Deformed quasiparticle random phase approximation formalism for single- and two-neutrino double b decay

We use a deformed quasiparticle random phase approximation formalism to describe simultaneously the energy distributions of the single b Gamow-Teller strength and the two-neutrino double b decay matrix elements. Calculations are performed in a series of double b decay partners with A=48, 76, 82, 96, 100, 116, 128, 130, 136, and 150, using deformed Woods-Saxon potentials and deformed Skyrme Hartree-Fock mean fields. The formalism includes a quasiparticle deformed basis and residual spin-isospin forces in the particlehole and particle-particle channels. We discuss the sensitivity of the parent and daughter Gamow-Teller strength distributions in single b decay, as well as the sensitivity of the double b decay matrix elements to the deformed mean field and to the residual interactions. Nuclear deformation is found to be a mechanism of suppression of the two-neutrino double b decay. The double b decay matrix elements are found to have maximum values for about equal deformations of parent and daughter nuclei. They decrease rapidly when differences in deformations increase. We remark on the importance of a proper simultaneous description of both double b decay and single Gamow-Teller strength distributions. Finally, we conclude that for further progress in the field, it would be useful to improve and complete the experimental information on the studied Gamow-Teller strengths and nuclear deformations.