The structure and size of the proton have been studied by means of high-energy electron scattering. The elastic scattering of electrons from protons in polyethylene has been investigated at the following energies in the laboratory system: 200, 300, 400, 500, and 550 Mev. The range of laboratory angles examined has been 30° to 135°. At the largest angles and the highest energy, the cross section for scattering shows a deviation below that expected from a point proton by a factor of about nine. The magnitude and variation with angle of the deviations determine a structure factor for the proton, and thereby determine the size and shape of the charge and magnetic-moment distributions within the proton. An interpretation, consistent at all energies and angles and agreeing with earlier results from this laboratory, fixes the rms radius at (0.77±0.10) ×10−13 cm for each of the charge and moment distributions. The shape of the density function is not far from a Gaussian with rms radius 0.70×10−13 cm or an exponential with rms radius 0.80×10−13 cm. An equivalent interpretation of the experiments would ascribe the apparent size to a breakdown of the Coulomb law and the conventional theory of electromagnetism.
In the experiment just relative cross sections were measured. The absolute values were ascribed at each energy after multiplying experimental data by a co nstant factor to obtain the best fit with theory assuming the diffuse proton model with charge and magnetic moment rms radii 0.08 fm.. The values in the table are extracted from the graphs (see figs. 6 - 9) byZOV.
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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 116 in., passed through the gas and was collected in a lead Faraday cup. Ilford C−2 emulsions, 50 μ thick, which were arranged symmetrically about the beam, detected the recoil protons. Measurements of the recoil angle γ 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°<~γ<~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 σexpσtheor=0.988±0.021 (probableerror), using a proton radius of 7.7×10−14 cm, and including a 2.74% radiative correction; the result is not sensitive to the choice of proton radius.
The radiative corrections were not applied in the calculation of the cross sections from the experimental data. Thus the cross sections given in the table are experiment-dependent because the radiative correction depends on the resolution of an experiment. The errors given in the table include systematic and statistical errors combined quadratically. The statistical error varies from 3.5% at 77 DEG to 23.6% at 55 DEG.
These cross sections were recalculated by ZOV from the experimental ones using a radiative correction (see fig.15). Thus they may be considered as an experiment-independent cross sections of a 'pure' process E- P --> E- P.
A measurement of the ratio of the magnetic form factor of the neutron to that of the proton has been carried out by comparing large- and small-angle elastic electron-deuteron scattering at constant four-momentum transfers. The experimental result for the average value of the ratio in the range of momentum transfers from 1.6 f−1 to 2.25 f−1 is F2nFp=(0.91±0.05)±0.07; the first error is a standard deviation arising from experimental uncertainties, and the second from theoretical uncertainties in the analysis. Measurements of the ratio of the nucleon isotopic scalar form factors have also been obtained from this experiment. The average value of F2sF1s for the same range of momentum transfers has been found to be (+0.06±0.09) ±0.13. The small-angle scattering data have been used to determine the charge form factor of the deuteron in the range of momentum transfers from 0.98 f−1 to 2.8 f−1. The results are consistent with a repulsive-core model of the deuteron.
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This paper reports experimental findings on the Dirac (F1) and Pauli (F2) form factors of the proton. The form factors have been obtained by using the Rosenbluth formula and the method of intersecting ellipses in analyzing the elastic electron-proton scattering cross sections. A range of energies covering the interval 200-1000 Mev for the incident electrons is explored. Scattering angles vary from 35° to 145°. Values as high as q2≅31 f−2 (q=energy−momentumtransfer) are investigated, but form factors can be reliably determined only up to about q2=25 f−2. Splitting of the form factors is confirmed. The newly measured data are in good agreement with earlier Stanford data on the form factors and also with the predictions of a recent theoretical model of the proton. Consistency in determining the values of the form factors at different energies and angles gives support to the techniques of quantum electrodynamics up to q2≅25 f−2. At the extreme conditions of this experiment (975 Mev, 145°) the behavior of the form factors may be exhibiting some anomaly.
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We have measured the electron-proton scattering cross section at 248.9 Mev, 104.81°; 209.6 Mev, 149.75°; and 139.3 Mev, 104.19°. We find the following values: F1=0.767±0.025, F2=0.707±0.028, and F1F2=1.085±0.025 at −q2=2.98 f−2. F=0.902±0.011 at −q2=1.05 f−2. The last result agrees with previous measurements. The others are new contributions.
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