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Tomotsugu Wakasa

Publications and source records attributed to Tomotsugu Wakasa.

17 recordsLinked to original sources
arXiv2025

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 (published in Results in Physics)

In the previous paper, we predicted reaction cross sections $σ_{\rm R}$ for $^{40-60,62,64}$Ca+$^{12}$C scattering at $280$~MeV/nucleon, since Tanaka {\it el al.} measured interaction cross sections $σ_{\rm I}$ for $^{42-51}$Ca in RIKEN and determined neutron skin $r_{\rm skin}({\rm RIKEN})$ using the optical limit of the Glauber model with the Woos-Saxon densities. Our purpose is to reanalyze the $r_{\rm skin}$ from the $σ_{\rm I}$. Our analysis is superior to theirs, since the chiral $g$-matrix folding model (the GHFB and GHFB+AMP densities) is much better than the optical limit of the Glauber model (the Woos-Saxon densities). Our model is the chiral $g$-matrix folding model with the densities scaled from the GHFB and GHFB+AMP densities. We scale the GHFB and GHFB+AMP densities so that the $σ_{\rm R}$ of the scaled densities can agree with the central values of $σ_{\rm I}$ under the condition that the proton radius of the scaled proton density equals the data determined from the isotope shift based on the electron scattering. The $r_{\rm skin}$ thus determined are close to their results $r_{\rm skin}^{42-51}({\rm RIKEN})$. For $^{48}$Ca, our value $r_{\rm skin}^{48}$ is 0.105 $\pm$ 0.06~fm, while their value is $r_{\rm m}^{48}({\rm RIKEN})=0.146 \pm 0.06$~fm. We take the weighted mean and its error of $r_{\rm skin}^{48}(σ_{\rm I})= 0.105 \pm 0.06$~fm and $r_{\rm skin}^{48}(E1{\rm pE}) =0.17 \pm 0.03$~fm of the high-resolution $E1$ polarizability experiment (E1{\rm pE}). Our final result is $r_{\rm skin}^{48}=0.157 \pm 0.027$~fm. Our conclusion is $r_{\rm skin}^{48}=0.157 \pm 0.027$~fm for $^{48}$Ca. For $^{42-47,49-51}$Ca, our results on $r_{\rm skin}$ are similar to theirs. Our result for $^{48}$Ca is related to CREX.

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arXiv2025

Folding-model approach to reaction cross section of $^{4,6,8}$He+$^{12}$C scattering at 790 MeV (published in Results in Physics)

Tanihata {\it et al.} determined matter radii $r_{m}(σ_{\rm I})$ for $^{4,6,8}$He from interaction cross sections $σ_{\rm I}$ of $^{4,6,8}$He+$^{12}$C scattering at 790 MeV per nucleon, using the optical limit of the Glauber model. Lu {\it et al.} determined proton radii $r_{p}({\rm AIS})$ for $^{4,6,8}$He with the atomic isotope shifts (AIS). We investigate whether the Love-Franey $t$-matrix folding model is good for $^{4,6,8}$He+$^{12}$C scattering at 790 MeV per nucleon.

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arXiv2025

Reaction cross section of proton scattering consistent with PREX-II (published in Results in Physics)

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 $σ_R$ is useful to determine the matter radius $R_m$ and $R_{\rm skin}$. For proton scattering, the reaction cross section $σ_R$ 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 D1S-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 $σ_R$. Aim: Our aim is to find the $σ_R$ of proton scattering consistent with $R_{\rm skin}^{\rm PV}$. Conclusion: The $σ_R$ of proton scattering consistent with $R_{\rm skin}^{\rm PV}$ are $σ_R^{\rm exp}$ at $E_{\rm in} = 534.1, 549, 806$ MeV.

