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)
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2020
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| author | Takechi, Maya Wakasa, Tomotsugu Matsui, Shingo Tagami Jun Yahiro, Masanobu |
| author_facet | Takechi, Maya Wakasa, Tomotsugu Matsui, Shingo Tagami Jun Yahiro, Masanobu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_00796 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | 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) Takechi, Maya Wakasa, Tomotsugu Matsui, Shingo Tagami Jun Yahiro, Masanobu Nuclear Theory Nuclear Experiment 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. |
| title | 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) |
| topic | Nuclear Theory Nuclear Experiment |
| url | https://arxiv.org/abs/2009.00796 |