Molecular-orbital structure in neutron-rich C isotopes

Abstract

The moleculelike structure of the C isotopes $(A=12,14,16)$ is investigated using a microscopic $\ensuremath{\alpha}+\ensuremath{\alpha}+\ensuremath{\alpha}+n+n+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}$ model. The valence neutrons are classified based on the molecular-orbit model, and both $\ensuremath{\pi}$ orbit and $\ensuremath{\sigma}$ orbit are introduced around three $\ensuremath{\alpha}$ clusters. The valence neutrons which occupy the $\ensuremath{\pi}$ orbit increase the binding energy and stabilize the linear chain of $3\ensuremath{\alpha}$ against the breathinglike breakup. However, ${}^{14}\mathrm{C}$ with the $\ensuremath{\pi}$ orbit does not show a clear energy minimum against the bendinglike path. The combination of the valence neutrons in the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ orbits is promising to stabilize the linear-chain state against the breathing and bending modes, and it is found that the excited states of ${}^{16}\mathrm{C}$ with the ${(3/2}_{\ensuremath{\pi}}^{\ensuremath{-}}{)}^{2}{(1/2}_{\ensuremath{\sigma}}^{\ensuremath{-}}{)}^{2}$ configuration for the four valence neutrons is one of the most promising candidates for such a structure.