$e^+e^- \to \gamma X(3872)$ near the $D^* {\bar D}^*$ threshold

We evaluate the cross section of the process $e^+e^- \to \gamma X(3872)$ in terms of the content of the $D^{*0} {\bar D}^0$ `molecular' component in the wave function of the resonance X(3872). If this component is dominating, the cross section of the reaction $e^+e^- \to \gamma X(3872)$ can reach up to about $10^{-3}$ of that for $e^+e^- \to D^* {\bar D}^*$ at energy slightly above the $D^* {\bar D}^*$ threshold, and the considered process can be a realistic source of the X(3872) particles for the studies of this resonance.