Observation of $h_{c}$ radiative decay $h_{c} rightarrow gamma eta$ and evidence for $h_{c} rightarrow gamma eta$

u007fA search for radiative decays of the $P$-wave spin singlet charmonium resonance $h_c$ is performed based on $4.48 times 10^{8}$ $psi$ events collected with the BESIII detector operating at the BEPCII storage ring. Events of the reaction channels $h_{c} rightarrow gamma eta$ and $gamma eta$ are observed with a statistical significance of $8.4 sigma$ and $4.0 sigma$, respectively, for the first time. The branching fractions of $h_{c} rightarrow gamma eta$ and $h_{c} rightarrow gamma eta$ are measured to be $mathcal{B}(h_{c} rightarrow gamma eta)=(1.52 pm 0.27 pm 0.29)times10^{-3}$ and $mathcal{B}(h_{c} rightarrow gamma eta)=(4.7 pm 1.5 pm 1.4)times10^{-4}$, respectively, where the first errors are statistical and the second are systematic uncertainties.