This Letter reports a search for the production by ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ annihilation of a single photon accompanied by particles that interact only weakly in matter. The search was performed at the SLAC ${e}^{+}$${e}^{\mathrm{\ensuremath{-}}}$ storage ring PEP (\ensuremath{\surd}s =29 GeV) with a new detector, ASP. No unexpected signal was observed. The limit ${N}_{\ensuremath{\nu}}$14 (90% C.L.) is placed on the number of light neutrino species, and the mass of scalar electrons predicted by theories of supersymmetry is constrained to ${m}_{e\ifmmode \tilde{}\else \~{}\fi{}}$>51 GeV/${c}^{2}$ (90% C.L.) for ${m}_{\ensuremath{\gamma}\ifmmode \tilde{}\else \~{}\fi{}}$=0 and degenerate e\ifmmode \tilde{}\else \~{}\fi{} mass states.