  We use a deformed QRPA formalism to describe simultaneously the energy
distributions of the single beta Gamow-Teller strength and the two-neutrino
double beta decay matrix elements. Calculations are performed in a series of
double beta 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 particle-hole and particle-particle channels. We
discuss the sensitivity of the parent and daughter Gamow-Teller strength
distributions in single beta decay, as well as the sensitivity of the double
beta 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 beta decay. The double beta 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 the importance of a proper simultaneous description of both
double beta 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.
