Anti-halo effects on reaction cross sections for $^{14,15,16}$C isotopes

We study anti-halo effects on reaction cross sections $\sigma_{\rm R}$ for $^{14,15,16}$C scattering from a $^{12}$C target at 83~MeV/nucleon, using the $g$-matrix double-folding model. $^{15}$C is described by the $^{14}$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. $^{16}$C is described by the $^{14}$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 $^{14}$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 $r$. Anti-halo effects due to the "partial shell inversion" make $\sigma_{\rm R}$ for $^{16}$C smaller than that for $^{15}$C. We also investigate projectile breakup effects on the mass-number dependence of $\sigma_{\rm R}$ with the continuum discretized coupled-channels method.