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A new data set for the helicity-dependent differential cross section of thesingle-meson photoproduction reaction $\gamma p \to p \pi^{0}$ was obtained forthe photon energy interval 150-400 MeV. The experiment was performed at the A2tagged photon facility of the Mainz Microtron MAMI using a circularly polarizedphoton beam and a longitudinally polarized proton target. The reaction productswere detected with the large acceptance Crystal Ball/TAPS calorimeter covering97\% of the full solid angle. These new results, obtained with a fine energyand polar angle binning, greatly increase both the existing quantity andquality of the data available for this observable. A moment analysis, based ona finite expansion in Legendre polynomials, was applied to these data by usinga bootstrap-based fitting method to correctly account for their systematicuncertainties. From the resulting decomposition of the differential crosssections, the $E2/M1$ ratio for the $N\to \Delta(1232)$ transition wasdetermined to be $[-2.38 \pm 0.16{\hbox{ (stat.+sys.)}} \pm 0.10 {\hbox{(model)}}] \%$. Combining this value with previous results also allowed us toevaluate the most precise available estimate of the $E2/M1$ ratio to be usedfor all further reference and model comparisons.

Evaluation of the E2/M1 ratio in the $N\to \Delta(1232)$ transition from the $ \vec{\gamma} \vec{p} \to p \pi^0 $ reaction