Charged-Particle Interactions: Radiation Loss, Range

The sudden deflection of an electron by the Coulomb field of nuclei can cause the electron to radiate, producing a continuous spectrum of x-rays called bremsstrahlung. The fraction of electron energy converted into bremsstrahlung increases with increasing electron energy and is greater for media of high atomic number. (This process is important in the production of x-rays in conventional x-ray tubes.) According to the classical theory of electrodynamics [J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), p. 509], the acceleration produced by a nucleus of charge Ze on an incident particle of charge ze and mass M is proportional to Zze/M. The intensity of radiation emitted is proportional to (ze × acceleration) ~ (Zze/M) . Notice the (Z/M) dependence; this shows that bremsstrahlung is more important in a high-Z medium. Also it is more important for electrons and positrons than for protons and α -particles. Another way to understand the (Z/M) dependence is to recall the derivation of stopping power in Lec13 where the momentum change due to a collision between the incident particle and a target nucleus is (2ze/vb) x Z. The factor Z represents the Coulomb field of the nucleus (in Lec13 this was unity since we had an atomic electron as the target). The recoil velocity of the target nucleus is therefore proportional to Z/M, and the recoil energy, which is the intensity of the radiation emitted, is therefore proportional to (Z/M). In an individual deflection by a nucleus, the electron can radiate any amount of energy up to its kinetic energy T. The spectrum of bremsstrahlung wavelength for a thick target is of the form sketched below, with λmin = hc /T . This converts to a frequency spectrum which is a constant up the maximum frequency of ν max = T / h . The