Based on the beyond-mean-field Skyrme-Hartree-Fock model, we investigate the energy spectra and possible cluster structure in ¹²C and its Λ hypernucleus _0.16em0ex0.16em0exΛ¹³C. The up-to-date Skyrme-type NΛ interaction SLL4 and the reduced $NN$ interaction SGII are employed. Low-lying energy spectra of ¹²C, including the lowest five 0⁺ states, are predicted and discussed in detail, and found in good agreement with experimental results. The electric quadrupole transition rates and the monopole matrix elements between the 0⁺ states are also examined. Although typical cluster structures for the 0₂⁺ and 0₃⁺ states are absent, a linear-chain-like 3α structure is found for the 0₄⁺ state. An energy spectrum including both the positive- and negative-parity levels is also given and structures of the corresponding hypernuclear states are discussed in detail. Impurity effects of a Λₛ or Λₚ hyperon on the nuclear core states of _0.16em0ex0.16em0exΛ¹³C are demonstrated by the change of collective wave functions.
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Xue et al. (2024) studied this question.
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