Linear-chain structure of three α-clusters in 16C and 20C

Using a Skyrme mean-field model, we investigate the linear-chain configurations of three α-clusters with four or eight additional valence neutrons in 16C and 20C and discuss the relation between the stability of such states and the neutron number. The Hartree–Fock solution is sought from an initial configuration with three α-clusters and the additional neutrons are prepared in wave functions of various symmetries. We find at least five different chain configurations in 16C and one “closed shell” configuration in 20C that appear as highly converged states in the Hartree–Fock iterations. We investigate their stability with respect to quadrupole and octupole distortions and find that they appear unstable with respect to bending deformations, but show lifetimes that may lead to observable resonances.