Multi-cluster dynamics in ${}_{\Lambda }^{13}\mathrm{C}$ and analogy to clustering in ${}^{12}\mathrm{C}$

Abstract

We investigate structure of ${}_{\Lambda }^{13}\mathrm{C}$ and discuss the difference and similarity between the structures of ${}^{12}\mathrm{C}$ and ${}_{\Lambda }^{13}\mathrm{C}$ by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in ${}^{12}\mathrm{C}$, survives, or new structure states appear or not. We introduce a microscopic cluster model called, Hyper-Tohsaki-Horiuchi-Schuck-Röpke (H-THSR) wave function, which is an extended version of the THSR wave function so as to describe $\Lambda$ hypernuclei. We obtained two bound states and two resonance (quasi-bound) states for $J^{\pi }=0^{+}$ in ${}_{\Lambda }^{13}\mathrm{C}$, corresponding to the four $0^{+}$ states in ${}^{12}\mathrm{C}$. However, the inversion of level ordering between the spectra of ${}^{12}\mathrm{C}$ and ${}_{\Lambda }^{13}\mathrm{C}$, i.e. that the $0_3^{+}$ and $0_4^{+}$ states in ${}_{\Lambda }^{13}\mathrm{C}$ correspond to the $0_4^{+}$ and $0_3^{+}$ states in ${}^{12}\mathrm{C}$, respectively, is shown to occur. The additional $\Lambda$ particle reduces sizes of the $0_2^{+}$ and $0_3^{+}$ states in ${}_{\Lambda }^{13}\mathrm{C}$ very much, but the shrinkage of the $0_4^{+}$ state is only a half of the other states. In conclusion, the Hoyle state becomes quite a compact object with ${}_{\Lambda }^9\mathrm{Be}+\alpha$ configuration in ${}_{\Lambda }^{13}\mathrm{C}$ and is no more gaslike state composed of the $3\alpha$ clusters. Instead, the $0_4^{+}$ state in ${}_{\Lambda }^{13}\mathrm{C}$, coming from the ${}^{12}\mathrm{C}(0_3^{+})$ state, appears as a gaslike state composed of $\alpha +\alpha {+}_{\Lambda }^5\mathrm{He}$ configuration, i.e. the Hoyle analog state. A linear-chain state in a $\Lambda$ hypernucleus is for the first time predicted to exist as the $0_3^{+}$ state in ${}_{\Lambda }^{13}\mathrm{C}$ with more shrunk arrangement of the $3\alpha$ clusters along $z$-axis than the $3\alpha$ linear-chain configuration realized in the ${}^{12}\mathrm{C}(0_4^{+})$ state.

9 pages, 6 figures, figures rearranged, accepted for publication in PLB

References in corpus (13)

• Microscopic Clustering in Light Nuclei
• Evidence for Triangular D_3h Symmetry in 12C
• Alpha-particle condensation in 16O via a full four-body OCM calculation
• Status of Alpha-Particle Condensate Structure of the Hoyle State
• Negative parity states of ${}^{11}$B and ${}^{11}$C and the similarity with $^{12}C
• Extended-soft-core Baryon-Baryon Model I. Nucleon-Nucleon Scattering (ESC04) Extended-soft-core Baryon-Baryon Model I. Nucleon-Nucleon Scattering (ESC04)
• Deformation of hypernuclei studied with antisymmetirzed molecular dynamics
• Alpha particle clusters and their condensation in nuclear systems
• Density-induced suppression of the alpha-particle condensate in nuclear matter and the structure of alpha cluster states in nuclei
• $\alpha +\alpha +t$ cluster structures and Hoyle-analogue states in ${}^{11}$B
• Breathing-like excited state of the Hoyle state in ${}^{12}\mathrm{C}$
• Effects of $\alpha$-cluster breaking on 3$\alpha$ cluster structures in ${}^{12}$C
• Monopole excitation of the Hoyle state and linear-chain state in 12C

Cited by in corpus (8)

• Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei
• Container evolution for cluster structures in ${}^{16}\mathrm{O}$
• Resonant and Scattering States in the $\alpha +\alpha$ System from the Non-Localized Cluster Model
• Excitation energy shift and size difference of low-energy levels in $p$-shell $\Lambda$ hypernuclei
• Three-body resonant states of ${}_{\Lambda }^9$Be with $\alpha +\alpha +\Lambda$ cluster model
• Structures of $p$-shell double-$\Lambda$ hypernuclei studied with microscopic cluster models
• Cluster structures of the $0^{+}$ states of ${}_{\Lambda }^{13}\mathrm{C}$ with the 3$\alpha +\Lambda$ four-body orthogonality condition model
• Cluster-shell competition and effect of adding hyperons