Spin–orbit splitting and the tensor component of the Skyrme interaction

Abstract

We study the role of the tensor term of the Skyrme effective interactions on the spin-orbit splittings in the N=82 isotones and Z=50 isotopes. The different role of the triplet-even and triplet-odd tensor forces is pointed out by analyzing the spin-orbit splittings in these nuclei. The experimental isospin dependence of these splittings cannot be described by Hartree-Fock calculations employing the usual Skyrme parametrizations, but is very well accounted for when the tensor interaction is introduced. The capability of the Skyrme forces to reproduce binding energies and charge radii in heavy nuclei is not destroyed by the introduction of the tensor term. Finally, we also discuss the effect of the tensor force on the centroid of the Gamow-Teller states.PACS numbers:

Tensor interaction in mean-field and density functional theory approaches to nuclear structure

“…For instance, in 208 Pb, when the tensor force SLy5 T introduced in Ref. [55] is employed the total binding energy is changed only by about 0.5%. However, recently there has been ample discussion whether a fine agreement with the experimental masses can be reached at the level of less than ≈ 1 MeV, or several hundreds of keV.…”

“…2.3, but still we can state that the tensor force was essentially dropped in most Skyrme parameter sets which have been used widely in nuclear structure calculations in the 1980s and 1990s. Serious and systematic attempts to assess the impact of the tensor force on single-particle states have been performed only in the last decade [56,66,55,35,58,67].…”

“…In subsequent works, it has been shown that the inclusion of tensor terms in the Skyrme HF calculations (with positive values of β T and negative values of α T ) can bring considerable success in explaining some features of the evolution of single-particle states along isotopic or isotonic chains [55,35,67]. The tensor terms were added perturbatively in Refs.…”

“…The tensor terms were added perturbatively in Refs. [55,67] and [35] to the existing standard parameterizations SLy5 [73] and SIII [65], respectively.…”

Tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin

“…The first studies of the effective tensor interaction within selfconsistent mean-field approaches concentrated on singleparticle spectra in chains of semi-magic spherical nuclei covering all successful models, i.e. the non-relativistic Gogny force [3,4] and Skyrme interactions [2,[5][6][7], as well as relativistic mean-field approaches [8,9]. More recently, the impact of the tensor terms on more complex structure properties has been studied as well, such as the topography of deformation energy surfaces [10] and various spin-and spin-isospin excitation modes in Quasiparticle Random Phase Approximation (QRPA) using Skyrme functionals [11][12][13][14][15][16][17] and Gogny interactions [4].…”