Three-$\alpha$ configurations of the second $J^{\pi }=2^{+}$ state in ${}^{12}$C

Abstract

We investigate geometric configurations of $\alpha$ (${}^4$He nucleus) clusters in the second $J^{\pi }=2^{+}$ 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-$\alpha$ 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($0^{+}$)$+\alpha$ configuration. However, the ${}^8$Be$+\alpha$ 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.

arXiv comment7 pages, 3 figures

References in corpus (18)

• Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
• Microscopic Clustering in Light Nuclei
• Structure of ground and excited states of ${}^{12}$C
• Unambiguous Identification of the Second 2+ State in 12C and the Structure of the Hoyle State
• Single $\alpha$-particle orbits and Bose-Einstein condensation in ${}^{12}$C
• The algebraic cluster model. Three-body clusters
• Resonance states in 12C and alpha-particle condensation
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• New representation of orbital motion with arbitrary angular momenta
• Decay and structure of the Hoyle state
• Cluster structure of light nuclei
• New Treatment of Resonances with Bound State Approximation by Using Pseudo Potential
• A stringent upper limit on the direct 3$\alpha$ decay of the Hoyle State in ${}^{12}$C
• Phase-shift calculation using continuum-discretized states
• Transition densities and form factors in the triangular $\alpha$-cluster model of ${}^{12}$C with application to ${}^{12}$C+$\alpha$ scattering
• Binding two and three $\alpha$ particles in cold neutron matter
• Imprints of $\alpha$ clustering in the density profiles of ${}^{12}$C and ${}^{16}$O
• Three-$\alpha$ configurations in the $0^{+}$ states of ${}^{12}\mathrm{C}$