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.

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