  Two-photon and two-gluon annihilation rates of P-wave scalar charmonium and
bottomonium up to third radial excited states are estimated in the relativistic
Salpeter method. We solved the full Salpeter equation with a well defined
relativistic wave function and calculated the transition amplitude using the
Mandelstam formalism. Our model dependent estimates for the decay widths:
$\Gamma(\chi_{c0} \to 2\gamma)=3.78$ keV, $\Gamma(\chi'_{c0} \to 2\gamma)=3.51$
keV, $\Gamma(\chi_{b0} \to 2\gamma)=48.8$ eV and $\Gamma(\chi'_{b0} \to
2\gamma)=50.3$ eV. We also give estimates of total widths by the two-gluon
decay rates: $\Gamma_{tot}(\chi_{c0})=10.3$ MeV,
$\Gamma_{tot}(\chi'_{c0})=9.61$ MeV, $\Gamma_{tot}(\chi_{b0})=0.887$ MeV and
$\Gamma_{tot}(\chi'_{b0})=0.914$ MeV.
