Antihalo effects on reaction cross sections for ${}^{14,15,16}\mathrm{C}$ isotopes

We study antihalo effects on reaction cross sections ${\sigma }_{\mathrm{R}}$ for ${}^{14,15,16}\mathrm{C}$ scattering from a ${}^{12}\mathrm{C}$ target at 83 MeV/nucleon, using the $g$-matrix double-folding model. ${}^{15}\mathrm{C}$ is described by the ${}^{14}\mathrm{C}+n$ two-body model that reproduces the measured large $s$-wave spectroscopic factor, i.e., the shell inversion that the $1s_{1/2}$ orbital is lower than the $0d_{5/2}$ orbital in energy. ${}^{16}\mathrm{C}$ is described by the ${}^{14}\mathrm{C}+n+n$ three-body model with the phenomenological three-body force (3BF) that explains the measured small $s$-wave spectroscopic factor. The 3BF allows the single-particle energies of the ${}^{14}\mathrm{C}+n$ subsystem to depend on the position $r$ of the second neutron from the center of mass of the subsystem. The $1s_{1/2}$ orbital is lower than the $0d_{5/2}$ orbital for large $r$, but the shell inversion is restored for small $r$. Antihalo effects due to the “partial shell inversion” make ${\sigma }_{\mathrm{R}}$ for ${}^{16}\mathrm{C}$ smaller than that for ${}^{15}\mathrm{C}$. We also investigate projectile breakup effects on the mass-number dependence of ${\sigma }_{\mathrm{R}}$ with the continuum-discretized coupled-channel method.

Figure 1

$r$ dependence of single-particle energies in the ${}^{14}\mathrm{C}+n$ subsystem of ${}^{16}\mathrm{C}$. Panels (a) and (b) correspond to the results of the volume- and surface-type 3BFs, respectively. The solid (dashed) line corresponds to the $1s_{1/2} \left(0d_{5/2}\right)$ orbital.

Figure 2

Reaction cross sections ${\sigma }_{\mathrm{R}}$ for ${}^{14,15,16}\mathrm{C}{+}^{12}\mathrm{C}$ scattering at 83 MeV/nucleon. Panels (a) and (b) represent the results of DFM and CDCC calculations, respectively. For ${}^{14,15}\mathrm{C}$, the circles show the results of theoretical calculations. For ${}^{16}\mathrm{C}$, the circle and square correspond to the results of the volume-type and surface-type 3BFs, respectively. The experimental data are taken from Ref. [15] and are plotted with $2\sigma$ error (95.4% certainty).