Determination of theE2/M1ratio in theγN→Δ(1232)transition from a simultaneous measurement ofp(γ→,p)π0andp(γ→,π+)n

Tagged linearly polarized photons have been used at the Mainz Microtron (MAMI) for simultaneous measurements of the $p(\overrightarrow{\gamma },p){\pi }^0$ and $p(\overrightarrow{\gamma },{\pi }^{+})n$ reaction channels to study the $\gamma \overrightarrow{N}\Delta \mathrm{}\left(1232\right)\mathrm{}$ transition. The energy dependence of the magnetic dipole $M_{1+}^{3/2}$ and electric quadrupole $E_{1+}^{3/2}$ amplitudes have been extracted from these data in the photon energy range from $270$ to 420 MeV. The $E2/M1\mathrm{}$ ratio for the $\gamma \overrightarrow{N}\Delta \mathrm{}\left(1232\right)\mathrm{}$ transition has been determined to be $-(2.5\mathrm{}\pm {0.1}_{\mathrm{stat}}\pm {0.2}_{\mathrm{sys}})\%$ at the resonance position $({\delta }_{33}=90\mathrm{}°).\mathrm{}$