Energy Density Functional Approach to Superfluid Nuclei

Abstract

We show that within the framework of a simple local nuclear energy density functional (EDF), one can describe accurately the one-and two-nucleon separation energies of semimagic nuclei. While for the normal part of the EDF we use previously suggested parameterizations, for the superfluid part of the EDF we use the simplest possible local form compatible with known nuclear symmetries.PACS numbers: 21.60. Jz, 21.30.Fe A steady transition is taking place during the last several years from the mean-field description of nuclear properties in terms of effective forces to an energy density functional approach (EDF). A significant role is played in this transition process by the fact that an EDF approach has a strong theoretical underpinning [1]. The effective forces used to derive the EDF are nothing else but a vehicle, since in themselves they have no well-defined physical meaning. For example, the effective Skyrme two-particle interaction is neither a particle-hole nor a particle-particle interaction. The particle-hole interaction (or the Landau parameters) is defined only as the second order functional derivative of the total EDF with respect to various densities, while the particle-particle interaction responsible for the pairing correlations in nuclei has to be supplied independently and with no logical connection to the Skyrme parameters.We shall not attempt to even mention various meanfield approaches suggested so far, in this respect see Refs.[2], but we shall concentrate instead on a single aspect of the nuclear EDF, namely its pairing properties. Only recently it became clear that a theoretically consistent local EDF formulation of the nuclear pairing properties is indeed possible [3][4][5]. Even though the crucial role of the pairing phenomena in nuclei has been established firmly, it is surprising to realize how poor the quality of our knowledge still is. Phenomenologically, one cannot unambiguously decide whether the pairing correlations in nuclei have a volume or/and a surface character [6][7][8][9][10][11][12][13]. The isospin character of the nuclear pairing correlations requires further clarification as well. These questions become even sharper in the language of a local EDF.There is also the largely practical issue of whether one should use a zero-range or a finite-range effective pairing interaction. The only reason for the introduction of a finite-range was to resolve the formal difficulty with divergences in calculating the anomalous densities [10]. The majority of practitioners favor a much simpler approach, which embodies essentially the same physics, the introduction of an explicit energy cut-off. The best example are perhaps the works of the group [11,12], which so far is the leader in describing all known nuclear masses. An explicit finite-range of the pairing interaction r 0 (which can be translated into an energy cut-off E c ≈h 2 /mr 2 0 ) and a zero-range with an explicit energy cut-off E c in the final analysis are equivalent. Both approaches, however, are a poor's man solution to the r...

Pairing gaps in the Hartree-Fock-Bogoliubov theory with the Gogny D1S interaction

“…The next chain, the Z = 50 Sn isotopes, has 16 measured pairing gaps and has been the subject of many theoretical studies of pairing, eg. [16,25,26]. Our calculated gaps are shown in Fig.…”

“…There is no gap quenching associated with the s 1/2 subshell, probably because of a degeneracy with other subshells in the single-particle spectrum. These features are also present in HFB calculations based on the Skyrme [12] and the Fayans energy functionals [26], so they seem to be generic for HFB with short-ranged functionals. Experimentally, the gaps are rather large, and one sees the sharp decrease at N = 83.…”

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

“…Eqns. (14)(15)(16) below, between the two reference states involved. These transition density matrices, however, are at the origin of a major difficulty that arises in existing implementations of MR EDF calculations.…”

“…The EDF approach used in nuclear physics has formal similarities with Density Functional Theory (DFT) [2, 3,4,5,6,7,8] which provides a formal framework to obtain the exact ground-state energy and one-body density of electronic many-body systems in condensed-matter physics and quantum chemistry [9]. However, and even if it is often referred to as nuclear DFT [10,11,12,13,14,15], the nuclear EDF method has deeply rooted conceptual differences with standard Density Functional Theory; e.g. Ref.…”

Nuclear density functional theory with a semi-contact 3-body interaction

“…This very simple form has been used in Refs. [11,12] (see also [13]) to suggest a rather minimalist DFT-LDA functional for unitary gas where the energy density writes…”