| 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 parameterizations whose tensor terms have been adjusted on
properties of spherical nuclei: (i) $TIJ$ interactions proposed in the first
paper of this series [T.~Lesinski \\emph{et al.}, Phys.\\ Rev.\\ C \\textbf{76},
014312 (2007)] which were constructed through a complete readjustment of
the rest of the
functional (ii) parameterizations whose tensor terms have been added
perturbatively to existing Skyrme interactions, with or without
readjusting the spin-orbit coupling constant. We analyse 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
parameterizations. It is expected that findings of the present paper 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. |
