Figure 1

Illustrations of calculated branching ratios of the first-forbidden decay for different isotopes. The diagonal line indicates the approximate $r$-process path.Reuse & Permissions

Figure 2

The half-life dependence on $g_{\mathrm{pp}}$ for different even-even isotopes. The upper panel shows results with quenched axial vector coupling constant $g_A=0.75g_{A0}$, while the lower panel shows the bare one $g_{A0}=1.26$.Reuse & Permissions

Figure 3

A comparison of the calculated half-lives from Ref. [1] [(panels (a) and (b)] and this work [(panels (c) and (d)] with the experimental ones from RIKEN [3] and [24]. The experimental errors are taken into account for several isotopes with large error bars. The total errors are defined in (15). The left panels are comparison for even-even isotopes, and the right panels are for other types denoted by different symbols for the three cases of ($Z$, $N$). The three horizontal lines in each panel correspond to the ratios of 2, 1, and 0.5 respectively. Here, sep. is the abbreviation for separable force and rea. for realistic force.Reuse & Permissions

Figure 4

Low-lying GT (black) and effective FF (red) strength distributions (a), (b) and GT running sums (c) for ${}^{110}$Zr are shown. The effective strength $\overline{C\left(w\right)}$ for first-forbidden decay is defined in Eq. (8) in Ref. [17]. In addition to the results in the deformed basis (b), we also show the results for a spherical basis (a) [dashed lines in (c)]. The three vertical lines correspond to $S_n=4.72$ MeV, $S_{2n}=7.79$ MeV, and $Q=9.79$ MeV respectively, which are taken from Ref. [27]. Here, we use $g_{\text{pp}}=0.75$, which gives a half-life of $t_{1/2}=21.6$ ms and $\beta$-delayed one-neutron emission probability $P_n=1.9\%$ for the spherical case and $t_{1/2}=37.9$ and $P_n=10.5\%$ for the deformed case.Reuse & Permissions

Figure 5

A comparison among the calculated half-lives from Ref. [1] (red), this work (blue), and measured ones (if available) with error bars from RIKEN [3] for Kr to Tc isotopes. The total errors are defined in Ref. [1]. Here, as before, sep. is the abbreviation for separable force and rea. for realistic forces.Reuse & Permissions

Figure 6

A comparison among the calculated $\beta$-delayed neutron emission probability $P_n$ values from Ref. [1] (red), this work (blue), and measured ones (if available) with error bars from RIKEN [3] for Kr to Tc isotopes. Here sep. is the abbreviation for separable force and rea. for realistic forces. The empty squares are the $\beta$-delayed one-neutron emission probabilities $P_n$, while the solid ones are the total probabilities up to three-neutron emission.Reuse & Permissions