Measurement of the $e^+ e^- \to \gamma\gamma (\gamma)$ cross section at the LEP energies

The total and the differential cross-sections for the reaction $e^+e^-\rightarrow \gamma\gamma(\gamma)$ have been measured with the DELPHI detector at LEP % with at centre-of-mass energies from 1 30 %, 136, 161, 172 and to 183 GeV for an integrated luminosity of 78.19.~pb$^{-1}$. %CR An agreement with the QED predictions was found and consequently The results agree with the QED prediction s. The lower limits (obtained including previously published results at the $\Zzero$ energies) on the QED cutoff parameters are $\Lambda_{+} 253$~GeV and $\Lambda_{-} 225$~GeV and the lower bo und on the mass of an excited electron with an effective coupling constant $\lambda_{\gamma} = 1$ is 231~GeV/$c^2$. %Upper limits on the branching ratios for the decays ${\rm Z}^0\rightarrow %\gam ma\gamma$, ${\rm Z}^0\rightarrow \pi^0\gamma$, % ${\rm Z}^0\rightarrow \eta\gamma$ %and ${\rm Z}^0\rightarrow \gamma\gamma\gamma$ have been determined to be 2.5 % $\times$ $10^{-5}$, 2.5 $\times$ $ 10^{-5}$, % 4.0 $\times$ $10^{-5}$, %and 9.1 $\times$ $10^{-4}$ respectively. All the limits are at the 95$\%$ confidence level.