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 $e^+e^-tophito etagamma$. Here we present the results and some details of this study. We report an upper limit (90% c.l.) $Br(eta to pi^0 gamma gamma)<8.4times 10^{-4}$ 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.