determine the degree to which the $\ppp$ is mixed with an S-wave state [@Zhu; @KR; @YNY; @KL; @B88].

The rates for electric dipole ($E1$) transitions in quarkonium can be written \[eqn:rate\] = e\_Q\^2 \^3 C r \^2   , where $e_Q$ is the quark charge (in units of $|e|$), $\alpha = 1/137.036$ is the fine-structure constant, $\omega$ is the photon energy, and $\langle r
\rangle$ is the matrix element of $r$ between initial and final radial wave functions. The coefficients $C$ are summarized in Table II, where we compare relative rates for $E1$ transitions from $\ppp$ to $\chi_c$ states under the two extreme assumptions of a pure S-wave or a pure D-wave. The distinctive pattern associated with the pure $^3D_1$ configuration is a ratio ${\cal B}(\gamma + \chi_{c1})/{\cal B}(\gamma + \chi_{c0}) = 0.3$ and an almost complete suppression of the ratio ${\cal B}(\gamma + \chi_{c2})
/{\cal B}(\gamma + \chi_{c0})$.

  --------- ---------- ----- ------------------------------- -- ------ -------------------------------
    Final    $\omega$                                                  
    state     (MeV)     $C$   $\Gamma(^3P_J)/\Gamma(^3P_0)$      $C$    $\Gamma(^3P_J)/\Gamma(^3P_0)$
   $^3P_0$     338      1/9                 1                    2/9                  1
   $^3P_1$     250      1/3               1.22                   1/6                0.30
   $^3P_2$     208      5/9               1.16                   1/90               0.012
  --------- ---------- ----- ------------------------------- -- ------ -------------------------------

  : Comparison of transitions $\ppp \to \gamma \chi_c$ under the assumptions of 