Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking

Abstract

Models based on nuclear energy density functionals can provide access to a multitude of observables for thousands of nuclei in a single framework with microscopic foundations. Such models can rival the accuracy of more phenomenological approaches, but doing so requires adjusting parameters to thousands of nuclear masses. To keep such large-scale fits feasible, several symmetry restrictions are generally imposed on the nuclear configurations. One such example is timereversal invariance, which is generally enforced via the Equal Filling Approximation (EFA). Here we lift this assumption, enabling us to access the spin and current densities in the ground states of odd-mass and odd-odd nuclei and which contribute to the total energy of such nuclei through so-called 'time-odd' terms. We present here the Skyrme-based BSkG2 model whose parameters were adjusted to essentially all known nuclear masses without relying on the EFA, refining our earlier work [G. Scamps et al., EPJA 57, 333 (2021)]. Moving beyond ground state properties, we also incorporated information on the fission barriers of actinide nuclei in the parameter adjustment. The resulting model achieves a root-mean-square (rms) deviation of (i) 0.678 MeV on 2457 known masses, (ii) 0.027 fm on 884 measured charge radii, (iii) 0.44 MeV and 0.47 MeV, respectively, on 45 reference values for primary and secondary fission barriers of actinide nuclei, and (iv) 0.49 MeV on 28 fission isomer excitation energies. We limit ourselves here to a description of the model and the study the impact of lifting the EFA on ground state properties such as binding energies, deformation and pairing, deferring a detailed discussion of fission to a forthcoming paper.

The mass of odd-odd nuclei in microscopic mass models

“…Through the use of appropriate mass difference formulas, we will show that the answer is "no", confirming the discussions in Ref. [13,5]. We discuss possibilities to improve future models by accounting for this effect in a microscopic way.…”

“…Other microscopic mass models face similar problems, which is illustrated in Fig. 2 for BSkG2 [5] and BSk31 [3]. We also compare with the macroscopic-microscopic FRDM(2012) model [6] that explicitly includes a phenomenological term proportional to A −2/3 for odd-odd nuclei that models ∆ np .…”

“…Many forms of the EDF and parameter adjustment strategies have been proposed [2]. We focus here on those developed by the Brussels group: the BSk [3] and BSkG [4,5] series are based on EDFs of the Skyrme type and are fitted to essentially all known nuclear masses. These models describe the known nuclear masses with a root-mean-square (rms) error that is below 0.8 MeV [3,4,5], an accuracy that is competitive with more phenomenological microscopic-macroscopic approaches [6].…”

The mass of odd-odd nuclei in microscopic mass models

“…Other microscopic mass models face similar problems, which is illustrated in Fig. 2 for BSkG2 [5] and BSk31 [3]. We also compare with the macroscopic-microscopic FRDM(2012) model [6] that explicitly includes a phenomenological term proportional to A −2/3 for odd-odd nuclei that models ∆ np .…”

“…Many forms of the EDF and parameter adjustment strategies have been proposed [2]. We focus here on those developed by the Brussels group: the BSk [3] and BSkG [4,5] series are based on EDFs of the Skyrme type and are fitted to essentially all known nuclear masses. These models describe the known nuclear masses with a root-mean-square (rms) error that is below 0.8 MeV [3,4,5], an accuracy that is competitive with more phenomenological microscopic-macroscopic approaches [6].…”