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 struct
ure 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.
