PHY6040 Particle Detectors Dr C N Booth

Interactions of Electrons and Photons with Matter

This page contains a brief summary of the interactions of electrons and photons. Fuller details are given in the handout, PostScript and PDF versions of which are available, and links are given below to relevant sections of the Particle Detector BriefBook for an alternative presentation.

Electrons

Electrons are charged particles, and so interact with matter through their Coulomb field in a similar way to that discussed previously for other charged particles.  Small differences in the rate of energy loss by ionisation arise due to the fact that a high energy electron has the same mass as the atomic electrons to which energy is transferred, and because of the identity of the particles involved in the scattering process, as discussed in the notes.  There is, however, a much bigger effect.  Because of their low mass, electrons experience large accelerations in the field of atomic nuclei, and this leads to electromagnetic radiation known as bremsstrahlung (or "braking radiation").  The passage of a high energy electron through matter therefore results in the emission of high energy photons or gamma rays.  As derived in the notes, the rate of energy loss through material of density ρ can be expressed as
where X0 is known as the radiation length of the material through which the electron is passing, and sets the length scale for the energy loss.

The mean energy of the electron after passing through a thickness Δx of material is therefore

Note that for high energy electrons, the energy loss by radiation is much greater than that due to ionisation, which can be ignored until the electron's energy drops below a critical energy Ec often parametrised as

(where Z is the atomic number of the material) below which energy loss by ionisation dominates.


Photons

There are three processes by which a photon can interact with matter.  Their relative importance depends on the energy of the photon.
  1. Photoelectric effect  The energy of the photon supplies the binding energy of an atomic electron.  The cross section for this process falls rapidly with photon energy, and is only important for very low energy photons, below 0.1 MeV.

  2. Compton Scattering - elastic scattering of a photon with an electron.  The cross section falls (approximately) as the reciprocal of the energy of the photon.  This process is dominant below 5 to 10 MeV.

  3. Pair production  The photon converts into an electron-positron pair in the field of a heavy nucleus.  The Feynman diagram for this process is intimately related to that for bremsstrahlung, and the calculation of its probability is similar.  The result is that the attenuation of the photon beam is given by
  4. and hence the mean number of photons after passing through a thickness Δx of material falls as

    where X0 is the radiation length as defined above.
    The length scale for this process, 9/7X0, is known as the conversion length.
    Pair production is dominant for photon energies above about 10 MeV.


Note the similarities and differences between bremsstrahlung and pair production.  After passing through one radiation length:
 
A single electron passes through the medium.

Its energy is reduced to E0exp(−1) on average.

A (large) number of bremsstrahlung photons is produced.

A single photon:
  • either passes through the medium without energy loss
  • or is converted into e+e.
  • Probability of non-conversion is exp(−7/9)

    If we consider beams of particles:

    electrons
    photons
    N = N0E = E0exp(−1)
    N = N0exp(−7/9); E = E0
    Energy flux
    N E = N0E0exp(−1)
    N E = N0E0exp(−7/9)


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