Measurement of the slope parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:math>for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>η</mml:mi><mml:mo>→</mml:mo><mml:mn>3</mml:mn><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>decay with the Crystal Ball detector at the Mainz Microtron (MAMI-C)

The dynamics of the $\ensuremath{\eta}\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{0}$ decay have been studied with the Crystal Ball multiphoton spectrometer and the TAPS calorimeter. Bremsstrahlung photons produced by the 1.5-GeV electron beam of the Mainz microtron MAMI-C and tagged by the Glasgow photon spectrometer were used for $\ensuremath{\eta}$-meson production. The analysis of $3\ifmmode\times\else\texttimes\fi{}{10}^{6} \ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\eta}p\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{0}p\ensuremath{\rightarrow}6\ensuremath{\gamma}p$ events yields the value $\ensuremath{\alpha}=\ensuremath{-}0.032\ifmmode\pm\else\textpm\fi{}0.003$ for the $\ensuremath{\eta}\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{0}$ slope parameter, which agrees with the majority of recent experimental results and has the smallest uncertainty. The ${\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ invariant-mass spectrum was investigated for the occurrence of a cusplike structure in the vicinity of the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ threshold. The observed effect is small and does not affect our measured value for the slope parameter.