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Based on the beyond-mean-field Skyrme-Hartree-Fock model, we investigate the energy spectra and possible cluster structure in ^12C and its hypernucleus ₀. ₁₆₄₌{₀₄ₗ0. 16em{0ex}}^13C. The up-to-date Skyrme-type N 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 3 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 ₒ or hyperon on the nuclear core states of ₀. ₁₆₄₌{₀₄ₗ0. 16em{0ex}}^13C are demonstrated by the change of collective wave functions.
Xue et al. (Fri,) studied this question.