  Bulk and decay properties, including deformation energy curves, charge mean
square radii, Gamow-Teller (GT) strength distributions, and beta-decay
half-lives, are studied in neutron-deficient even-even and odd-A Hg and Pt
isotopes. The nuclear structure is described microscopically from deformed
quasiparticle random-phase approximation calculations with residual
interactions in both particle-hole and particle-particle channels, performed on
top of a self-consistent deformed quasiparticle Skyrme Hartree-Fock basis. The
observed sensitivity of the, not yet measured, GT strength distributions to
deformation is proposed as an additional complementary signature of the nuclear
shape. The $\beta$-decay half-lives resulting from these distributions are
compared to experiment to demonstrate the ability of the method.
