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

TL;DR

This paper investigates the cluster structures and monopole transitions in $^{12}$C and $^{14}$C using cluster models, revealing different configurations and the stabilizing role of valence neutrons in $^{14}$C.

Contribution

It provides new insights into the stability and structure of linear-chain and gas-like 3$ extalpha$ states, highlighting the influence of valence neutrons.

Findings

Gas-like 3$ extalpha$ state in $^{12}$C $0^+_2$

Linear-chain 3$ extalpha$ state in $^{14}$C $0^+_4$

Valence neutrons stabilize linear-chain states in $^{14}$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.