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

TL;DR

This study investigates how anti-halo effects influence reaction cross sections of carbon isotopes, revealing shell inversion dynamics and the impact of projectile breakup at 83 MeV/nucleon.

Contribution

It introduces a three-body model with a position-dependent three-body force to explain anti-halo effects and shell inversion in carbon isotopes.

Findings

Anti-halo effects reduce reaction cross sections for $^{16}$C compared to $^{15}$C.

Shell inversion depends on the neutron's distance from the core, affecting the single-particle energies.

Projectile breakup effects are significant in the mass-number dependence of reaction cross sections.

Abstract

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.