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We extend the microscopic particle-rotor model for hypernuclear low-lyingstates by including the derivative and tensor coupling terms in thepoint-coupling nucleon-$\Lambda$ particle ($N\Lambda$) interaction. Taking$^{13}_{~\Lambda}$C as an example, we show that a good overall description forexcitation spectra is achieved with four sets of effective $N\Lambda$interaction. We find that the $\Lambda$ hyperon binding energy decreasesmonotonically with increasing the strengths of the high-order interactionterms. In particular, the tensor coupling term decreases the energy splittingbetween the first $1/2^-$ and $3/2^-$ states and increases the energy splittingbetween the first $3/2^+$ and $5/2^+$ states in $^{13}_{~\Lambda}$C.

Low-energy hypernuclear spectra with microscopic particle-rotor model with relativistic point coupling hyperon-nucleon interaction