ABSTRACT
Most important for retardation of the high-energy charged particles is a bremsstrahlungthe process accompanying every change in the state of a charged particle. According to classical electrodynamics, describing the principal features of the bremsstrahlung with a good approximation, its intensity is proportional to the squared acceleration and inversely proportional to the particle mass. As a result, within the same field the bremsstrahlung of an electron is greater than that of a proton by a factor of several millions. Therefore, the bremsstrahlung caused by scattering of electrons from the Coulomb field of the atomic nuclei and electrons is most often observed and used in practice. For example, this process is used to generate high-energy photons due to the transmission of electrons through the high-density targets. Let us calculate the cross section of the electron bremsstrahlung by the Coulomb nucleus
field. In so doing we shall assume that the field may be allowed for by the perturbation theory methods, that is, the applicability criterion of the Born approximation is fulfilled
Zα
v ≪ 1,
where v is an electron velocity. The diagrams corresponding to the process:
e− + γ˜ → e− + γ (20.1) are pictured in Fig. 20.1. It is clear that the process (20.1) is another cross channel of the e−e+-pair production process in the Coulomb nucleus field. Therefore, the amplitude Me−γ˜→e−γ follows from that of the e−e+-pair production by means of the replacement:
p+ → −p1, p− → p2, k → −k. (20.2)
Particles, Fields, and Quantum
q
p1 − k
p2
kp1
p1
q
p2
k
p2 + k
FIGURE 20.1
The Feynman diagrams for the electron bremsstrahlung by the Coulomb nucleus field.
