The realizations of spin symmetry in the $\mathrm{\Lambda }$ hyperon spectra of hypernuclei ranging from light to heavy masses are investigated in the framework of the deformed Skyrme-Hartree-Fock approach. The effect of deformation on spin symmetry and its interplay with the required spin-orbit force is studied in detail. It is found that the spin symmetry prevails due to a small spin-orbit force. Moreover, for spin doublets with the same principal quantum number $n$, the reduced spin-orbit splitting $\mathrm{\Delta }{E}_{\text{s.o.}}$ shows a good linear relation with respect to the quantum number $l$, even for a large $\mathrm{\Lambda }N$ spin-orbit strength.

• Received 10 March 2023
• Accepted 5 April 2023

DOI:https://doi.org/10.1103/PhysRevC.107.044317