Multi-cluster dynamics in C13Λ and analogy to clustering in 12C

We investigate structure of ^C13_Λ and discuss the difference and similarity between the structures of ¹²C and ^C13_Λ by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in ¹²C, 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 ^C13_Λ, corresponding to the four 0⁺ states in ¹²C. However, the inversion of level ordering between the spectra of ¹²C and ^C13_Λ, i.e. that the 0₃⁺ and 0₄⁺ states in ^C13_Λ correspond to the 0₄⁺ and 0₃⁺ states in ¹²C, respectively, is shown to occur. The additional Λ particle reduces sizes of the 0₂⁺ and 0₃⁺ states in ^C13_Λ 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 ^Be9_Λ + α configuration in ^C13_Λ and is no more gaslike state composed of the 3α clusters. Instead, the 0₄⁺ state in ^C13_Λ, coming from the ¹²C (0₃⁺) state, appears as a gaslike state composed of α + α +_Λ⁵ He 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 ^C13_Λ with more shrunk arrangement of the 3α clusters along z-axis than the 3α linear-chain configuration realized in the ¹²C (0₄⁺) state. All the excited states are shown to appear around the corresponding cluster-decay threshold, reflecting the threshold rule.