Search for the process $\mathbf{e^+e^- \to\eta}$

A search for the rare decay eta -> e(+) e(-) is performed using the inverse process e(+) e(-) -> eta in the decay mode eta -> pi(0)pi(0)pi(0). We analyze data with an integrated luminosity of 654 nb(-1) accumulated at the VEPP-2000 e(+) e(-) collider with the SND detector at the center-of-mass energy E = m(eta)c(2) approximate to 548 MeV, and set the upper limit B(eta -> e(+) e(-)) <7 x 10(-7) at the 90% confidence level.