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We review the Skyrme interaction as rst used by Vautherin and Brink in the Hartree-Fock (HF) formalism to construct the energy density functional and more specically, the two-body spin-orbit term. Problems with this term were already pointed out by Skyrme himself and have been discussed in the past years by other authors. We present examples where existing Skyrme parametrizations are unable to properly describe spin-orbit splittings in nuclei. We also discuss possible options that allow for more exibility in the spin-orbit dependent terms of the energy density functional and of the self-consistent mean eld potential. Focusing in particular on the recently measured spectroscopic factors in germanium and selenium isotopes, we show that using dierent neutron and proton spin-orbit coupling constants, together with pairing and deformation, greatly improves the agreement with experiment. Results on spectroscopic factors, rms radii and other collective and single-particle properties of germanium and selenium isotopes obtained with the new and old parametrizations of the constrained HF(Sk3)+BCS potential are shown.We acknowledge the support of Ministerio de Ciencia e Innovaci´on (Spain) under Contract. Nos. FIS2008-01301 and CSPD-2007-00042@Ingenio2010, and UCM ‘Grupo de F´ısica Nuclear’- 910059.Peer Reviewe

Remodelling the spin-orbit term of Skyrme energy density functionals