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.

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The process γ+p→π0+p has been studied by detecting recoil protons from a liquid hydrogen target which was bombarded by the bremsstrahlung beam of the California Institute of Technology electron synchrotron. The angle and momentum of the recoil protons were measured by a magnetic spectrometer-three scintillation counter coincidence system. The process has been studied between photon laboratory energies of 490 and 940 Mev and between pion center-of-mass angles of 31.5° and 147°. Protons which arose from meson pair production were significant at forward laboratory angles. A correction for this contamination is discussed. The results of these measurements show two interesting features. One is that the total cross section, which falls very rapidly above the 32−32 resonance energy near 320 Mev, reaches a minimum at about 600 Mev, and then increases to a broad maximum near 800 or 900 Mev. The other striking feature of the data is that the shape of the angular distribution seems to change rather suddenly near 900 Mev.

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The bremsstrahlung beam of the Cornell Bev electron synchrotron has been used to study the reaction γ+p→π0+p over the photon energy range 250 Mev to 1 Bev, and for center-of-mass pion angles between 20° and 70°. The recoil protons, of energies between 10 and 60 Mev, were identified and their energies determined using a range telescope of eight thin plastic scintillators enclosed in a vacuum chamber with the thin liquid hydrogen target. Correlated pulse-height information was obtained by photographing an oscilloscope display and was used to sort out the protons from mesons and electrons. Corrections were made for the background of photoprotons from the Mylar target cup, the energy loss of the protons in the liquid hydrogen, absorption and scattering in the counter telescope, and the variation of beam intensity profile with energy. Compared with previous experiments and extrapolations the results show a somewhat smaller forward differential cross section above 400 Mev. The angular distributions obtained from a least-squares fit to all existing data indicate a d32 assignment for the 760-Mev resonance level. Other implications of the data are also discussed.

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Total cross sections for negative pions on protons were measured at laboratory energies of 230, 290, 370, 427, and 460 Mev. The measurements were made in the same pion beams as and at energies identical with those of our π−−p differential scattering experiments. Comparisons of the total and differential scattering can be made with the dispersion theory at a given energy without introducing the systematic errors that would normally enter due to uncertainties in the parameters of more than one pion beam. The measured total cross sections are found to agree within statistics with other measured values, and with the sums of elastic, inelastic, and charge-exchange cross sections measured at this laboratory. The results are:

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We report measurements of the differential cross section for photoproduction of π0 mesons from hydrogen, with the pion emerging near 0 deg, in the photon energy range 290 to 700 MeV. The results show no unusual behavior of the cross section in the forward direction. They are consistent with the angular distribution characteristic of a magnetic-dipole transition to a P32 state. The results agree reasonably well with theoretical predictions of Gourdin and Salin, but disagree with a prediction of DeTollis and Verganelakis. Least-squares fits in powers of cosθ have been made to the available angular distributions.

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Neutron angular distributions from the charge-exchange (π0n) and inelastic modes (π0π0n,π+π−n) of the π−−p interaction have been investigated at 313 and 371 MeV incident-pion kinetic energy. The data were obtained with an electronic counter system. Elastic and inelastic neutrons were separated in the all-neutral final states by time of flight. At both energies the charge-exchange differential cross section at the forward neutron angles differs from that determined by Caris et al. from measurements of the π0-decay gamma distributions, but generally agrees with the phase-shift-analysis calculations of Roper. The distribution of inelastic neutrons from both modes shows a strong preference for low center-of-mass neutron energies. The distribution of these neutrons does not correspond to that expected from the I=0, π−π interaction (ABC effect) suggested to account for the anomaly in p−d collisions observed by Abashian et al. Finally, all available charge-exchange differential-cross-section data from this and other experiments were combined by at least-squares fit to a Legendre expansion of the form dσdΩ*(cosθπ0*)=Σl=0NalPl(cosθπ0*) with the following results (in mb/sr):

Differential cross sections for elastic π−p scattering were measured at eight energies for positive pions and seven energies for negative pions. Energies ranged from 310 to 650 MeV. These measurements were made at the 3-GeV proton synchrotron at Saclay, France. A beam of pions from an internal BeO target was directed into a liquid-hydrogen target. Fifty-one scintillation counters and a matrix-coincidence system were used to measure simultaneously elastic events at 21 angles and charged inelastic events at 78 π−p angle pairs. Events were detected by coincidence of pulses indicating the presence of an incident pion, scattered pion, and recoil proton, and the results were stored in the memory of a pulse-height analyzer. Various corrections were applied to the data and a least-squares fit was made to the results at each energy. The form of the fitting function was a power series in the cosine of the center-of-mass angle of the scattered pion. Integration under the fitted curves gave values for the total elastic cross sections (without charge exchange). The importance of certain angular-momentum states is discussed. The π−−p data are consistent with a D13 resonant state at 600 MeV, but do not necessarily require such a resonant state.

