Gamow-Teller strength in deformed nuclei within the self-consistent charge-exchange quasiparticle random-phase approximation with the Gogny force

The charge-exchange excitations in nuclei are studied within the fully self-consistent proton-neutron quasiparticle random-phase approximation using the finite-range Gogny interaction. No additional parameters beyond those included in the effective nuclear force are included. Axially symmetric deformations are consistently taken into account, both in the description of the ground-states and spin-isospin excitations. We focus on the isobaric analog and Gamow-Teller resonances. A comparison of the predicted strength distributions to the existing experimental data is presented and the role of nuclear deformation analyzed. The Gamow-Teller strength is used to estimate the ${\beta }^{-}$-decay half-life of nuclei for which experimental data exist. A satisfactory agreement with experimental half-lives is found and justifies the additional study of the exotic neutron-rich $N=82$, 126, and 184 isotonic chains of relevance for the $r$-process nucleosynthesis.

Figure 1

pnQRPA Fermi (upper panels) and GT (middel panels) strength distributions in ${}^{90}$Zr, ${}^{114}$Sn, and ${}^{208}$Pb calculated with the D1M and D1S forces. The experimental energy peaks obtained from scattering data [33, 34, 35] are shown as diamonds on the $x$ axis. The lower panels show the folded GT strengths and the comparison with experimental data available for ${}^{90}$Zr [33].

Figure 2

The experimental GT widths of Sn isotopes [35] and the adopted parametrization (solid line).

Figure 3

pnQRPA GT strength distributions in ${}^{76}$Ge obtained with the D1M force for several values of the deformation parameter ${\beta }_2$, including the HFB ground-state minimum at ${\beta }_2=0.15$. The experimental low-energy data [45] as well as the energy position of the main GT peak are also shown.

Figure 4

pnQRPA GT strength distributions in ${}^{76}$Ge with the D1M force for ${\beta }_2=0$ and ${\beta }_2=0.15$ folded as described in the text. For comparison, the experimental strength [46] folded in a similar way is also given.

Figure 5

Ratio between the pnQRPA (obtained with the D1M interaction) and experimental [49] $\beta$-decay half-lives as a function of $A$, ${\beta }_2$, and $Q_{\beta }$ for 145 even-even nuclei with an experimental half-life $T_{1/2}\le 1000$ s. Error bars only include experimental uncertainties.

Figure 6

Comparison between experimental [49] and D1M + QRPA $\beta$-decay half-life predictions for the known isotopic chains of Kr, Sr, Zr, and Mo.

Figure 7

Comparison between our $\beta$-decay half-life predictions and the DF3 + QRPA calculation of the authors or Refs. [47, 51], including the GT contribution or both the GT plus FF contributions, for the neutron-rich nuclei along the $N=82,126,$ and 184 isotones. For the $N=82$ isotonic chain, experimental data [49], and shell model results [52] are also shown.