  We calculate the combined angular distribution functions of the polarized
photons ($\gamma_1$ and $\gamma_2$) and electron ($e^-$) produced in the
cascade process $\bar{p}p\rightarrow$ $^3D_3\rightarrow$
$^3P_2+\gamma_1\rightarrow$
$(\psi+\gamma_2)+\gamma_1\rightarrow(e^++e^-)+\gamma_1+\gamma_2$, when the
colliding $\bar{p}$ and $p$ are unpolarized. Our results are independent of any
dynamical models and are expressed in terms of the spherical harmonics whose
coefficients are functions of the angular-momentum helicity amplitudes of the
individual processes. Once the joint angular distribution of ($\gamma_1$,
$\gamma_2$) and that of ($\gamma_2$, $e^-$) with the polarization of either one
of the two particles are measured, our results will enable one to determine the
relative magnitudes as well as the relative phases of all the angular-momentum
helicity amplitudes in the radiative decay processes $^3D_3\rightarrow$
$^3P_2+\gamma_1$ and $^3P_2\rightarrow\psi+\gamma_2$.
