3$\alpha$-cluster structure and monopole transition in ${}^{12}$C and ${}^{14}$C

Abstract

3$\alpha$-cluster structures and monopole transitions of $0^{+}$ states in ${}^{12}$C and ${}^{14}$C were investigated with $3\alpha$- and ${}^{10}$Be+$\alpha$-cluster models. A gas-like $3\alpha$ state and a bending-chain $3\alpha$ state were obtained in the $0_2^{+}$ and $0_3^{+}$ states of ${}^{12}$C, respectively. In ${}^{14}$C, a linear-chain 3$\alpha$ structure is found in the $0_4^{+}$ state near the ${}^{10}$Be+$\alpha$ threshold, but a cluster gas-like state does not appear because valence neutrons attract $\alpha$ clusters and suppress spatial development of 3$\alpha$ clustering. It was found that the linear-chain state in ${}^{14}$C is stabilized against the bending and $\alpha$ escaping modes by valence neutrons. The monopole transition strengths in ${}^{12}$C are enhanced by $3\alpha$-cluster developing, whereas, those in ${}^{14}$C are not enhanced so much because of the tight binding of $\alpha$ clusters by valence neutrons.