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 Jπ=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+Λ5He 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.