Surface-peaked effective mass in the nuclear energy density functional and its influence on single-particle spectra

Abstract

Calculations for infinite nuclear matter with realistic nucleon-nucleon interactions suggest that the isoscalar effective mass of a nucleon at the saturation density m * /m equals 0.8 ± 0.1. This result is at variance with empirical data on the level density in finite nuclei, which are consistent with m * /m ≈ 1. Ma and Wambach suggested that these two contradicting results may be reconciled within a single theoretical framework by assuming a radial-dependent effective mass, peaked at the nuclear surface. The aim of this exploratory work is to investigate this idea within the density functional theory by using a Skyrme-type local functional enriched with new terms, τ (∇ρ) 2 and τ (dρ/dr), where τ and ρ denote the kinetic and particle densities, respectively. We show that each of these terms can give rise to a surface peak in the effective mass, but of a limited height. We investigate the influence of the radial profile of the effective mass on the spin-orbit splittings and centroids. In particular, we demonstrate that the τ (dρ/dr) term quenches the 1f 5/2 -1f 7/2 splitting in 40 Ca, which is strongly overestimated within conventional Skyrme parametrizations.

Nuclear energy functional with a surface-peaked effective mass: global properties

“…We now compare our results to the recent ones of Zalewski et al [28,29] where correction terms such as (4) as well as others have been studied. The main differences between our approach and that of Refs.…”

“…where the first term have been first introduced in Ref. [28,29] and induces a surface-peaked effective mass while the second term is introduced to moderate the effect of the first one in the mean field. The effective mass is obtained from the functional derivative of the energy H and is expressed as (q runs over neutrons and protons: q = n, p):…”

“…The main differences between our approach and that of Refs. [28,29] are: (i) the moderating term is not present in Refs. [28,29], (ii) the effective mass in the bulk of nuclei is close to 0.8m in our case, while in the Refs.…”

Sensitivity ofβ-decay rates to the radial dependence of the nucleon effective mass

“…Without the second term, the effects of the first term on the mean field are too large and drastically limit the possible values for the strength of the SPEM, as in Ref. [35]. The compensation was found to be optimal for intermediate mass and heavy nuclei if one uses the following constant relation between the two new parameters [8]:…”

Nuclear Equation of State for Compact Stars and Supernovae

“…The Skyrme-type effective interactions are zero-range density-dependent interactions and they are widely used in nuclear structure and in astrophysical applications since they allow for fast numerical computations. Since the pioneer work of Skyrme [443], several extensions have been proposed (see, e.g., [286,42,87,310,314,513,140,216,311,110]), allowing to include and study, for example, the tensor part of the EDF, the spin-density-dependent terms, as well as a surface-peaked effective-mass term. The accuracy in reproducing experimentally measured properties of finite nuclei has been greatly increased in recent wellcalibrated Skyrme-type EDFs (see, e.g., [187,188,189,92,190] for the most recent BSk models from the Brussels-Montreal collaboration, and [497,257]).…”