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

TL;DR

This paper validates the folding model for $^{12}$C+$^{12}$C scattering, accurately determining matter radii of $^{12}$C and $^{27}$Al from reaction cross sections, establishing $^{12}$C+$^{12}$C as a reference system for reaction cross section analysis.

Contribution

It demonstrates the reliability of the Kyushu folding model in extracting matter radii from reaction cross sections for specific nuclear systems.

Findings

Matter radius of $^{12}$C: 2.352 ± 0.013 fm

Matter radius of $^{27}$Al: 2.936 ± 0.012 fm

Model agrees with previous interaction cross section data

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 $\sigma_{\rm R}$ 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 $\sigma_{\rm R}({\rm exp})$, 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.}.