$\beta$-decay rates of odd-mass neutron-rich isotopes in the deformed quasiparticle random-phase approximation with realistic interactions

The deformed quasiparticle random-phase approximation with realistic nucleon-nucleon interactions is extended for the ${\beta }^{-}$ decay of odd-mass neutron-rich Kr, Sr, Zr, and Mo isotopes, from their longest-lived isotopes to the experimentally unknown nuclei. The particle-particle and particle-hole channels of residual interactions are handled in large single-particle model spaces, based on the Brückner $G$ matrix with charge-dependent Bonn nucleon-nucleon forces. Both allowed Gamow-Teller and first-forbidden transitions are considered and different treatments for odd-mass systems are emphasized. The sensitivity of the calculated results to the single-particle level scheme and the particle-particle strength is discussed. The calculated Gamow-Teller strengths are analyzed, together with the contributions from first-forbidden transitions. The calculated half-lives are found to agree well with the experimental data over the orders of magnitude from ${10}^{-2}$ to ${10}^3$ s.

Figure 1

Dependence of the calculated $\beta$-decay rates on the particle-particle strength $g_{pp}$ for the ${\beta }^{-}$ decay of ${}^{107}\mathrm{Zr}$: the calculated half-life vs the $g_{pp}$ value (black solid line) and the branching ratio for FF transitions versus the $g_{pp}$ value (red [gray] dashed line).

Figure 2

Cumulative values of the computed GT strength as a function of the excitation energy of the daughter nuclei for ${}^{93,105}\mathrm{Sr}$. The GT strengths are decomposed into the $\mathrm{\Delta }\nu =2$ (black solid lines) and $\mathrm{\Delta }\nu =0$ (red [gray] dashed lines) contributions.

Figure 3

Percentage of the contributions of FF transitions to the decay rates of the odd-mass neutron-rich Kr, Sr, Zr, and Mo isotopes.

Figure 4

Computed GT transition strengths as a function of the excitation energy $E_{\mathrm{ex}}$ in the daughter nucleus for the ${\beta }^{-}$ decays of ${}^{91,101}\mathrm{Sr}$. Calculations are, respectively, performed in the spherical approximation (denoted by blue [gray] lines, left) and with the deformed configurations given in the FRDM [56] (denoted by red [gray] lines, right). The $\beta$-decay energies $Q_{\beta }$ are also shown with solid vertical arrows.

Figure 5

Comparison of the calculated half-lives with the available experimental data (labeled Expt) for the odd-mass neutron-rich Kr and Sr isotopes. The theoretical results of Möller et al. (denoted FRDM) are also shown for comparison [16], including the contributions for both GT and FF transitions. Calculations are, respectively, performed with both GT and FF contributions (denoted GT + FF) and with only GT contributions (denoted GT).

Figure 6

Same as in Fig. 5, but for the odd-mass neutron-rich Zr and Mo isotopes.