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arXiv2025

Neutron skin in $^{48}$Ca determined from p+$^{48}$Ca and $^{48}$Ca+$^{12}$C scattering

In our previous paper, we determined $r_{\rm skin}^{208}({\rm exp})=0.278 \pm 0.035$~fm from $σ_{\rm R}$ for p+$^{208}$Pb scattering, using the Kyushu (chiral) $g$-matrix folding model with the densities calculated with D1S-GHFB with the angular momentum projection (AMP). The value agrees with that of PREX2. Reaction cross sections $σ_{\rm R}$ are available for p+$^{48}$Ca scattering, whereas interaction cross sections $σ_{\rm I}$ are available for $^{48}$Ca + $^{12}$C scattering. As for $^{48}$Ca, the high-resolution $E1$ polarizability experiment ($E1$pE) yields $r_{\rm skin}^{48}(E1{\rm pE}) =0.14 \sim 0.20~{\rm fm}$. We determine $r_{\rm skin}^{48}({\rm exp})$ from the data on $σ_{\rm R}$ for p+$^{48}$Ca scattering and from the data on $σ_{\rm I}$ for $^{48}$Ca+$^{12}$C scattering. We use the Kyushu $g$-matrix folding model with the densities calculated with the D1M-GHFB+AMP densities. The D1M-GHFB+AMP proton and neutron densities are scaled so as to reproduce the data under the condition that the radius $r_{\rm p}$ of the scaled proton density equals the data $r_{\rm p}({\rm exp})$ determined from the electron scattering. We deduce skin values $r_{\rm skin}=r_{\rm n}({\rm exp})-r_{\rm p}({\rm exp})$ from the resulting $r_{\rm n}({\rm exp})$ and the $r_{\rm p}({\rm exp})$ determined from electron scattering. The same procedure is taken for D1S-GHFB+AMP. We regard $r_{\rm skin}^{48}(E1{\rm pE})$ as a reference skin value. Using the reference skin value and taking D1M-GHFB+AMP, we determine $r_{\rm skin}^{48}({\rm exp})=0.158 \pm 0.025$~fm for p+$^{48}$Ca scattering and $0.160 \pm 0.058$~fm for $^{48}$Ca + $^{12}$C scattering. We take the weighted mean and its error for the two skin values. The result is $r_{\rm skin}^{48}({\rm exp})=0.158 \pm (0.023)_{\rm exp} \pm (0.012)_{\rm th}~{\rm fm}$.

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arXiv2025

Matter radii and skins of $^{6,8}$He from reaction cross section of proton+$^{6,8}$He scattering based on the Love-Franey $t$-matrix model (published in Results in Physics)

For $^{4,6,8}$He, Tanihata et al. determined matter radii $r_{m}(σ_{\rm I})=1.57(4), 2.48(3), 2.52(3)$~fm from interaction cross sections $σ_{\rm I}$ for $^{4,6,8}$He scattering on Be, C Al targets at 790~MeV/nucleon. Lu et al. measured the atomic isotope shifts (AIS) for $^{4,6,8}$He and determined proton radii $r_{p}({\rm AIS})$ for $^{4,6,8}$He. As for p+$^{4,6,8}$He scattering, reaction cross sections $σ_{\rm R}({\rm exp})$ are available at 700~MeV with high accuracy. Our aim is to determine matter radii $r_{m}$ and skins $r_{\rm skin}$ for $^{6,8}$He from the $σ_{\rm R}({\rm exp})$ and the $r_{p}({\rm AIS})$. {\bf Method:} Our model is the Love-Franey $t$-matrix folding model, since the model is better than the optical limit of Glauber model. Our results for $^{6,8}$He are $r_{m}({\rm exp})=2.48(3), 2.53(2)$~fm and $r_{\rm skin}=$0.78(3), 0.82(2)~fm. For $^{6,8}$He, our results $r_{m}(σ_{\rm R})$ agree with those of Tanihata {\it et al.}. For $^{8}$He, the distance between $^{4}$He and the center of mass of valence four neutrons is 2.367~fm.

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arXiv2025

Slope parameters determined from CREX and PREX2 (published in Results in Physics)

[Background] Very lately, the CREX group presents a skin value $ΔR_{\rm skin}^{48}({\rm CREX}) =0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}=0.071\sim 0.171$~fm. Meanwhile, the PREX group reported a skin value $ΔR_{\rm skin}^{208}({\rm PREX2}) = 0.283\pm 0.071=0.212 \sim 0.354$~fm. In our previous paper, we determined both the $L$--$ΔR_{\rm skin}^{48}$ relation and the $L$--$ΔR_{\rm skin}^{208}$ one, using 206 EoSs, where $L$ is a slope parameter. [Purpose] We determine $L$ from $ΔR_{\rm skin}^{48}({\rm CREX})$ and $ΔR_{\rm skin}^{208}({\rm PREX2}) $, using 207 EoSs. [Results] The $ΔR_{\rm skin}^{48}({\rm CREX})$ yields $L({\rm CREX})=0 \sim 51$~MeV and the $ΔR_{\rm skin}^{208}({\rm PREX2}) $ does $L({\rm PREX2})=76 \sim 165$~MeV. [Conclusion] There is no overlap between $L({\rm CREX})$ and $L({\rm PREX2})$. This is a big problem to be solved.

