Impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals

Abstract

Background: In the framework of nuclear energy density functional (EDF) methods, many nuclear phenomena are related to the deformation of intrinsic states. Their accurate modeling relies on the correct description of the change of nuclear binding energy with deformation. The two most important contributions to the deformation energy have their origin in shell effects that are correlated to the spectrum of single-particle states, and the deformability of nuclear matter, that can be characterized by a model-dependent surface energy coefficient a surf .Purpose: With the goal of improving the global performance of nuclear EDFs through the fine-tuning of their deformation properties, the purpose of this study is threefold. First, to analyze the impact of systematic variations of a surf on properties of nuclei; second, to identify observables that can be safely used to narrow down the range of appropriate values of a surf to be targeted in future parameter fits; third, to analyze the interdependence of a surf with other properties of a nuclear EDF.Methods: Results for a large variety of relevant observables of deformed nuclei obtained from self-consistent mean-field calculations with a set of purpose-built SLy5sX parametrizations of the Skyrme EDF are correlated with the value of a surf .Results: The performance of the SLy5sX parametrizations for characteristic energies of the fission barriers of 180 Hg, 226 Ra, and 240 Pu, excitation energies, electromagnetic moments and moments of inertia of superdeformed states in the A ≈ 190 region, properties of shape coexisting states at normal deformation in the Pb, Kr, and Zr region, properties of octupole-deformed 144 Ba, even-even Th isotopes, and 110 Zr, separation energies along isotopic and isotonic chains are compared with available experimental data. Conclusions:The three main conclusions are that there is an evident preference for a comparatively low value of a surf , as expected from the performance of existing parametrizations; that the isospin dependence of the surface energy also needs further fine-tuning in order to describe trends across the chart of nuclei; and that a satisfying simultaneous description of fission barriers and superdeformed states requires a better description of the singleparticle spectra.

Iterative approaches to the self-consistent nuclear energy density functional problem

“…For most parametrisations at NLO, the isoscalar ρ 0 (r)∆ρ 0 (r) term dominates the evolution of the SCF iteration, as among the contributions to the potentials with two external gradients it is the one with largest coupling constant. As this term provides a dominant contribution to the surface tension [64], for realistic parametrisations its coupling constant is always of the same sign and takes very similar values. This is different for the homologues of this term in the other spinisospin channels that often vary over a large range, which can result in the need to fine-tune numerical parameters.…”

“…[22], the two-basis method consists of determining the quasi-particle basis that diagonalises H in terms of the HF basis. It has been used in 3d coordinate-space calculations since [22,67,64]. It has also been implemented into the 1d spherical coordinate-space HFB solver Lenteur [36] and the 3d HO code HFODD [68], in both cases with an exact diagonalisation ofĥ at each self-consistent field iteration.…”

“…The goal of this section is to compare the convergence properties of the schemes that we have developed in the two previous sections with what we have used in the past for typical situations encountered when calculating complex nuclei. The most detailed tests are performed with the SLy5s1 parametrisation of the Skyrme NLO functional [19], which provides a good description of the deformation properties of heavy nuclei [64]. For this parametrisation, we will study the convergence for calculations of the ground state of even-even spherical, axially deformed, triaxially deformed and octupole-deformed nuclei, and give also an example from a calculation with broken time-reversal symmetry.…”

“…As a first example we address the axially-deformed ground state of 240 Pu. For this parametrisation, it takes a quadrupole deformation of β 20 0.28 that is accompanied by an energy gain of about 15 MeV compared to the spherical configuration [64]. Figure 14 shows the evolution of the relative change in energy δE (i) , the weighted dispersion (dh 2 ) (i) , and the change of quadrupole moment δQ…”

“…Quadrupole deformation β and triaxiality angle γ as a function of the iterations of a non-constrained calculation of64 Ge with the four algorithms as indicated, drawn against a backdrop of the converged deformation energy surface. Contour lines are at every 100 keV and diamonds at every 100th iteration.…”