Influence of 2p-2h configurations on $\beta$-decay rates

The effects of the phonon-phonon coupling on the $\beta$-decay rates of neutron-rich nuclei are studied in a microscopic model based on Skyrme-type interactions. The approach uses a finite-rank separable approximation (FRSA) of the Skyrme-type particle-hole (p-h) residual interaction. Very large two-quasiparticle spaces can thus be treated. A redistribution of the Gamow–Teller (G-T) strength is found due to the tensor correlations and the 2p-2h fragmentation of G-T states. As a result, the ${\beta }^{-}$-decay half-lives are decreased significantly. By using the Skyrme interaction SGII together with a volume-type pairing interaction, we illustrate this reduction effect by comparing with available experimental data for Ni isotopes and neutron-rich $N=50$ isotones. We give predictions for ${}^{76}\mathrm{Fe}$ and ${}^{80}\mathrm{Ni}$ in comparison with the case of the doubly magic nucleus ${}^{78}\mathrm{Ni}$ which is an important waiting point in the $r$ process.

Figure 1

Energies and $B\left(E2\right)$ values for up transitions to the ${\left[2_1^{+}\right]}_{\text{QRPA}}$ states in the neutron-rich $N=50$ isotones. Results of the calculations without the tensor interaction (open triangles) and with the tensor interaction (filled triangles) are shown. Experimental data (filled diamonds) are taken from Ref. [39].

Figure 2

Same as Fig. 1, but for the neutron-rich Ni isotopes.

Figure 3

The phonon-phonon coupling effect on the $\beta$-transition rates in ${}^{80}\mathrm{Zn}$. The left and right panels correspond to the calculations within the QRPA and take into account the 2p-2h configurations, respectively. Results of the calculations without (with) the tensor interaction are shown in the upper (lower) panels.

Figure 4

Same as Fig. 3, but for ${}^{72}\mathrm{Ni}$.

Figure 5

The phonon-phonon coupling effect on ${\beta }^{-}$-decay half-lives of the neutron-rich $N=50$ isotones. Results of the calculations without the tensor interaction (open triangles, circles, squares) and with the tensor interaction (filled triangles, circles, squares) are shown. The squares correspond to the half-lives calculated with inclusion of the phonon-phonon coupling, the triangles are the QRPA calculations. Results including the ${[1_i^{+}\otimes 2_{i^{\prime }}^{+}]}_{\text{QRPA}}$ configurations are denoted by the circles. Experimental data (filled diamonds) are from Refs. [42, 43].

Figure 6

Same as Fig. 5, but for the neutron-rich Ni isotopes. Experimental data are taken from Refs. [42, 43, 44].