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arXiv2025

Skin values of $^{208}$Pb and $^{48}$Ca determined from reaction cross sections (published in Results in Physics)

The PREX and the CREX group reported their skin values. Using the Love-Franey (LF) $t$-matrix folding model with the neutron and proton densities scaled to the neutron radius $r_{\rm n}^{208}({\rm PREX2})$ and the proton radius of the electron scattering, we found that the model reproduces $σ_R$ for p+ $^{208}$Pb scattering at $E_{\rm lab} = 534.1, 549, 806$MeV. Zenihiro {\it el al. } deduce neutron radii $r_{\rm n}^{48,40}({\rm exp})$ from proton elastic scattering, whereas we determine $r_{\rm m}^{\rm 40}({\rm exp})=3.361 \pm 0.075$fm from measured $σ_R$ for $^{4}$He+ $^{40}$Ca scattering. Our first aim is to determine $r_{\rm skin}^{\rm 208}$ from measured $σ_R$ of p+$^{208}$Pb scattering at $E_{\rm lab} = 534.1, 549, 806$MeV by using the LF $t$-matrix folding model. Our second aim is to determine $r_{\rm skin}^{\rm 48}$ from the $r_{\rm m}^{\rm 40}({\rm exp})$ and $Δ\equiv r_{\rm m}^{\rm 48}({\rm exp})-r_{\rm m}^{\rm 40}({\rm exp})$ that is evaluated from the $r_{\rm n}^{48,40}({\rm exp})$ and the $r_{\rm p}^{48,40}({\rm exp})$ calculated with the isotope shift method based on the electron scattering. For the first aim, we use the LF $t$-matrix model with the densities scaled from the D1S-GHFB+AMP neutron density. The D1M-GHFB+AMP is used to estimate a theoretical error. The resulting skin values are $r_{\rm skin}^{\rm 208}= 0.324 \pm 0.047$fm for D1S and $r_{\rm skin}^{\rm 208}({\rm exp})=0.333 \pm 0.047 $fm for D1M. The $Δ=0.109$fm and $r_{\rm m}^{\rm 40}({\rm exp})=3.361 \pm 0.075$fm yield $r_{\rm m}^{\rm 48}=3.470 \pm 0.075$fm, leading to $r_{\rm skin}^{\rm 48}=0.144 \pm 0.075$fm. We conclude that $r_{\rm skin}^{208}({\rm exp})=0.324 \pm (0.047)_{\rm exp} \pm (0.009)_{\rm th}~{\rm fm}$ for p scattering at $E_{\rm lab} = 534.1, 549, 806$MeV. Our skin values are consistent with the PREX2 and CREX values.

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arXiv2025

Skin values and matter radii of $^{208}$Pb and $^{58,60,64}$Ni based on reaction cross section of $^{3,4}$He scattering (published in Results in Physics)

