$\beta$-decay properties of neutron-rich Ge, Se, Kr, Sr, Ru, and Pd isotopes from deformed quasiparticle random-phase approximation

$\beta$-decay properties of even- and odd-$A$ neutron-rich Ge, Se, Kr, Sr, Ru, and Pd isotopes involved in the astrophysical rapid neutron capture process are studied within a deformed proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme-Hartree-Fock calculations with pairing correlations. Residual interactions in the particle-hole and particle-particle channels are also included in the formalism. The isotopic evolution of the various nuclear equilibrium shapes and the corresponding charge radii are investigated in all the isotopic chains. The energy distributions of the Gamow-Teller strength as well as the $\beta$-decay half-lives are discussed and compared with the available experimental information. It is shown that nuclear deformation plays a significant role in the description of the decay properties in this mass region. Reliable predictions of the strength distributions are essential to evaluate decay rates in astrophysical scenarios.

Figure 1

Potential energy curves for even-even neutron-rich Ge, Se, Kr, Sr, Zr, Mo, Ru, and Pd isotopes obtained from constrained HF + BCS calculations with the Skyrme force SLy4.

Figure 2

Isotopic evolution of the quadrupole deformation parameter $\beta$ (a) and charge radius (b) corresponding to the energy minima obtained from the Skyrme interaction SLy4 for Ge isotopes. Ground-state results are encircled.

Figure 3

Same as in Fig. 2, but for Se isotopes.

Figure 4

Same as in Fig. 2, but for Kr isotopes. Experimental charge radii are from [59].

Figure 5

Same as in Fig. 2, but for Sr isotopes. Experimental charge radii are from [59].

Figure 6

Same as in Fig. 2, but for Ru isotopes.

Figure 7

Same as in Fig. 2, but for Pd isotopes.

Figure 8

QRPA-SLy4 Gamow-Teller strength distributions for Ge isotopes as a function of the excitation energy in the daughter nucleus. The calculations correspond to the various equilibrium deformations found in the PECs.

Figure 9

Same as in Fig. 8, but for Se isotopes.

Figure 10

Same as in Fig. 8, but for Kr isotopes.

Figure 11

Same as in Fig. 8, but for Sr isotopes.

Figure 12

Same as in Fig. 8, but for Ru isotopes.

Figure 13

Same as in Fig. 8, but for Pd isotopes.

Figure 14

QRPA-SLy4 accumulated GT strengths in Ge isotopes calculated for the various equilibrium shapes. $Q_{\beta }$ and $S_n$ energies are shown by solid and dashed vertical arrows, respectively.

Figure 15

Same as in Fig. 14, but for Se isotopes.

Figure 16

Same as in Fig. 14, but for Kr isotopes.

Figure 17

Same as in Fig. 14, but for Sr isotopes.

Figure 18

Same as in Fig. 14, but for Ru isotopes.

Figure 19

Same as in Fig. 14, but for Pd isotopes.

Figure 20

Measured $\beta$-decay half-lives for Ge isotopes compared to theoretical QRPA-SLy4 results calculated from different shapes. Circles are experimental values (open circles are experimental values from systematics) [44].

Figure 21

Same as in Fig. 20, but for Se isotopes.

Figure 22

Same as in Fig. 20, but for Kr isotopes. Experimental half-lives are from [23, 44].

Figure 23

Same as in Fig. 20, but for Sr isotopes. Experimental half-lives are from [23, 44].

Figure 24

Same as in Fig. 20, but for Ru isotopes.

Figure 25

Same as in Fig. 20, but for Pd isotopes.

Figure 26

Ratio of calculated to experimental $\beta$-decay half-lives for two sets of calculations, with the spherical approximation (open dots) and with the deformation that corresponds to the minimum of the PECs (solid dots). The ratios are plotted as a function of the experimental half-lives (a) and as a function of the quadrupole deformation at the minimum of the PECs (b).