We perform a systematic study of the impact of the J2 tensor term in the Skyrme energy functional
on properties ofspherical nuclei. In the Skyrme energy functional, the tensor terms originate both
from zero-range central and tensor forces. We build a set of 36 parameterizations which cover a wide
range of the parameter space of the isoscalar and isovector tensor term coupling constants with a
fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of
the tensor terms on a large variety of observables in spherical mean-field calculations, such as the
spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit
splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies
of radii. The major findings of our study are (i) tensor terms should not be added perturbatively to
existing parameterizations, a complete refit of the entire parameter set is imperative. (ii) The free
variation of the tensor terms does not lower the X2 within a standard Skyrme energy functional.
(iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead
to instabilities of the spherical shell structure, or even the coexistence of two configurations with
different spherical shell structure. (iv) The standard spin-orbit interaction does not scale properly
with the principal quantum number, such that single-particle states with one or several nodes have
too large spin-orbit splittings, while those of nodeless intruder levels are tentatively too small. Tensor
terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling
constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the
evolution of spin-orbit splittings in chains of Ca, Ni and Sn isotopes. (vi) For the same values of
the tensor term coupling constants, however, the overall agreement of the single-particle spectra
in doubly-magic nuclei is deteriorated, which can be traced back to features of the single-particle
spectra that are not related to the tensor terms. We conclude that the currently used central and
spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the
presence of large tensor terms. |
