Three-a configurations of the second J^p=2⁺ state in ¹²C

We investigate geometric configurations of alpha (He-4 nucleus) clusters in the second J(pi) = 2(+) state in C-12, which has been discussed as a rotational band member of the second 0(+) state, the Hoyle state. The ground and excited 0(+) and 2(+) states are described by a three-alpha cluster model. The three-body Schrodinger equation with orthogonality conditions is accurately solved by the stochastic variational method with correlated Gaussian basis functions. To analyse the structure of these resonant states in a convenient form, we introduce a confining potential. The two-body density distributions together with the spectroscopic information clarify the structure of these states. We find that main configurations of both the second 0(+) and 2(+) states are acute-angled triangle shapes originating from the Be-8(0(+))+alpha configuration. However, the 8Be + alpha components in the second 2(+ )state become approximately 2/3 because the 8Be subsystem is hard to excite, indicating that the state is not an ideal rigid rotational band member of the Hoyle state.