Angular distribution functions in the decays of ψ' and ψ'' directly produced in unpolarized bar pp collisions

We calculate the combined angular distribution of the two photons and of the electron in the triple cascade process bar pp→ψ',ψ''→χJ+γ1→(ψγ2) +γ1→(e+e-)+γ2+γ1 (J=0,1,2) when bar p and p are unpolarized. The answer is given in the ψ',ψ'' restframe or the bar pp c.m. frame. By measuring this angular distribution one can determine the magnitudes as well as the relative phases of the angular momentum helicity amplitudes in the radiative decay processes ψ',ψ''→χJ+γ1 and χJ→ψ+γ2 (J=0,1,2) as well as the relative magnitudes of the angular momentum helicity amplitudes in the processes bar pp→ψ'ψ'' and ψ→e+e-