RadiativeM1 transitions of the narrow resonances

We study the radiative transitions among the ${\psi }^{\prime }$, $\hat{\chi }=\chi \mathrm{}\left(3.45\right)\mathrm{}$, $\frac{J}{\psi }$, and $X\mathrm{}\left(2.83\right)\mathrm{}$ (2.83) states, within the framework of the charmonium model. Numerical results are given for a superposition of a linear vector potential, a linear scalar potential, and an $r^{-1\mathrm{}}$ term. We show that the systematic inclusion of relativistic effects leads to discrepancies between experiment and theory which are considerably smaller than those obtained in calculations in which these effects are ignored. In particular, the factor of 2 × ${10}^3$ between the experimental and theoretical value for $B({\psi }^{\prime }\to \hat{\chi }+\gamma )B(\hat{\chi }\to \psi +\gamma )$ can be reduced to a factor of 20 or so, without the introduction of new parameters. An analysis in which the spin-spin interaction is treated nonperturbatively is also developed.