Observation of J/psi -> gamma eta pi(0)

We present the first study of the process J/psi -> gamma eta pi(0) using (223.7 +/- 1.4) x 10(6) J/psi events accumulated with the BESIII detector at the BEPCII facility. The branching fraction for J/psi -> gamma eta pi(0) is measured to be B(J/psi -> gamma eta pi(0)) = (2.14 +/- 0.18(stat) +/- 0.25(syst)) x 10(-5). With a Bayesian approach, the upper limits of the branching fractions B(J/psi -> gamma a(0)(980), a(0)(980) -> eta pi(0)) and B(J/psi -> gamma a(2)(1320), a(2)(1320) -> eta pi(0)) are determined to be 2.5 x 10(-6) and 6.6 x 10(-6) at the 95% confidence level, respectively. All of these measurements are given for the first time.