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

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

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