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

Abstract

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 $\ddot{I}{ƒ}_{\mathrm{R}}$ 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 $r_m(\exp )$ of ${}^{12}$C from the accurate $\ddot{I}{ƒ}_{\mathrm{R}}(\exp )$, using the Kyushu $g$-matrix folding model. Our result is $r_{\mathrm{m}}^{12}(\exp )=2.352\pm 0.013$~fm for ${}^{12}$C. The model is applied for the accurate data on ${}^{12}$C+${}^{27}$Al scattering, and yields $r_{\mathrm{m}}(\exp )=2.936\pm 0.012$~fm for ${}^{27}$Al. Our conclusion is that $r_{\mathrm{m}}(\exp )=2.352\pm 0.013$~fm agrees with $r_{\mathrm{m}}(\exp )=2.35\pm 0.02$~fm determined from interaction cross sections by Tanihata {\it et. al.}.

arXiv admin note: text overlap with arXiv:2306.09609