Systematic analysis of reaction cross sections of carbon isotopes

Abstract

We systematically analyze total reaction cross sections of carbon isotopes with $N=$ 6--16 on a $^{12}\mathrm{C}$ target for wide range of incident energy. The intrinsic structure of the carbon isotope is described by a Slater determinant generated from a phenomenological mean-field potential, which reasonably well reproduces the ground-state properties for most of the even $N$ isotopes. We need separate studies not only for odd nuclei but also for $^{16}\mathrm{C}$ and $^{22}\mathrm{C}$ to improve their wave functions. The density of the carbon isotope is constructed by eliminating the effect of the center-of-mass motion. For the calculations of the cross sections, we take two schemes, the Glauber approximation and the eikonal model using a global optical potential. Both the reaction models successfully reproduce low and high incident energy data on the cross sections of $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, and $^{16}\mathrm{C}$ on $^{12}\mathrm{C}$. The calculated reaction cross sections of $^{15}\mathrm{C}$ are found to be considerably smaller than the empirical values observed at low energy. We find a consistent parametrization of the nucleon-nucleon scattering amplitude, differently from previous ones. Finally, we predict the total reaction cross section of $^{22}\mathrm{C}$ on $^{12}\mathrm{C}$.