Abstract
The realizations of spin symmetry in the $\mathrm{\ensuremath{\Lambda}}$ 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 $\mathrm{\ensuremath{\Delta}}{E}_{\text{s.o.}}$ shows a good linear relation with respect to the quantum number $l$, even for a large $\mathrm{\ensuremath{\Lambda}}N$ spin-orbit strength.
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