β-decay rates of $r$-process nuclei in the relativistic quasiparticle random phase approximation

The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of β-decay half-lives of neutron-rich nuclei in the $N\approx 50$ and $N\approx 82$ regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogoliubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the $T=1$ pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains but overestimate the lifetimes of Ni isotopes and predict a stable ${}^{132}\mathrm{Sn}$.

Figure 1

Radial dependence of the spin-orbit term of the single-nucleon potential in self-consistent solutions for the ground state of ${}^{132}\mathrm{Sn}$. The curves correspond to RMF calculations with the DD-ME1 and DD-ME1${}^{*}$ effective interactions. For the latter the contributions of the first and second term in Eq. (22) are plotted separately.

Figure 2

Neutron and proton single-particle levels in ${}^{78}\mathrm{Ni}$ calculated with DD-ME1 (a), DD-ME1${}^{*}$ (b), and with two nonrelativistic Skyrme interactions: SkO' [4] (c) and SkSC17 [18] (d).

Figure 3

Same as in Fig. 2 for ${}^{132}\mathrm{Sn}$.

Figure 4

$\pi 2p_{3/2}$ and $\pi 1f_{5/2}$ single-particle levels in heavy copper isotopes, calculated with the DD-ME1${}^{*}$ interaction in comparison with experimental data [28].

Figure 5

Comparison of the calculated half-lives of Fe isotopes, for two values of the $T=0$ pairing strength, with available experimental data [30].

Figure 6

Probabilities of β transitions for the semimagic ${}^{76}\mathrm{Fe}$ for different values of the $T=0$ pairing strength.

Figure 7

Calculated half-lives of Ni isotopes, in comparison with experimental values. The data are from Ref.30, except for ${}^{78}\mathrm{Ni}$ where the value $T_{1/2}=104+126-57$ ms [29] is used.

Figure 8

Calculated half-lives of Zn isotopes, without and with the inclusion of $T=0$ pairing in comparison with experimental and extrapolated values[30].

Figure 9

Calculated half-lives of $N=50$ isotones for three values of the $T=0$ pairing strength. The data are from Ref. 30, except for ${}^{78}\mathrm{Ni}$, where the value $T_{1/2}=104+126-57$ ms [29] is used.

Figure 10

Calculated half-lives of ${}^{78}\mathrm{Zn}$, ${}^{80}\mathrm{Zn}$, ${}^{82}\mathrm{Zn}$, and ${}^{82}\mathrm{Ge}$ as functions of the $T=0$ pairing strength.

Figure 11

Calculated half-lives of Cd isotopes for two values values of the $T=0$ pairing strength, in comparison with available experimental data [30].

Figure 12

Calculated half-lives of Sn (left panel) and Te (middle panel) isotopes for two values of the $T=0$ pairing strength, in comparison with experimental data [30]. In the right panel the results for the $N=82$ isotones are compared with the shell-model results [31].