- A measurement of the single photon production cross-section is presented based on a data-sample of 40.5 pb−1 collected with the OPAL detector at centre-of-mass energies within 3 GeV of the Z0 mass. Single photon events arise from initial state radiation and the production of an “invisible” final state consisting of neutrinos or possibly particles such as sneutrinos or photinos. The single photon topology is also sensitive to new Z0 decays such as\(Z^0 \to \bar vv* \to \bar vv\gamma \) orZ0→γX, X→invisible particles. A total of 447 single photon candidates were observed with energy exceeding 1.75 GeV in the polar angle region |cosθ|<0.7. The estimated background from processes with visible reaction products, mainly e+e−→e+e−γ, is 37±6 events. Interpreting the cross-sections as being solely due to Z0 decay to invisible particles and the expected W-contributions, the Z0 invisible with is determined to be 539±26±17 MeV corresponding toNv=3.23±0.16±0.10 light neutrino generations. The differential cross-section with photon energy is presented. Upper limits are set on additional invisible contributions to the Z0 width, on possible non-resconant processes, and on Z0 decays to single photons. The energy spectra are used to constrain exotic sources of high energy single photons. In particular, the radiative twobody decay of the Z0 to a new particle X, with mass below 64 GeV and an invisible signature, has a Z0 branching ratio of less than 4.3×10−6 at 95% confidence level.