Multi-cluster dynamics in CΛ13 and analogy to clustering in ¹²C

We investigate structure of CΛ13 and discuss the difference and similarity between the structures of C12 and CΛ13 by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in C12, 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 Λ hypernuclei. We obtained two bound states and two resonance (quasi-bound) states for J^π=0⁺ in CΛ13, corresponding to the four 0⁺ states in C12. However, the inversion of level ordering between the spectra of C12 and CΛ13, i.e. that the 0₃ ⁺ and 0₄ ⁺ states in CΛ13 correspond to the 0₄ ⁺ and 0₃ ⁺ states in C12, respectively, is shown to occur. The additional Λ particle reduces sizes of the 0₂ ⁺ and 0₃ ⁺ states in CΛ13 very much, but the shrinkage of the 0₄ ⁺ state is only a half of the other states, in spite of the fact that attractive Λ-N interaction makes nucleus contracted so much when the Λ particle occupies an S-orbit. In conclusion, the Hoyle state becomes quite a compact object with BeΛ9+α configuration in CΛ13 and is no more gaslike state composed of the 3α clusters. Instead, the 0₄ ⁺ state in CΛ13, coming from the C12(0₃ ⁺) state, appears as a gaslike state composed of α+α+_Λ ⁵He configuration, i.e. the Hoyle analog state. A linear-chain state in a Λ hypernucleus is for the first time predicted to exist as the 0₃ ⁺ state in CΛ13 with more shrunk arrangement of the 3α clusters along z-axis than the 3α linear-chain configuration realized in the C12(0₄ ⁺) state. All the excited states are shown to appear around the corresponding cluster-decay threshold, reflecting the threshold rule.