Investigation of the Conjectured Nucleon Deformation at Low Momentum Transfer

We report new precise $\mathrm{H}(e,e^{\prime }p){\pi }^0$ measurements at the $\Delta (1232)$ resonance at $Q^2=0.127(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$ obtained at the MIT-Bates out-of-plane scattering facility which are particularly sensitive to the transverse electric amplitude ($E2$) of the ${\gamma }^{*}N\to \Delta$ transition. The new data have been analyzed together with those of earlier measurements to yield precise quadrupole to dipole amplitude ratios: $\mathrm{R}\mathrm{e}(E_{1+}^{3/2}/M_{1+}^{3/2})=(-2.3\pm {0.3}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.6}_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}})\%$ and $\mathrm{R}\mathrm{e}(S_{1+}^{3/2}/M_{1+}^{3/2})=(-6.1\pm {0.2}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.5}_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}})\%$ for $M_{1+}^{3/2}=(41.4\pm {0.3}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}+\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}\pm {0.4}_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}})({10}^{-3}/m_{{\pi }^{+}})$. The derived amplitudes give credence to the conjecture of deformation in hadrons favoring, at low $Q^2$, the dominance of mesonic effects.