Global description of ${\beta }^{-}$ decay with the axially deformed Skyrme finite-amplitude method: Extension to odd-mass and odd-odd nuclei

We use the finite-amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute $\beta$-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron-rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.

Figure 1

Differences between computed and experimental $Q$ values for even-even (a) and odd (b) nuclei. The red line is the average difference and the blue band shows one standard deviation, the values of which are given in the legend. The inset shows the normalized histogram of differences under a normal distribution with the same mean and standard deviation as the data.

Figure 2

Corrections of half-lives in odd nuclei. Half-lives for which we calculate strength functions are in (a). Red circles are for the 224 suspicious nuclei and blue squares for the 100 nuclei from the random sample. (b) Half-lives that are corrected as described in the main text, with corrected values indicated by black arrowheads. Orange triangles are corrected versions of originally negative half-lives.

Figure 3

Examples in which contour integration fails. The dashed vertical line indicates the left bound of the contour from Eq. (18), while the solid line indicates the adjusted bound required to correct the rate. (a) and (b) The Gamow-Teller ($K=1$) strength function for ${}^{63}\mathrm{Co}$ and ${}^{53}\mathrm{Sc}$, respectively. (c) Illustration of an imaginary pole in the response function of ${}^{173}\mathrm{Er}$, and (d) the response in the full complex plane, indicating poles near $\omega =\pm 0.1i$.

Figure 4

Same as Fig. 2 but compared with 2019 ENSDF half-life data and vs experimental half-life. Only odd nuclei are shown.

Figure 5

First-forbidden contribution to the rates. Dashed lines indicate the magic numbers 28, 50, and 82 for protons, and 28, 50, 82, 126, and 184 for neutrons.

Figure 6

Bayesian fit to the bias function and one- and two-standard-deviation bands.

Figure 7

Comparison of error-evaluation parameters among results of Refs. [12] (Marketin), [11] (Möller), [46] (Costiris), [10] (Nakata), and [17] (Homma).

Figure 8

Base-10 logarithm of the ratio of our half-lives to those of (a) Ref. [12] and (b) Ref. [11]. Dashed lines indicate the same magic numbers as in Fig. 5.