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Register a new userReaction cross section of proton scattering consistent with PREX-II
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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.
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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.
{bf Background:} Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with GHFB+AMP, we determined $r_{rm skin}^{208}=0.25$fm from the central values of $sigma_{rm R}$ of p+$^{208}$Pb scattering in $E_{rm in}=40-81$MeV. The high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{rm skin}^{48}(E1{rm pE}) =0.14-0.20$fm. The data on $sigma_{rm R}$ are available as a function of $E_{rm in}$ for $p$+$^{48}$Ca scattering. {bf Aim:} Our aim is to determine $r_{rm skin}^{48}$ from the central values of $sigma_{rm R}$ for $p$+$^{48}$Ca scattering by using the folding model. {bf Results:} As for $^{48}$Ca, we determine $r_n(E1{rm pE})=3.56$fm from the central value 0.17fm of $r_{rm skin}^{48}(E1{rm pE})$ and $r_p({rm EXP})=3.385$fm of electron scattering, and evaluate $r_m(E1{rm pE})=3.485$fm from the $r_n(E1{rm pE})$ and the $r_p({rm EXP})$ of electron scattering. The folding model with GHFB+AMP densities reproduces $sigma_{rm R}$ in $23 leq E_{rm in} leq 25.3$ MeV in one-$sigma$ level, but slightly overestimates the central values of $sigma_{rm R}$ there. In $23 leq E_{rm in} leq 25.3$MeV, the small deviation allows us to scale the GHFB+AMP densities to the central values of $r_p({rm EXP})$ and $r_n(E1{rm pE})$. The $sigma_{rm R}(E1{rm pE})$ obtained with the scaled densities almost reproduce the central values of $sigma_{rm R}$ when $E_{rm in}=23-25.3$MeV, so that the $sigma_{rm R}({rm GHFB+AMP})$ and the $sigma_{rm R}(E1{rm pE})$ are in 1-$sigma$ of $sigma_{rm R}$ there. In $E_{rm in}=23-25.3$MeV, we determine the $r_{m}({rm EXP})$ from the central values of $sigma_{rm R}$ and take the average for the $r_{m}({rm EXP})$. The averaged value is $r_{m}({rm EXP})=3.471$fm. Eventually, we obtain $r_{rm skin}^{48}({rm EXP})=0.146$fm from $r_{m}({rm EXP})=3.471$fm and $r_p({rm EXP})=3.385$fm.
A microscopic calculation of the optical potential for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all the particle-hole (p-h) excitation states in the target and to all relevant pickup channels. These p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and to long-lived compound nucleus resonances. We calculated the reaction cross sections for the nucleon induced reactions on the targets $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm using the QRPA description of target excitations, coupling to all inelastic open channels, and coupling to all transfer channels corresponding to the formation of a deuteron. The results of such calculations were compared to predictions of a well-established optical potential and with experimental data, reaching very good agreement. The inclusion of couplings to pickup channels were an important contribution to the absorption. For the first time, calculations of excitations account for all of the observed reaction cross-sections, at least for incident energies above 10 MeV.
The precise determination of the proton radius from recent elastic scattering electron-proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that such precision is two orders of magnitude higher than the precision on the cross section, that is the measured observable. Different fits on the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be even orders of magnitude larger than commonly assumed.
Background: Using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with Gogny-HFB (GHFB) with the angular momentum projection (AMP), we determined the central values of matter radius and neutron skin from the central values of reaction cross sections $sigma_{rm R}({rm EXP})$ of p+$^{40,48}$Ca and p+$^{208}$Pb scattering. As for p+$^{58}$Ni scattering, $sigma_{rm R}({rm EXP})$ are available as a function of incident energy $E_{rm in}$. Aim: Our aim is to determine matter radius $r_{m}$ and skin $r_{rm skin}$ for $^{58}$Ni from the $sigma_{rm R}({rm EXP})$ of p+$^{58}$Ni scattering by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. Results: For p+$^{58}$Ni scattering, the Kyushu $g$-matrix folding model with the GHFB+AMP densities reproduces $sigma_{rm R}({rm EXP})$ in $8.8 leq E_{rm in} leq 81$MeV. For $E_{rm in}=81$MeV, we define the factor $F$ as $F=sigma_{rm R}({rm EXP})/sigma_{rm R}({rm AMP})=0.9775$. The $Fsigma_{rm R}({rm AMP})$ be much the same as the center values of $sigma_{rm R}({rm EXP})$ in $8.8 leq E_{rm in} leq 81$MeV. We then determine $r_{rm m}({rm EXP})$ from the center values of $sigma_{rm R}({rm EXP})$, using $sigma_{rm R}({rm EXP})=C r_{m}^{2}({rm EXP})$ with $C=r_{m}^{2}({rm AMP})/ (Fsigma_{rm R}({rm AMP}))$. The $r_{m}({rm EXP})$ thus obtained are averaged over $E_{rm in}$. The averaged value is $r_{m}({rm EXP})=3.697$fm. Eventually, we obtain $r_{rm skin}({rm EXP})=0.023$fm from $r_{rm m}=3.697$fm and $r_p({rm EXP})=3.685$fm of electron scattering.
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