX-II is presented in Phys. Rev. Lett. {bf 126}, 172502 (2021). The reaction cross section $sigma_R$ is useful to determine the matter radius $R_m$ and $R_{rm skin}$. For proton scattering, the reaction cross section $sigma_R$ are available for $E_{rm in} > 400$ MeV. Method and results: We determine $R_n^{rm exp}=5.727 pm 0.071$ fm and $R_m^{rm exp}=5.617 pm 0.044$ fm from $R_p^{rm exp}$ = 5.444 fm and $R_{rm skin}^{rm PV}$. The $R_p^{rm GHFB}$ calculated with Gongny-D1S HFB (GHFB) with the angular momentum projection (AMP). agrees with $R_p^{rm exp}$. The neutron density calculated with GHFB+AMP is scaled so as to $R_n^{rm scaling}=5.727$ fm. The Love-Franey $t$-matrix model with the scaled densities reproduces the data on $sigma_R$. Aim: Our aim is to find the $sigma_R$ of proton scattering consistent with $R_{rm skin}^{rm PV}$. Conclusion: The $sigma_R$ of proton scattering consistent with $R_{rm skin}^{rm PV}$ are $sigma_R^{rm exp}$ at $E_{rm in} = 534.1, 549, 806$ MeV.

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

The reaction cross section $sigma_R$ is useful to determine the neutron radius $R_n$ as well as the matter radius $R_m$. The chiral (Kyushu) $g$-matrix folding model for $^{12}$C scattering on $^{9}$Be, $^{12}$C, $^{27}$Al targets was tested in the incident energy range of $30 lsim E_{rm in} lsim 400 $ MeV, and it is found that the model reliably reproduces the $sigma_R$ in $30 lsim E_{rm in} lsim 100 $ MeV and $250 lsim E_{rm in} lsim 400$ MeV. item[Aim] We determine $R_n$ and the neutron skin thickness $R_{rm skin}$ of ${}^{208}{rm Pb}$ by using high-quality $sigma_R$ data for the $p+{}^{208}{rm Pb}$ scattering in $30 leq E_{rm in} leq 100$ MeV. The theoretical model is the Kyushu $g$-matrix folding model with the densities calculated with Gongny-D1S HFB (GHFB) with the angular momentum projection (AMP). item[Results] The Kyushu $g$-matrix folding model with the GHFB+AMP densities underestimates $sigma_{rm R}$ in $30 leq E_{rm in} leq 100$~MeV only by a factor of 0.97. Since the proton radius $R_p$ calculated with GHFB+AMP agrees with the precise experimental data of 5.444 fm, the small deviation of the theoretical result from the data on $sigma_R$ allows us to scale the GHFB+AMP neutron density so as to reproduce the $sigma_R$ data. In $E_{rm in}$ = 30--100 MeV, the experimental $sigma_R$ data can be reproduced by assuming the neutron radius of ${}^{208}{rm Pb}$ as $R_n$ = $5.722 pm 0.035$ fm. item[Conclusion] The present result $R_{rm skin}$ = $0.278 pm 0.035$ fm is in good agreement with the recent PREX-II result of $r_{rm skin}$ = $0.283pm 0.071$ fm.

High rate production of polarized 3He with meta-stability exchange method

Keywords: polarized 3He, meta-stability exchange, infrared laser