Three-α configurations of the second Jπ=2+ state in 12C.

We investigate geometric configurations of α ( 4 He nucleus) clusters in the second J π = 2 + state of 12 C, 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- α cluster model. The three-body Schrödinger 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 8 Be( 0 + ) + α configuration. However, the 8 Be + α components in the second 2 + state become approximately 2/3 because the 8 Be subsystem is hard to excite, indicating that the state is not an ideal rigid rotational band member of the Hoyle state. [ABSTRACT FROM AUTHOR]