The PREX group reported a new skin value, $r_{\rm skin}^{208}({\rm PREX2}) = 0.283 \pm 0.071{\rm fm}$. Using the chiral (Kyushu) $g$-matrix folding model with the proton and neutron densities determined with D1S+GHFB+AMP, we determined neutron skin thickness $r_{\rm skin}^{208}({\rm exp})$ from reaction cross sections $σ_{\rm R}({\rm exp})$ of p+$^{208}$Pb scattering. The method also yielded $r_{\rm skin}^{208}({\rm exp})$ from $σ_{\rm R}({\rm exp})$ of $^{4}$He+$^{208}$Pb scattering. We accumulated the 206 EoSs and determined a sloop parameter from the 206 EoSs. The value yields $r_{\rm skin}^{208}=0.102 \sim 0.354~{\rm fm}$. As the first aim, we first determine $r_{\rm skin}^{208}({\rm exp})$ from $σ_{\rm R}({\rm exp})$ of $^{3}$He scattering on $^{208}$Pb target and take the weighted mean and its error for $r_{\rm skin}^{208}({\rm PREX2})$, three skin values of p+$^{208}$Pb, $^{3, 4}$He+$^{208}$Pb scattering and the $r_{\rm skin}^{208}$ based on the 206 EoSs. As the second aim, we determine matter radii $r_{m}({\rm exp})$ of $^{58,60,64}$Ni from $σ_{\rm R}({\rm exp})$ of $^{3,4}$He scattering on $^{58,60,64}$Ni targets. Our result is $r_{\rm skin}^{208}({\rm exp}) =0.512 \pm 0.268~{\rm fm}$ for $^{3}$He+$^{208}$Pb scattering. Our conclusion is $r_{\rm skin}^{208} =0.285 \pm 0.030~{\rm fm}$. It is determined from the 5 skin values mentioned above.

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arXiv2025

Determination of matter radius and neutron-skin thickness of $^{60,62,64}$Ni from reaction cross section of proton scattering on $^{60,62,64}$Ni targets (published in Results in Physics)

In our previous work, we determined matter radii $r_{\rm m}({\rm exp})$ and neutron-skin thickness $r_{\rm skin}({\rm exp})$ from reaction cross sections $σ_{\rm R}({\rm exp})$ of proton scattering on $^{208}$Pb, $^{58}$Ni, $^{40,48}$Ca, $^{12}$C targets, using the chiral (Kyushu) $g$-matrix folding model with the densities calculated with Gogny-D1S-HFB (D1S-GHFB) with angular momentum projection (AMP). The resultant $r_{\rm skin}({\rm exp})$ agree with the PREX2 and CREX values. As for $^{58}$Ni, our value is consistent with one determined from the differential cross section for $^{58}$Ni+$^{4}$He scattering. As for p+$^{60,62,64}$N scattering, $σ_{\rm R}({\rm exp})$ are available as a function of incident energies $E_{\rm in}$, where $E_{\rm in}=22.8 \sim 65.5$~MeV for $^{60}$Ni, $E_{\rm in}=40,60.8$~MeV for $^{62}$Ni, $E_{\rm in}=40, 60.8$~MeV for $^{64}$Ni. Our aim is to determine matter radii $r_{\rm m}({\rm exp})$ for $^{60,62,64}$Ni from the $σ_{\rm R}({\rm exp})$. Our method is the Kyushu $g$-matrix folding model with the densities scaled from D1S-GHFB+AMP densities, Our skin values are $r_{\rm skin}({\rm exp})=0.076 \pm 0.019,~0.106 \pm 0.192,~0.162 \pm 0.176$~fm, and $r_{\rm m}({\rm exp})=3.759 \pm 0.011,~3.811 \pm 0.107,~3.864 \pm 0.101$~fm for $^{60,62,64}$Ni, respectively.

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arXiv2025

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

The reaction cross section $σ_R$ 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 $σ_R$ 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 $σ_R$ 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 $σ_{\rm R}$ 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 $σ_R$ allows us to scale the GHFB+AMP neutron density so as to reproduce the $σ_R$ data. In $E_{\rm in}$ = 30--100 MeV, the experimental $σ_R$ 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 $r_{\rm skin}$ = $0.283\pm 0.071$ fm.

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arXiv2024

The consistent analyses for determination of the point-nucleon distributions by electron and proton scatterings

Electron scattering cross section, as well as proton scattering cross section, observes the point-proton and the point-neutron distributions, but both cross sections are not able to determine them separately. If they are analyzed consistently with each other, there is a possibility to determine them with less ambiguity.The consistency can be examined through the moments of the charge distribution, which linearly depend on the moments of the point-proton and -neutron distributions.

