Skin values of $^{208}$Pb and $^{48}$Ca determined from reaction cross sections (published in Results in Physics)
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| Formato: | Preprint |
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2022
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| _version_ | 1866915362568667136 |
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| author | Wakasa, Tomotsugu Tagami, Shingo Yahiro, Masanobu |
| author_facet | Wakasa, Tomotsugu Tagami, Shingo Yahiro, Masanobu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_05312 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Skin values of $^{208}$Pb and $^{48}$Ca determined from reaction cross sections (published in Results in Physics) Wakasa, Tomotsugu Tagami, Shingo Yahiro, Masanobu Nuclear Theory Nuclear Experiment 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. |
| title | Skin values of $^{208}$Pb and $^{48}$Ca determined from reaction cross sections (published in Results in Physics) |
| topic | Nuclear Theory Nuclear Experiment |
| url | https://arxiv.org/abs/2211.05312 |