| 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.
-
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.
-
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.
-
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
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 = N0; E = E0exp(−1)
|
N = N0exp(−7/9);
E = E0
|
| Energy flux |
N E = N0E0exp(−1)
|
N E = N0E0exp(−7/9)
|
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