We study systematically the impact of the time-even tensor terms of the Skyrme energy density functional, i.e., terms bilinear in the spin-current tensor density, on deformation properties of closed-shell nuclei corresponding to $20,28,40,50,82$, and $126$ neutron or proton shell closures. We compare results obtained with three different families of Skyrme parametrizations whose tensor terms have been adjusted on properties of spherical nuclei: (i) $\mathrm{T}\mathit{IJ}$ interactions proposed in the first article of this series [T. Lesinski et al., Phys. Rev. C 76, 014312 (2007)] that were constructed through a complete readjustment of the rest of the functional and (ii) parametrizations whose tensor terms have been added perturbatively to existing Skyrme interactions, with or without readjusting the spin-orbit coupling constant. We analyze in detail the mechanisms at play behind the impact of tensor terms on deformation properties and how studying the latter can help screen out unrealistic parametrizations. It is expected that findings of the present article  are to a large extent independent of remaining deficiencies of the central and spin-orbit interactions and will be of great value for the construction of future, improved energy functionals.

• Received 20 September 2009

DOI:https://doi.org/10.1103/PhysRevC.80.064302