Nuclear energy density optimization: Shell structure

Abstract

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. In this work, we propose a new parameterization UNEDF2 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 parameterization UNEDF1, 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 UNEDF2 parameterization is comparable with UNEDF1. 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 parameterizations, the parameter confidence interval for UNEDF2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF2 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.Comment: 18 pages, 13 figures, 12 tables; resubmitted for publication to Phys. Rev. C after second review by refere

Fission barriers and probabilities of spontaneous fission for elements with Z≥ 100

“…The trends seen in such variations are the robust against the detailed choice of reference energy and integration limits. The basic citations for the models and parametrisation are: Gogny [94],SkM * [49], SkP [95], SkT6 [96], SLy6 [97], SkI3 [98], BSk1 [99], SV-min [100], UNEDF2 [101], NL-Z2 [102], DD-PC and DD-ME [103].…”

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

“…The present M3Y parameterizations are in qualitative agreement with BHF calculations only for the 1 S 0 , 3 S 1 -3 D 1 , 1 P 1 and 3 P 0 components up to the saturation density. We suggest this analysis is of particular interest to determine more precise parameterizations, as the fit of such quantities could provide a reasonable starting point for a complete fit in finite nuclei [32]. 20…”

“…In this article we contribute to it, trying in particular to show how a zero-range interaction can constitute a reliable approximation of a finite-range one. This leads us to consider the next-to-next-to-next to leading order momentum expansion of the Skyrme pseudo-potential [30,31] which represents an extension of the standard Skyrme model [2,32]. It is currently referred to as N3LO Skyrme pseudo-potential, a term introduced in Ref.…”

Shell evolution aboveZ,N=50within Skyrme density functional theory: The impact of deformation and tensor interactions

“…(16) and (18) [33], 132 Sn and 208 Pb may be regarded as "anchor" nuclei. The fact that UNE2T1, and UNE2T2 systematically underestimate their binding energies with respect to the unedf2 results might indicate prospects for general improvements, were the rest of the parameters of UNE2T1 and UNE2T2 re-adjusted.…”

“…I use unedf1 [32], unedf2 [33], and unedf1 SO [30] EDFs with the pairing properties (cutoff energies and pairing strengths) provided in their respective original papers.…”