a pure S-wave or D-wave initial state. Coefficients $C$ are those in the expression (\[eqn:rate\]) for electric dipole transitions.

A more detailed model can be constructed by assuming that the $\ppp$ is a mixture of a $1^3D_1$ and a $2^3S_1$ state [@B88]: \[eqn:mix\] = +   ,    = - +    . The leptonic widths of $\ppp$ and $\pp$ are then [@Nov] (e\^+ e\^-) = | R\_[2S]{}(0) + \_[1D]{}(0) |\^2  , (e\^+ e\^-) = | R\_[2S]{}(0) - \_[1D]{}(0) |\^2  , where $e_c = 2/3$, $R_{2S}(0) = (4 \pi)^{1/2} \Psi_{2S}(0)$ is the radial $2S$ wave function at $r=0$, and ${R''}_{1D}(0)$ is the second derivative of the radial $2D$ wave function at the origin. The values $R_{2S}(0) =
0.734$ GeV$^{3/2}$ and $5R_{1D}''(0)/(2 \sqrt{2}m_c^2) = 0.095$ GeV$^{3/2}$ were taken in Ref. [@B88]. Assuming a common QCD correction to $\pp$ and $\ppp$ leptonic widths, we then fit the ratio = | |\^2 = 0.128 0.023  , with solutions $\phi = (12 \pm 2)^{\circ}$ or $\phi = -(27 \pm 2)^{\circ}$. These values agree with those of Kuang and Yan [@KY90], whose $\theta$ is the same as our $- \phi$. As they note, the smaller-$|\phi|$ solution is consistent with coupled-channel estimates [@EGKLY; @CC] and with the ratio of 