Search for the radiative decay $\eta \to \pi^0 \gamma \gamma$ in the SND experiment at VEPP-2M

The $\eta \to \pi^0 \gamma \gamma$ decay was investigated by the SND detector at VEPP-2M $e^+e^-$ collider in the reaction $e^+e^-\to\phi\to \eta\gamma$. Here we present the results and some details of this study. We report an upper limit (90% c.l.) $Br(\eta \to \pi^0 \gamma \gamma)<8.4\times 10^{-4}$ as our final result. Our upper limit does not contradict the earlier measurement by GAMS spectrometer. To facilitate future studies a rather detailed review of the problem is also given.