Abstract : A search is performed for long-lived neutral particles decaying into a photon and invisible particles. An example of such a signature is the decay of the lightest neutralino with nonzero lifetime into a gravitino and a photon in gauge-mediated supersymmetry, with the neutralino as the next-to-lightest supersymmetric particle and the gravitino as the lightest. The search uses events containing photons, missing transverse energy, and jets. The impact parameter of the photon relative to the beam-beam collision point can be reconstructed using converted photons. The method is sensitive to lifetimes of the order of 0.1 to 1 ns. The data sample corresponds to an integrated luminosity of 2.23 inverse femtobarns in pp collisions at sqrt(s) = 7 TeV, recorded in the first part of 2011 by the CMS experiment at the LHC. Cross-section limits are presented on pair production for such particles, each of which decays into a photon and invisible particles. The observed 95% confidence level limits vary between 0.11 and 0.21 pb, depending on the neutral particle lifetime.