Deformation and spin-orbit splitting of Λ hypernuclei in the Skyrme-Hartree-Fock approach

The realizations of spin symmetry in the Λ 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 ΔEs.o. shows a good linear relation with respect to the quantum number l, even for a large ΛN spin-orbit strength.