Monopole excitation of the Hoyle state and linear-chain state in 12C

Abstract

Background: Two new $J^{\pi }=0^{+}$ states are recently observed around a few MeV above the Hoyle state (the second $0^{+}$ state in 12C). The characters of them are only poorly discussed in theory and are still mysterious. Purpose: I give for the first time a comprehensive understanding of the structures of the $0^{+}$ states by analyzing their wave functions, and discuss relationship with the Hoyle state, similarities, and differences between the states. Method: I extend a microscopic $\alpha$-cluster model called Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function so as to incorporate $2\alpha +\alpha$ asymmetric configuration explicitly. The so-called $r^2$-constraint method to effectively eliminate spurious continuum components is also used. Results: The $0_3^{+}$ state is shown to have a very large squared overlap with a single configuration of the extended THSR wave function in an orthogonal space to the Hoyle state as well as to the ground state. The $0_4^{+}$ state has a maximal squared overlap with a single extended THSR wave function with an extremely prolately-deformed shape. Conclusions: The $0_3^{+}$ state appears as a family of the Hoyle state to have a higher nodal structure in the internal motions of the $3\alpha$ clusters, due to the orthogonalization to the Hoyle state. The $0_4^{+}$ state dominantly has a linear-chain structure, where the $3\alpha$ clusters move freely in a non-localized way, like a one-dimensional gas of the $3\alpha$ clusters.

8 pages, 8 figures, 1 table, and the title is slightly changed. To be published in PRC

References in corpus (3)

• Evidence for Triangular D_3h Symmetry in 12C
• Investigation of ${}^9$Be from nonlocalized clustering concept
• Effects of $\alpha$-cluster breaking on 3$\alpha$ cluster structures in ${}^{12}$C

Cited by in corpus (8)

• The radiative width of the Hoyle state from $\gamma$-ray spectroscopy
• Direct probing of the cluster structure in ${}^{12}$Be via $\alpha$-knockout reaction
• Optimization of basis functions for the multi-configuration mixing using the Replica Exchange Monte-Carlo method and its application to ${}^{12}$C
• Cluster structures of the $0^{+}$ states of ${}_{\Lambda }^{13}\mathrm{C}$ with the 3$\alpha +\Lambda$ four-body orthogonality condition model
• Low-energy ${}^{12}$C continuum states in three-$\alpha$ model
• Bose-Einstein condensation of five $\alpha$ clusters in ${}^{20}$Ne and supersolidity
• Six-$\alpha$ cluster Bose-Einstein condensation and supersolid ${}^{12}$C($0_2^{+})$+${}^{12}$C($0_2^{+})$ molecular structure in ${}^{24}$Mg
• Examination of the $\alpha$-cluster breaking in the four $0^{+}$ bands of ${}^{12}$C with the variation of multiple bases of the antisymmetrized molecular dynamics