  Here we present the two-photon and two-gluon decay widths of the S-wave
($\eta_{Q\in c,b}$) and P-wave ($\chi_{Q\in c,bJ}$) charmonium and bottonium
states and the radiative transition decay widths of $c\bar c$, $b\bar b$ and
$c\bar b$ systems based on Coulomb plus power form of the inter-quark potential
($CPP_\nu$) with exponent $\nu$. The Schr$\ddot{o}$dinger equation is solved
numerically for different choices of the exponent $\nu$. We employ the masses
of different states and their radial wave functions obtained from the study to
compute the two-photon and two-gluon decay widths and the E1 and M1 radiative
transitions. It is found that the quarkonia mass spectra and the E1 transition
can be described by the same interquark model potential of the $CPP_\nu$ with
$\nu=1.0$ for $c\bar c$ and $\nu=0.7$ for $b\bar b$ systems, while the M1
transition (at which the spin of the system changes) and the decay rates in the
annihilation channel of quarkonia are better estimated by a shallow potential
with $\nu<1.0$.
