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 typically imposed on the nuclear configurations. One such example is time-reversal 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, 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.

R-Process Nucleosynthesis in Neutron Star Merger Ejecta and Nuclear Dependences

“…For example, as shown in Fig. 1, deviations up to typically ±5 MeV can be observed for exotic nuclei between HFB-31 ) and D1M or BSkG2 (Scamps et al 2021;Ryssens et al 2022) mass predictions, especially around the N = 126 and 184 shell closures. Neutron capture rates can consequently deviate by three to five orders of magnitude with such mass differences, essentially due to different local variations in the pairing and shell description.…”

“…Finally, α-decays are taken into account for all heavy species, the theoretical rates being extracted from Koura et al (2002). By default, the r-process calculations are performed using the BSkG2 mass model (Ryssens et al 2022), the β-decay rates from the relativistic mean field plus relativistic random phase approximation (RMF+RRPA) of Marketin et al (2016), the fission rates based on the BSk14 Skyrme interaction (Goriely et al 2010), and the fission fragment distributions obtained within the so-called scissionpoint yield (SPY) model (Lemaître et al 2021).…”

“…With respect to the 2457 measured masses for Z, N ≥ 8 nuclei , the 32 HFB mass models give an rms deviation ranging between 0.52 MeV for HFB-27 and 0.82 MeV for HFB-1. Alternatively, new Skyrme-HFB mass models were recently adjusted using a three-dimensional coordinate-space representation, allowing for both axial and triaxial deformations during the adjustment process (Scamps et al 2021;Ryssens et al 2022). In particular, while nuclei with an odd number of nucleons were traditionally described within the so-called equal filling approximation, the BSkG2 mass mode treats them on the same footing as eveneven nuclei by breaking time-reversal symmetry.…”

“…For this reason, further improvements of the mass model are required. These include development of relativistic as well as non-relativistic mean field models, but also the inclusion within such approaches of the state-of-the-art beyond-mean-field corrections, like the quadrupole or octupole correlations by the generator coordinate method (Bender et al 2006;) and a proper treatment of odd-A and odd-odd nuclei with time-reversal symmetry breaking (Ryssens et al 2022). Such models should reproduce not only nuclear masses at best but also as many experimental observables as possible.…”

Nuclear properties for nuclear astrophysics studies

“…With respect to the 2457 measured masses for Z , N ≥ 8 nuclei [3], the 32 HFB mass models give an rms deviation ranging between 0.52 MeV for HFB-27 and 0.82 MeV for HFB-1. Recently, a new family of Skyrme-HFB models (BSkG) has been constructed using a three-dimensional coordinate-space representation, allowing for both axial and triaxial deformations during the adjustment process [84,85]. In particular, while nuclei with an odd number of nucleons were traditionally described within the so-called equal filling approximation, the BSkG2 mass model treats them on the same footing as even-even nuclei by breaking timereversal symmetry, yielding an rms deviation of 0.68 MeV with respect to the 2457 known masses.…”