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The self-consistent quasiparticle random-phase approximation (QRPA) approachis formulated in the canonical single-nucleon basis of the relativisticHatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study theisobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Snisotopes as examples. It is found that self-consistent treatment of theparticle-particle residual interaction is essential to concentrate the IAS in asingle peak for open-shell nuclei and the Coulomb exchange term is veryimportant to predict the IAS energies. For the GTR, the isovector pairing canincrease the calculated GTR energy, while the isoscalar pairing has animportant influence on the low-lying tail of the GT transition. Furthermore,the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. Withan isospin-dependent pairing interaction in the isoscalar channel, theRHFB+QRPA approach almost completely reproduces the experimental $\beta$-decayhalf-lives for nuclei up to the Sn isotopes with half-lives smaller than onesecond. Large discrepancies are found for the Ni, Zn, and Ge isotopes withneutron number smaller than $50$, as well as the Sn isotopes with neutronnumber smaller than $82$. The potential reasons for these discrepancies arediscussed in detail.

physical review. c

Self-consistent relativistic quasiparticle random-phase approximation  and its applications to charge-exchange excitations and $\beta$-decay  half-lives