Spin-isospin response of deformed neutron-rich nuclei in a self-consistent Skyrme energy-density-functional approach

We develop a new framework for the self-consistent deformed proton-neutron quasiparticle-random-phase approximation (pnQRPA), formulated in the Hartree-Fock-Bogoliubov (HFB) single-quasiparticle basis. The same Skyrme force is used in both the HFB and pnQRPA calculations, except in the proton-neutron particle-particle channel, where an S = 1 contact force is employed. A numerical application is performed for Gamow-Teller (GT) strength distributions and beta-decay rates in the deformed neutron-rich Zr isotopes located around the path of rapid-neutron-capture-process nucleosynthesis. It is found that the GT strength distributions are fragmented due to deformation. Furthermore, we find that the momentum-dependent terms in the particle-hole residual interaction lead to a stronger collectivity of the GT giant resonance. The T = 0 pairing enhances the low-lying strengths cooperatively with the T = 1 pairing correlation, which shortens the beta-decay half-lives by at most an order of magnitude. The new calculation scheme reproduces well the observed isotopic dependence of the beta-decay half-lives of deformed Zr100-110 isotopes.