Nuclear energy density optimization: Shell structure
Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. Here, we propose a new parametrization UNEDF 2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDERS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parametrization UNEDF 1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting UNEDF 2 parametrization is comparable with UNEDF 1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous UNEDF parametrizations, the parameter confidence interval for UNEDF 2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF 2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits, and significant changes to the form of the functional are needed.