$\beta$ decays of isotones with neutron magic number of $N=126$ and $r$-process nucleosynthesis

$\beta$ decays of the isotones with $N=126$ are studied by shell-model calculations taking into account both the Gamow-Teller (GT) and first-forbidden (FF) transitions. The FF transitions are found to be important to reduce the half-lives, by nearly twice to several times, from those by the GT contributions only. Possible implications of the short half-lives of the waiting point nuclei on the $r$-process nucleosynthesis during the supernova explosions are discussed. A slight shift of the third peak of the element abundances in the $r$ process toward a higher mass region is found.

Figure 1

GT strengths for the isotone with $Z=64$, 68, and 72 obtained by the shell-model calculation at energies from the parent state.

Figure 2

The same as in Fig. 1 for the spin-dipole strengths with $J^{\pi }=1^{-}$ (upper figures) and the corresponding average shape factors (lower figures) for the isotones.

Figure 3

(a) Calculated half-lives for the $N=126$ isotones. Results of the present shell-model calculations with GT and with GT + FF transitions are denoted by dashed and solid curves, respectively. The quenching factor of $g_A/g_A^{\mathrm{free}}=0.7$ is used for both the GT and FF transitions except for $0^{-}$ transitions (see text). Half-lives of Ref. [12] denoted as FRDM are shown by a dotted curve. (b) The same as in Fig. 3a for the shell-model calculations with contributions from both the GT and FF transitions. The solid curve and the curve denoted as FRDM are the same as in (a), while the long-dashed and dotted curves are obtained by using a different quenching factor of $g_A/g_A^{\mathrm{free}}=0.34$ with further quenching of $g_V/g_V^{\mathrm{free}}=0.67$. In case of the dotted curve, the $Q$ values are increased by 1 MeV for the isotones in the FF transitions.

Figure 4

The abundances of elements in the $r$-process nucleosynthesis obtained by using the present $\beta$-decay half-lives for the $N=126$ isotones (denoted as “modified”) and standard half-lives of Ref. [12] (denoted as “standard”). The quenching factor of $g_A/g_A^{\mathrm{free}}=0.7$ ($g_V/g_V^{\mathrm{free}}=1.0$) is used both for the GT and FF ($1^{-}$ and $2^{-}$) transitions. The right figure displays the same result in the restricted range of $A\ge 180$.

Figure 5

The same as in Fig. 4 at $A\ge 180$ for the quenching factors of $(g_A/g_A^{\mathrm{free}},g_V/g_V^{\mathrm{free}})=(0.34,0.67)$ for the $1^{-}$ transitions. The figure on the right side includes the effect of the increase of the $Q$ values.