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arXiv2023

$^{12}$C+$^{12}$C scattering as the reference system for reaction cross section

In our previous paper, we tested the chiral (Kyushu) folding model for $^{12}$C+$^{12}$C scattering, since the profile function in the Glauber mode is constructed for the system. We found that the folding model is reliable for reaction cross sections $σ_{\rm R}$ in $30 \lsim E_{\rm lab} \lsim 100 $~MeV and $250 \lsim E_{\rm lab} \lsim 400 $~MeV. Accurate data are available for $^{12}$C scattering on $^{9}$Be, $^{12}$C, $^{27}$Al targets in $30 \lsim E_{\rm lab} \lsim 400 $~MeV. We determine matter radius $r_{m}({\rm exp})$ of $^{12}$C from the accurate $σ_{\rm R}({\rm exp})$, using the Kyushu $g$-matrix folding model. Our result is $r_{\rm m}^{12}({\rm exp}) =2.352 \pm 0.013$~fm for $^{12}$C. The model is applied for the accurate data on $^{12}$C+$^{27}$Al scattering, and yields $r_{\rm m}({\rm exp}) =2.936 \pm 0.012$~fm for $^{27}$Al. Our conclusion is that $r_{\rm m}({\rm exp}) =2.352 \pm 0.013$~fm agrees with $r_{\rm m}({\rm exp}) =2.35 \pm 0.02$~fm determined from interaction cross sections by Tanihata {\it et. al.}.

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arXiv2023

Neutron skin thickness of $^{116,118,120,122,124}$Sn determined from reaction cross sections of proton scattering

The cross sections of SDR in the Sb isotopes have been measured. Within the model used, the neutron-skin thicknesses $r_{\rm skin}({\rm exp})$ deduced $0.12 \pm 0.06$fm for $^{116}$Sn, $0.13 \pm 0.06$fm for $^{118}$Sn, $0.18 \pm 0.07$fm for $^{120}$Sn, $0.22 \pm 0.07$fm for $^{122}$Sn, $0.19 \pm 0.07$fm for $^{124}$Sn. We tested the chiral (Kyushu) $g$-matrix folding model for $^{12}$C+$^{12}$C scattering, and found that the Kyushu $g$-matrix folding model is reliable for reaction cross sections $σ_{\rm R}$ in $30 < E_{\rm in} < 100 $MeV and $250 < E_{\rm in} < 400$MeV. We determine neutron skin thickness $r_{\rm skin}({\rm exp})$, using measured $σ_{\rm R}$ of $^{4}$He+$^{116,120,224}$Sn scattering. The results are $r_{\rm skin}({\rm exp})=0.242 \pm 0.140$fm for $^{116}$Sn, $r_{\rm skin}({\rm exp})=0.377 \pm 0.140$fm for $^{120}$Sn, $r_{\rm skin}({\rm exp})=0.180 \pm 0.142$fm for $^{124}$Sn. The $σ_{\rm R}$ are available for proton scattering on $^{116,118,120,122,124}$Sn with high accuracy. Our aim is to determine $r_{\rm skin}({\rm exp})$ for $^{116,118,120,122,124}$Sn with small errors by using the Kyushu $g$-matrix folding model. Our model is the folding model with the densities scaled from the D1S-GHFB+AMP neutron density. The proton radii of D1S-GHFB+AMP agree with those calculated with the isotope shift method based on the electron scattering. We then scale the neutron densities so as to reproduce the $σ_{\rm R}({\rm exp})$. In $30 < E_{\rm in} < 65$MeV, we determine $r_{\rm skin}({\rm exp})$ from measured $σ_{\rm R}$. The values are $r_{\rm skin}({\rm exp})=0.118 \pm 0.021$~fm for $^{116}$Sn, $0.112 \pm 0.021$fm for $^{118}$Sn, $0.124 \pm 0.021$fm for $^{120}$Sn, $0.156 \pm 0.022$fm for $^{124}$Sn. As for $^{122}$Sn, the skin value in $30 < E_{\rm in} < 50$MeV is $0.122 \pm 0.024$fm. Our results are consistent with the previous values.

