Elastic electron-proton scattering

The study of elastic ep scattering will set the stage for the remarkable and unexpected results that we shall find when we investigate inelastic ep scattering. 

The Fj q ) are the electromagnetic elastic structure functions or elastic form factors of the proton, which can only depend on the momentum transfer q. In (15.2.2) k is the anomalous magnetic moment of the proton measured in Bohr magnetons, k = 1.79, and the term K/2mp is factored out for convenience. 

When we come to deal with neutrino scattering we shall have a current that is not conserved and the F3 type form factor will appear. The form factors Fi,F2 are defined in such a way that for q = 0, which physically corresponds to the proton interacting with a static electro-magnetic field, one has 

The cross-section for ep — ep is structurally the same as for ep ep except that 7 at the muon vertex is replaced by Fa in the proton vertex. Thus (15.1.2) becomes 

Note that we recover the e/x result by putting Fi = 1, F2 = 0 and rUp = nifi. We can thus say that the elastic form factor of a point-like particle such as the // is a constant, independent of This fact is of vital importance for the parton idea. 

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R. Rosenfelder, Coulomb corrections to elastic electron-proton scattering and the proton charge radius, Phys. Lett. B 479 (2000) 381-386. 

Model dependence of the Zemach correction, as well as its dependence on the proton radius is theoretically unsatisfactory. A much better approach is suggested in [8], where the values of the proton and deuteron first Zemach moments were determined in a model independent way from the analysis of the world data on the elastic electron-proton and electron-deuteron scattering. The respective moments turned out to be [8]... 

J. I. Friedman and H. W. Kendall (Massachusetts Institute of Technology) and R. E. Taylor (Stanford) pioneering investigations concerning deep elastic scattering of electrons on protons and bound neutrons, of essential importance for the development of the quark model in particle physics. 

An example of the features of the spectrum of secondary electrons emitted in H° impact on water molecules from the work of Bolorizadeh and Rudd [67] is shown in Fig. 16. Compared to the simple spectrum of electrons emitted by proton impact shown as the solid line in Fig. 16 the spectrum from H° impact has an additional peak centered at an electron energy of approximately 82 eV. This broad peak is from the superposition of the spectrum of electrons stripped (elastically scattered) from the projectile on the spectrum of electrons ejected from the target. Because the stripped projectile electrons originate as bound electrons in the rest frame of the moving projectile, their laboratory energy is given approximately hy W = meE jM and the width of the peak is determined by the Compton profile of electrons in the projectile frame, but also transformed to the laboratory frame-of-reference. The results shown in Fig. 16 clearly illustrate that the cross-sections for... 

In an elastic-scattering experiment (such as diffraction) the actual position of the atomic nuclei is given by the neutron scattering. This may be quite different from the barycentre of the electronic environment observed using X-rays, for example in CgHg, the electronic cloud around the hydrogen atoms is shifted some 10 pm with respect to the position of the proton. 

The Compton scattering of X-rays is incoherent with respect to the incident beam and is best described as the elastic collision of an X-ray proton with an electron where both energy and momentum are conserved. This means that the X-ray wavelength is increased. In effect. X-rays are considered as particles and not as waves. Compton scattering increases with the angle 16, but is always small compared with that of Thomson scattering. 

Recent years have seen a considerable extension of the experimental methods used in quantum chemistry and in investigations of the nature of chemical bonds in crystals. It is worth mentioning methods based on the studies of the elastic and the inelastic scattering (by crystals) of X rays, electrons, neutrons, protons, mesons, a and other particles, as well as the x ray spectroscopic methods. Methods based on the use of positron annihilation are also of considerable interest. 

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