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

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

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