Investigating $\beta$-decay properties of spherical nuclei along the possible $r$-process path

The spherical quasiparticle random-phase approximation method is used for calculations of the $\beta$-decay properties of neutron-rich nuclei in the region near the neutron magic numbers $N=82$ and $N=126$ which are important for determination of the $r$-process path. Our calculations differ from previous works by the use of realistic forces for the proton-neutron interaction. Both allowed and first-forbidden $\beta$ decays are included. Detailed comparisons with the experimental measurements and the previous shell-model calculations are performed. The results for half-lives and $\beta$-delayed neutron emission probabilities will serve as input for $r$-process nucleosynthesis simulations.

Figure 1

Comparison of half-lives between shell-model calculations (SMI [10], SMII [8], and QRPA calculations) with separable Gamow-Teller forces (GTF) in [12], continuum QRPA in [16, 30], and this work for $N=82$ and $N=126$ isotonic chains.

Figure 2

Comparison of total $\beta$-delayed neutron emission probability between shell-model calculations [8, 10] and QRPA calculations in [12, 16, 30] and this work for $N=82$ and $N=126$ isotonic chains.

Figure 3

Comparison of ratios of first-forbidden part of the total decay width between shell-model calculations [8, 10] and QRPA calculations in [12, 16, 30] and this work for $N=82$ and $N=126$ isotonic chains.

Figure 4

The $Q_{\beta }$ values we adopt in our calculation for $N=80$, 82, and 84 and $N=124$, 126, and 128 isotones. The meanings of the symbols are explained in the text.

Figure 5

The calculated half-lives from Ref. [12] and our calculations with two mass sets for $N=80$, 82, and 84 and $N=124$, 126, and 128 isotones. The comparison between experiments and theories has been presented.

Figure 6

The calculated $P_n$ values from Ref. [12] and our calculations with two mass sets for $N=80$, 82, and 84 isotones. The comparison between experiments and theories has also been presented.