  In this work we study the E1 decay processes, $^3P_1$ $\rightarrow$
$^3S_1\gamma$, and $^3S_1$ $\rightarrow$ $^3P_1\gamma$ in the framework of
Bethe-Salpeter equation and calculate their decay widths. We have used
algebraic forms of Salpeter wave functions obtained through analytic solutions
of mass spectral equations for ground and excited states of $^3S_1$, and
$^3P_1$ equal mass quarkonia in approximate harmonic oscillator basis to do
analytic calculations of their decay widths. These decay widths have been
compared with data and other models.
