# The tensor part of the Skyrme energy density functional. I. Spherical nuclei

## TL;DR

This study systematically investigates how the J^2 tensor term influences spherical nuclei properties within the Skyrme energy functional, revealing limitations in current functional flexibility to incorporate large tensor effects.

## Contribution

It introduces a comprehensive set of 36 Skyrme parameterizations exploring tensor term variations and assesses their impact on nuclear observables.

## Key findings

- Tensor terms significantly affect spin-orbit splittings and spectra.
- Current Skyrme functionals lack flexibility for large tensor contributions.
- Tensor effects do not improve agreement with experimental data.

## Abstract

We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical 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 covers 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 charge radii. Our main conclusion is 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.