Proton Form Factors Research Articles

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsGev andGmv are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useGes(s)≈Gev(s) andGms(s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionFπ in terms of the scattering lengtha1 and the effective ranger1 of the π-π-scattering in the stateL=T=1.a1 is roughly known from pion production by pions. With this value and a suitabler1,Fπ has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π+−π− cross section with neglect of other states thanL=T=1. Under this assumption the π−π cross section has a resonance for low energy-momentum transfer.

Inelastic Electron-Deuteron Scattering and the Electromagnetic Structure of the Neutron

The neutron charge and magnetic moment form factors F/sub in/ and F/sub 2n/ are calculated from data on the reaction e + d yields e + p + n. Proton form factors that are used in the calculations are those found in e-p scattering. The cross sections for e + d yields e + p + n are calculated by means of a completely covariant theory, using dispersion relations. These cross sections are used to find F/sub in/ and F/sub 2n/, for momentum transfers of q/sup 2/ = 5 to 21 f/sup -2/. (T.F.H.)

The nucleon core in high-energy neutrino processes

The effects of the electromagnetic nucleon form factors on the cross sections of the reactions nu + p yields n + e/sup +/ and nu + n yields p + e/sup -/ are investigated. It is assumed that the proton magnetic form factor falls off more rapidly than (1 + k/sup 2//a/sup 2/)/sup -//sup 2/, where k/sup 2/ is the momentum trsnsfer and a is the incident nu energy. The proton charge form factor is assumed to have a plateau at -0.42. The total cross sections at vsrious nu energies and the differential e/sup plus or minus / production cross sections at fixed energy are calculated. The cross sections calculated using exponential form factors are compared with those using the proton form factors described above. (T.F.H.)

Electric and Magnetic Structure of the Proton and Neutron

The electric and magnetic form factors of the proton and neutron are derived theoretically as functions of the momentum transfer invariant (q/sup 2/). It is proposed that the proton and nucleon are two aspects of the nucleon, which differ only in isctopic spin. The neutron and proton form factors are accordingly divided into scalar and vector parts, and the effects of core charges and Yukawa clouds are discussed. It is noted that the neutron electric form factor is positive, thus requiring a pcsitive outer fringe of charge for the neutron. (T.F.H.)

Splitting of the Proton Form Factors and Diffraction in the Proton

Separate proton form factors were obtained from electron scattering studies by choosing a pair of experimentally measured cross sections at the same value for the square of the momentum transfer but at different values of electron energy and scattering angle. The proton form factors obtained were plotted against the square of the momentum transfer. The new F/sub 2/ indicated that the Pauli magnetic moment cloud is a spread-out distribution. The constancy of F, however, suggested that the Dirac electric/magnetic cloud has a small, perhaps point-like, core. (M.C.G.)

Charge distribution of the nucleon

Experimental data on the charge distribution in the nucleon are checked for fitness to the asymptotical behavior of the nucleon structure as described by Bosco and de Alfaro. Gocd fit was found for the proton form factor whereas very poor agreement was found for the neutron form factor. The experimental data were compared to that value of C/sub v/ obtained by continuation of A/sub 2/( nu , DELTA /sup 2/) and B/sub 2/( nu , DELTA /sup 2/) in the point nu = 0 and DD =-4 mu /sup 2/. Agreement was found to be very poor. (C.J.G.)