Global description of ${\beta }^{-}$ decay in even-even nuclei with the axially-deformed Skyrme finite-amplitude method

We use the finite-amplitude method for computing charge-changing Skyrme–quasiparticle random-phase approximation (QRPA) transition strengths in axially-deformed nuclei together with a modern Skyrme energy-density functional to fit several previously unconstrained parameters in the charge-changing time-odd part of the functional. With the modified functional we then calculate rates of ${\beta }^{-}$ decay for all medium-mass and heavy even-even nuclei between the valley of stability and the neutron drip line. We fit the Skyrme parameters to a limited set of $\beta$-decay rates, a set of Gamow-Teller resonance energies, and a set of spin-dipole resonance energies, in both spherical and deformed nuclei. Comparison to available experimental $\beta$-decay rates shows agreement at roughly the same level as in other global QRPA calculations. We estimate the uncertainty in our rates all the way to the neutron drip line through a construction that extrapolates the errors of known $\beta$-decay rates in nuclei with intermediate $Q$ values to less stable isotopes with higher $Q$ values.

Figure 1

The differences between computed and experimental $Q$ values, with SV-min (a) and $\mathrm{SkO}{}^{\prime }$ (b). The insets show the distribution of differences. The errors in our computed $Q$ values follow a normal distribution with an average of 0.154 MeV and a standard deviation of 0.576 MeV, with no noticeable bias when moving to higher $Q$ values.

Figure 2

Reproduction of target data in those of our fits that use the target set E. The four-parameter fits 3A and 3B yield almost the same results as the two-parameter fits 1D and 1E, with only a small decrease in the penalty function.

Figure 3

Comparison of the mean and standard deviation of the ${\log }_{10}t$ values in our fits with those of previous work. The labels for our fits correspond to those of Table 1. The results from prior work are contained in [5] (Mö), [3] (Ho), [6] (Na), [11] (Co), and [9] (Ma). Only even-even isotopes are considered.

Figure 4

The contributions of different allowed and first-forbidden multipoles to the total computed $\beta$-decay rates. Only even-even nuclei are considered.

Figure 5

Comparison of our computed half-lives in neutron-rich nuclei with those of Ref. [5].

Figure 6

The fit 3A with the mean (green line) and one- and two-standard-deviation bands from our uncertainty model.

Figure 7

Our predictions for the 14 half-lives of neutron-rich even-even nuclei measured only recently [46] and not included in the ENSDF data set. All the measured half-lives fall within our $1\sigma$ error bars, suggesting that our uncertainty estimates are too pessimistic in this particular region.