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arXiv2022

Neutron-skin values and matter and neutron radii determined from reaction cross sections of proton scattering on $^{12}$C, $^{40,48}$Ca, $^{58}$Ni, $^{208}$Pb

Very lately, the PREX and the CREX collaboration present skin values, $r_{\rm skin}^{208}({\rm newPREX2}) =0.278 \pm 0.078\ {\rm (exp)} \pm 0.012\ {\rm (theor.)}\,{\rm fm}$ and $r_{\rm skin}^{48}=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$, respectively. We recently determined a neutron-skin value $r_{\rm skin}^{208}=0.278 \pm 0.035$fm from measured reaction cross sections $σ_{\rm R}({\rm exp})$ of p+$^{208}$Pb scattering in a range of incident energies $10 \lsim E_{\rm in} \lsim 100$ MeV where the chiral (Kyushu) $g$-matrix folding model is reliable for $^{12}$C+$^{12}$C scattering. The data $σ_{\rm R}({\rm exp})$ are available for proton scattering on $^{58}$Ni, $^{40,48}$Ca, $^{12}$C targets. Our first aim is to test the Kyushu $g$-matrix folding model for p+$^{208}$Pb scattering in $20 \lsim E_{\rm in} \lsim 180$ MeV. Our second aim is to determine skin values $r_{\rm skin}$ and matter and neutron radii, $r_{\rm m}$ and $r_{\rm n}$, for $^{208}$Pb, $^{58}$Ni, $^{40,48}$Ca, $^{12}$C from the $σ_{\rm R}({\rm exp})$. Our method is the Kyushu $g$-matrix folding model with the densities scaled from the D1S-GHFB+AMP densities, where D1S-GHFB+AMP stands for Gogny-D1S HFB (GHFB) with the angular momentum projection (AMP). As for proton scattering, we find that our model is reliable in $20 \lsim E_{\rm in} \lsim 180$ MeV. For $^{208}$Pb, the skin value deduced from $σ_{\rm R}({\rm exp})$ in $20 \lsim E_{\rm in} \lsim 180$ MeV is $r_{\rm skin}^{208}(σ_{\rm R})=0.299 \pm 0.020$ fm. Our results on $r_{\rm skin}$ are compared with the previous works. Our result $r_{\rm skin}^{208}(σ_{\rm R}) = 0.299 \pm 0.020$ fm agrees with $r_{\rm skin}^{208}({\rm PREX2}) = 0.283\pm 0.071$ fm. In addition, our result $r_{\rm skin}^{48}=0.103 \pm 0.022$ fm is consistent with the CREX value.

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arXiv2020

Determination of matter radius and neutron skin of $^{58}$Ni from reaction cross section of proton+$^{58}$Ni scattering based on chiral $g$-matrix model

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 $σ_{\rm R}({\rm EXP})$ of p+$^{40,48}$Ca and p+$^{208}$Pb scattering. As for p+$^{58}$Ni scattering, $σ_{\rm R}({\rm EXP})$ 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 $σ_{\rm R}({\rm EXP})$ 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 $σ_{\rm R}({\rm EXP})$ in $8.8 \leq E_{\rm in} \leq 81$MeV. For $E_{\rm in}=81$MeV, we define the factor $F$ as $F=σ_{\rm R}({\rm EXP})/σ_{\rm R}({\rm AMP})=0.9775$. The $Fσ_{\rm R}({\rm AMP})$ be much the same as the center values of $σ_{\rm R}({\rm EXP})$ in $8.8 \leq E_{\rm in} \leq 81$MeV. We then determine $r_{\rm m}({\rm EXP})$ from the center values of $σ_{\rm R}({\rm EXP})$, using $σ_{\rm R}({\rm EXP})=C r_{m}^{2}({\rm EXP})$ with $C=r_{m}^{2}({\rm AMP})/ (Fσ_{\rm R}({\rm AMP}))$. 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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arXiv2020

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

{\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 $σ_{\rm R}$ 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 $σ_{\rm R}$ 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 $σ_{\rm R}$ 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 $σ_{\rm R}$ in $23 \leq E_{\rm in} \leq 25.3$ MeV in one-$σ$ level, but slightly overestimates the central values of $σ_{\rm R}$ 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 $σ_{\rm R}(E1{\rm pE})$ obtained with the scaled densities almost reproduce the central values of $σ_{\rm R}$ when $E_{\rm in}=23-25.3$MeV, so that the $σ_{\rm R}({\rm GHFB+AMP})$ and the $σ_{\rm R}(E1{\rm pE})$ are in 1-$σ$ of $σ_{\rm R}$ there. In $E_{\rm in}=23-25.3$MeV, we determine the $r_{m}({\rm EXP})$ from the central values of $σ_{\rm R}$ 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.

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