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Register a new userNeutron removal cross section as a measure of neutron skin
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We study the relation between neutron removal cross section ($sigma_{-N}$) and neutron skin thickness for finite neutron rich nuclei using the statistical abrasion ablation (SAA) model. Different sizes of neutron skin are obtained by adjusting the diffuseness parameter of neutrons in the Fermi distribution. It is demonstrated that there is a good linear correlation between $sigma_{-N}$ and the neutron skin thickness for neutron rich nuclei. Further analysis suggests that the relative increase of neutron removal cross section could be used as a quantitative measure for the neutron skin thickness in neutron rich nuclei.
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{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.
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.
We present and discuss numerical predictions for the neutron density distribution of $^{208}$Pb using various non-relativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.
Neutron skin thickness ($Delta r_{rm np}$) of nuclei and the inferred nuclear symmetry energy are of critical importance to nuclear physics and astrophysics. It is traditionally measured by nuclear processes with significant theoretical uncertainties. We recently proposed an indirect measurement of the $Delta r_{rm np}$ by charged hadron multiplicities in central isobaric collisions at relativistic energies, which are sensitive to nuclear densities. In this paper we propose a direct measurement of the $Delta r_{rm np}$ by using net-charge multiplicities in ultra-peripheral (grazing) collisions of those isobars, under the assumption that they are simple superimposition of nucleon-nucleon interactions. We illustrate this novel approach by the TRENTO and URQMD models.
Single neutron- and proton-removal cross sections have been systematically measured for 72 medium-mass neutron-rich nuclei around Z=50 and energies around 900A MeV using the FRagment Separator (FRS) at GSI. Neutron-removal cross sections are described by considering the knock-out process together with initial- and final-state interactions. Proton-removal cross sections are, however, significantly smaller than predicted by the same calculations. The observed difference can be explained as due to the knockout of short-correlated protons in neutron-proton dominating pairs.
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