Nuclear and atomic spectroscopy measurements have provided a great number o
f data on the neutron-deficient Pt and Hg nuclei. The odd-A Pt and Hg with
A < 186 have a prolate shape, and the even-even isotopes have a triaxial sh
ape, while the nuclear shape of the odd-A Pt and Hg with A >186 is stilt an
open question. The energy of the low-lying levels and the nuclear moments
have been calculated in the framework of a semimicroscopic. "axial-rotor 1 quasiparticle" coupling model. The predictions are compared with the expe
rimental data and discussed. The results strongly suggest a prolate shape f
or the negative-parity low-tying states of the odd-A Pt187-191 and Hg187-19
3 isotopes. (C) 2001 MAIK "Nauka/Interperiodica".