$^{12}$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 $\sigma_{\rm R}$ 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.}.