Deep Inelastic Scattering of Electrons from Protons

The construction of the Stanford Linear Accelerator Center (SLAC), which accelerates electrons up to $40 \mbox{ GeV}$, allowed experiments like Hofstadter's to be carried out at much higher energies. At these energies many of the collisions between electrons and protons and neutrons are inelastic -- generally a great mess of short-lived particles is spewed out, and are very difficult to interpret. However, the so-called deep inelastic collisions, where the electron scatters through a large angle and therefore transfers a large momentum, $q$, to the proton, yield very interesting results. In particular, these collisions occur essentially with a probability proportional to $q^{-4}$ -- just as in the Geiger-Marsden experiment!

The electron is a point particle as far as we know. However, previous experiments showed the proton to have a finite size, of order $10^{-15} \mbox{ m}$. Therefore, the scattering probability should drop off more rapidly with increasing momentum transfer $q$ than $q^{-4}$, as in the earlier Hofstadter experiments.

James Bjorken and Richard Feynman showed a way out of this dilemma. They proposed that the proton actually consists of a small number of point particles bound together by weakly attractive forces. A sufficiently energetic photon is able to knock a single one of these particles out of the proton, as illustrated in the right panel of figure 18.6. This leads to a subsequent set of reactions which produce the profusion of particles seen in the left panel of this figure. Feynman called the particles which make up the proton partons. However, we now know that they are actually quarks, spin 1/2 particles with fractional electronic charge which are thought to be the fundamental building blocks of matter, and gluons, the massless spin 1 intermediary particles which carry the strong force.

Figure 18.6: Deep inelastic scattering of a high energy electron by a proton occurs when the momentum transfer $q$ is large and many particles are produced. According to the Bjorken-Feynman theory of this process, the proton consists of a number of partons flying in ``loose formation''. A sufficiently energetic photon, i. e., with large momentum transfer $q$, kicks out just one of these partons, leaving the others undisturbed.