The polarization of the recoil proton in neutral single-pion photoproduction from hydrogen, γ+p→p+π0, has been measured for pion center-of-mass angles near 90° at 7 photon energies from 450 to 900 MeV. The polarization rises to a maximum of 0.58 near 600 MeV and is still 0.42 at 900 MeV. The sign of the polarization is negative in the sense of k×q, where k is the photon momentum and q is the pion momentum. The measured values are given as functions of laboratory photon energy and c.m. pion angle as follows: 450 MeV, 109°, -0.16±0.14; 525 MeV, 84°, -0.36±0.19; 585 MeV, 86°, -0.58±0.15; 660 MeV, 77°, -0.51±0.17; 755 MeV, 76°, -0.55±0.15; 810 MeV, 89°, -0.45±0.17; 895 MeV, 90°, -0.42±0.16. The recoil protons were momentum-analyzed with a magnetic spectrometer. Nuclear emulsion was used as scatterer and detector. The emulsion technique is discussed in detail. The number of individual scatterings in emulsion used for each measurement varied between 750 and 1000.

Absolute measurements of the elastic electron-proton cross section have been made with a precision of about 4% for values of the square of the four-momentum transfer, q2, in the range 6.0 to 30.0 F−2 and for electron scattering angles in the range 45° to 145°. To within the experimental errors, it is found that the charge and magnetic form factors of the proton have a common dependence on q2 when normalized to unity at q2=0, and that an accurate representation of the behavior of the form factor and that of the cross sections themselves can be given in terms of a three-pole approximation to the dispersion theory of nucleon form factors.

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The azimuthal asymmetry Σ=(σ⊥−σII)(σ⊥+σII) in π+ photoproduction by linearly polarized bremsstrahlung was measured at photon energies from 475 to 750 MeV at 90° and 135° in the center-of-mass system. The experimental results show that even in this energy region, π+ are produced predominantly in the plane of the magnetic vector.

The differential cross section for the reaction γ+p→π++n was measured using the Caltech 1.5-GeV electron synchrotron. The positive pions were detected and momentum analyzed in a multichannel magnetic spectrometer and the data were recorded in the memory of a pulse-height analyzer. The energy resolution was improved over previous experiments and an attempt was made to minimize systematic errors. The data are presented in the form of energy distributions at 12 lab angles from 34° to 155°, and the range of lab proton energies extended from 500 to 1350 MeV. Data were not taken at all energies for each angle, since the maximum useful momentum of the spectrometer, 600 MeVc, restricted the maximum energy for lab angles less than or equal to 74°.

Cross sections for the photoproduction of neutral pions have been measured at the 1.1-GeV Frascati electron synchrotron for bombarding photon energies k between 400 and 800 MeV and for π0 c.m. angles of θπ*=90∘, 120∘, and 135∘. The main feature of the experiment is good resolution in incident photon energy. The results are in good agreement with the existing theories in the energy range of 450 to 550 MeV. The cross sections exhibit a smooth behavior as a function of energy for k=400−600 MeV. No immediate evidence is found of a contribution of the P11 resonance. An anomaly at the limit of statistical significance appears for k≃700−740 MeV, indicating a possible structure of the so-called second resonance. We attempt to interpret the observed anomaly as a reflection of the sharp opening of the η production channel (η cusp effect).

The polarization parameter in elastic π−p scattering has been measured, at the Berkeley 184-in. synchrocyclotron, with the use of a polarized proton target. At 318-, 337-, and 390-MeV incident pion kinetic energy, the angular range from 70° to 180° in the center-of-mass system was covered. At 229 MeV, polarization measurements were made in the angular range 150° to 180°. Phase-shift analyses, using these and other published data, were made at the two lowest energies.

The differential asymmetry ratio for the process γ+n→p+π− was measured at 90° in the center-of-mass system and for incident photon energies from 352 to 550 MeV. The observed asymmetries are larger than the values predicted from the theory by Berends, Donnachie, and Weaver. A smaller M1- amplitude gives better agreement between the experiment and the theory.

Approximately 700 events of the reaction K − d → K − π − pp s produced by 5.5 GeV/ c kaons were used to measure the cross section for Kπ elastic scattering in the T = 3 2 state by a Chew-Low extrapolation. The cross section does not exceed 2.1 mb and has no structure for Kπ masses from threshold up to 2.0 GeV.

The differential cross sections for the γ + n → π O + n reaction have been measured at the photon energies of 500–900 MeV. The ratios, R oo = [ d δ d Ω(γ n → π o n ) ] [ d δ d Ω(γ p → π o p ) ] , have been obtained at the c.m. pion angles of 60 O , 90 O , 105 O , 120 O , and 140 O .

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