  The isomeric ratios of $^{198}$Au, $^{197}$Hg and $^{195}$Hg produced by
$\alpha$-particle induced reactions on natural platinum were investigated
experimentally up to 29 MeV by using the standard stacked foil activation
technique and $\gamma$-ray spectrometry. The isomeric ratios of $^{197}$Hg and
$^{195}$Hg determined by the conventional activation cross section formula
showed strong cooling time dependence. The time dependence was resolved by
adjusting the isomeric transition branching ratios for the two isotopes within
a simultaneous decay curve analysis framework. Our analysis suggests
94.5$\pm$0.7% and 48.9$\pm$1.8% as the isomeric transition branching ratios of
$^{197m}$Hg (24 h) and $^{195m}$Hg (42 h), respectively. The isomeric ratios
and independent production cross sections of $^{198}$Au, $^{197}$Hg, $^{195}$Hg
and some other Hg, Au and Pt isotopes were also measured down to 6 MeV with
these corrected isomeric transition branching ratios, and compared with
predictions of statistical and pre-equilibrium models by TALYS-2.0 to discuss
spin cuto? parameter dependence. We found the measured isomeric ratios are
better predicted if we reduce the spin cuto? parameter to half or less from
that estimated with the rigid body moment of inertia.
