Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>production in two-photon collisions

The reaction ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ has been analyzed using 97 ${\mathrm{pb}}^{\ensuremath{-}1}$ of data taken with the Crystal Ball detector at the DESY ${e}^{\ensuremath{-}}{e}^{+}$ storage ring DORIS II at beam energies around 5.3 GeV. For the first time we have measured the cross section for $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ for ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ mvariant masses ranging from threshold to about 2 GeV. We measure an approximately flat cross section of about 10 nb for $W={m}_{{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}}&lt;0.8$ GeV, which is below 0.6 GeV, in good agreement with a theoretical prediction based on an unitarized Born-term model. At higher invariant masses we observe formation of the ${f}_{2}(1270)$ resonance and a hint of the ${f}_{0}(975)$. We deduce the following two-photon widths: ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}\ensuremath{\gamma}}({f}_{2}(1270))=3.19\ifmmode\pm\else\textpm\fi{}{0.16\ifmmode\pm\else\textpm\fi{}}_{0.28}^{0.29}$ keV and ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}\ensuremath{\gamma}}({f}_{0}(975))&lt;0.53$ keV at 90% C.L. The decay-angular distributions show the ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ system to be dominantly spin 0 for $W&lt;0.7$ GeV and spin 2, helicity 2 in the ${f}_{2}(1270)$ region, with helicity 0 contributing at most 22% (90% C.L.).