Impact of finite-range spin-orbit and tensor terms in Gogny EDF

TL;DR

The paper introduces a fully finite-range Gogny EDF extension (DG) that incorporates a long-range tensor term and a short-range spin-orbit term, aimed at capturing long-range correlations beyond mean-field. The authors generalize the Gogny fitting protocol with emulators and new TBME-based constraints to determine spin-orbit and tensor parameters consistently, and they validate DG through nuclear-matter properties, bulk finite-nucleus observables, and fission characteristics. DG improves the description of structure phenomena such as the Pb kink in charge radii, near-ground-state spectra in sd-shell nuclei, and reduces monopole-driven shifts, while also yielding lower fission barriers that align more closely with experiment. The work demonstrates the potential of fully finite-range spin-orbit and tensor terms to enhance EDF performance across the nuclear chart and outlines pathways for uncertainty quantification and cross-EDF benchmarks to guide future parameter optimizations.

Abstract

Energy Density Functionals are of major interest for the study of the atomic nucleus as, coupled with mean-field and beyond N-body approaches, they are applicable to the whole nuclear chart, including superheavy elements. On the one hand, the growing need for nuclear data and, on the other hand, the large amount of experimental data on exotic nuclei explain the work carried out on these phenomenological forms of the nucleon-nucleon interaction to analyze the richness of the nuclear phenomena. In this paper, we propose a fully finite-range extension of the Gogny EDF, including a short-range spin-orbit term and a long-range tensor term. The original fitting protocol of the Gogny interaction has been adapted to include both finite range spin-orbit and tensor terms, adding new constraints and filters linked to relevant data. Nuclear matter, spectroscopic and fission properties are discussed, highlighting ways of improving EDFs when all spin and isospin exchanges are introduced with finite-range terms.

Figures (5)

• Figure 1: Contributions of spin-isospin channels to the SNM EoS (Panels (a) to (d)). Panel (e) represents the difference $\delta$E between the $^3$P$_1$ and $^3$P$_0$ partial waves as defined in the text. Calculations have been done for various Gogny interactions. BBG predictions including 2-body (G-2B) and 3-body (G-3B) contributions are also indicated Baldo1vidanahugo.
• Figure 2: Differences between HFB and experimental BE $\delta$E (panels (a)-(c)) and charge radii $\delta R_{\rm ch}$ (panel (d)). Experimental data have been extracted from Refs. WangRadiiExp.
• Figure 3: Panel (a): Kink $\delta {\rm R^{2}_{ch}}$ in Pb isotopes. Experimental data have been extracted from RadiiExp. Panel (b): The 1i$_{11/2}$-2g$_{9/2}$ gap in $^{208}$Pb. A comparison is done for D1S, D2 and DG Gogny interactions (see text).
• Figure 4: Difference (in MeV) between first experimental excited states and the MPMH ones predicted with the same total angular momentum and parity. Panels (a) to (c) correspond to the results obtained with DG, D2 and D1S for odd sd-shell isotopes.
• Figure 5: Mass fission yields of (a) $^{236}$U, (b) $^{240}$Pu and (c) $^{252}$Cf. Calculations have been done for DG, D2 and D1S Gogny interactions. Experimental data have been extracted from romanoUzeynalovUsimongeltenbortUmuellertsuchiyaschillebeeckxnishiogeltenbortwagemanszeylanovromanogookbudtzaladili.