Alpha decay of ${}_{}{}^{186}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{184}{}_{}{}^{}\mathrm{Hg}$: The influence of mixing of $0^{+}$ states on α-decay transition probabilities

Fine structure in the α decay of mass-separated ${}_{}{}^{186}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{184}{}_{}{}^{}\mathrm{Hg}$ has been studied at the GSI on-line mass separator. Alpha singles spectra as well as α-x-t and α-e-t coincidence events were collected. The α decay of ${}_{}{}^{186}{}_{}{}^{}\mathrm{Pb}$ revealed feeding to a low-lying $0^{+}$ state at 328(12) keV in ${}_{}{}^{182}{}_{}{}^{}\mathrm{Hg}$. This state can be interpreted as being the bandhead of the deformed rotational band observed previously in in-beam studies. In the α decay of ${}_{}{}^{184}{}_{}{}^{}\mathrm{Hg}$, feeding towards the first excited $2^{+}$ state at 153 keV and the $0_2^{+}$ state at 478 keV in ${}_{}{}^{180}{}_{}{}^{}\mathrm{Pt}$ was observed. The hindrance factor of the α decay towards the excited $0^{+}$ state gives information about the particle-hole character of the states connected in the α decay. A two-level mixing calculation is introduced. From the mixing in Pt and the α-decay hindrance factors, small mixing is deduced fro ground stattes of neutron-deficient Hg and Pb nuclei.