Measurement of the Radiative Correction to Electron-Proton Scattering by Observation of the Absolute Cross Section

The scattering of 139.5-Mev electrons in hydrogen gas at one-atmosphere pressure has been investigated using photographic emulsions. The beam of electrons from the Stanford Mark III linear accelerator, collimated to a diameter of $\frac{1}{16}$ in., passed through the gas and was collected in a lead Faraday cup. Ilford $C-2\mathrm{}$ emulsions, 50 μ thick, which were arranged symmetrically about the beam, detected the recoil protons. Measurements of the recoil angle $\gamma$ and the range in the emulsion were made on the proton tracks. Only those events were accepted whose measured range and angle correlated within ±2.33 standard deviations of the distribution about the elastic kinematic range-angle curve calculated from the multiple scattering in the emulsion and the uncertainty in angle measurement. A total of 2350 tracks have been tabulated in the angular interval $54°<~\gamma <~78°$ giving a statistical error matching the systematic errors in plate geometry, beam integration, and track measurement. The results are compared with the Mott cross section integrated over the interval. The theoretical cross section was corrected for (a) proton recoil, (b) the proton magnetic moment, (c) the finite size of the proton's charge and magnetic moment, (d) the radiative correction, including the effect on the cross section of emission of real photons contributing to the observed recoil protons. The result is $\frac{{\sigma }_{\exp }}{{\sigma }_{\mathrm{theor}}}=0.988\mathrm{}\pm 0.021 \left(\mathrm{probable}\mathrm{error}\right),$ using a proton radius of 7.7×${10}^{-14\mathrm{}}$ cm, and including a 2.74% radiative correction; the result is not sensitive to the choice of proton radius.