Large-Scale Calculations of $β$-Decay Rates and Implications for $r$-Process Nucleosynthesis

TL;DR

The paper develops global beta-decay rates for thousands of neutron-rich nuclei using axially-deformed relativistic energy density functionals (DD-PC1 and DD-PCX) within a quasiparticle random-phase approximation, including both Gamow-Teller and first-forbidden transitions. The rates, computed via contour integration around the $Q_\beta$ window and benchmarked against Nubase2020, show good consistency with the SkO' model but predict slower decays past the $N=126$ shell closure, leading to reduced neutron-induced fission and modified r-process flow. Across parameterized and astrophysical trajectories, this slower beta decay delays fission cycling and alters final abundance patterns, particularly around the second and third peaks and actinide region. The work emphasizes the significant impact of nuclear-structure input on r-process outcomes and provides publicly available data and tools to enable uncertainty quantification and broader exploration of nuclear physics inputs in astrophysical nucleosynthesis.

Abstract

Nuclear $β$ decay is a key element of the astrophysical rapid neutron capture process ($r$-process). In this paper, we present state-of-the-art global $β$-decay calculations based on the quantified relativistic nuclear energy density functional theory and the deformed proton-neutron quasiparticle random-phase approximation. Our analysis considers contributions from allowed and first-forbidden transitions. We used two point-coupling functionals with carefully calibrated time-odd terms and isoscalar pairing strength. The new calculations display consistent results for both employed functionals, especially near the neutron drip line, suggesting slower $β$ decays past the $N=126$ neutron shell closure than in commonly used $β$-decay models. The new rates, along with the existing rates based on the latest non-relativistic calculations, are found to slow down the synthesis of heavy elements in the $r$-process and significantly reduce the contribution of neutron-induced fission.

Figures (7)

• Figure 1: Global comparison between (a) mean averaged half-lives $\bar{r}$ and (b) their spread $\sigma$ obtained in this work (DD-PC1 and DD-PCX) with the results of SkO' model Ney2020, D3C* Marketin_RQRPA_2016, and FRDM Moller2003. The experimental data are taken from Ref. Nubase2020. Averaging in Eq. (\ref{['eq:mean']}) is performed over the nuclei with half-lives up to the maximum experimental half-life $T_{1/2}^{\rm exp,max}$ in the range from $10^{-1}$ s to $10^4$ s.
• Figure 2: Comparison of theoretical $\beta$-decay rates relative to predictions of our DD-PC1 EDF model: (a) our DD-PCX model, (b) SkO' model Ney2020, (c) D3C* model Marketin_RQRPA_2016, and (d) FRDM model Moller2019.
• Figure 3: The residuals, $Q_\beta^{\rm calc} - Q_\beta^{\rm exp}$, between calculated and experimental $Q_\beta$-values for DD-PC1 (a) and DD-PCX (b) EDFs, as a function of experimental $Q_\beta^{\rm exp}$-values taken from AME2020 Wang2021. The dataset is split into even-even (+), odd-$A$ (circles), and odd-odd (x) nuclei. The solid line indicates the mean value, and the band shows the $1\sigma$ interval. Distribution of the residuals, along with the normal distribution fitted to the data, is shown in insets.
• Figure 4: Correction procedure for half-lives to eliminate the spurious contribution of the negative strength for odd-$A$ and odd-odd nuclei. Panels (a) and (b) show the GT strength, decomposed into $K = 0$ and $K = 1$ components, together with their sum (Total) in ${}^{51}$Sc (a) and ${}^{52}$Sc (b). The vertical dashed line marks the manual correction made to remove the negative strength contribution, while the solid line denotes the limit (\ref{['eq:estimate']}). The result of the correction is shown in panel (c), resulting in a significant decrease of ${}^{51}$Sc and ${}^{52}$Sc half-lives. Calculations are performed by employing the DD-PC1 interaction.
• Figure 5: Contribution of first-forbidden (FF) transition (in %) for DD-PC1 (a) and DD-PCX (b) predictions of this work, and SkO' results (c) from Ref. Ney2020.