Thermal X-ray radiation (PDF) - SRON

3.6.8 Compton ionisation
Scattering of a photon on an electron generally leads to energy transfer from one
of the particles to the other. In most cases only scattering on free electrons is
considered. But Compton scattering also can occur on bound electrons. If the energy
transfer from the photon to the electron is large enough, the ionisation potential can
be overcome leading to ionisation. This is the Compton ionisation process.
Figure 3.21: Compton ionisation cross section for neutral atoms of H, He, C, N, O,
Ne and Fe.
In the Thomson limit the differential cross section for Compton scattering is
given by
dσ
dΩ = 3σ T
16π (1 + cos2 θ), (3.44)
with θ the scattering angle and σ T the Thomson cross section (6.65 × 10 −29 m −2 ).
The energy transfer ∆E during the scattering is given by (E is the photon energy):
∆E =
E 2 (1 − cosθ)
m e c 2 + E(1 − cosθ) . (3.45)
Only those scatterings where ∆E > I contribute to the ionisation. This defines a
critical angle θ c , given by:
cosθ c = 1 −
m ec 2 I
E 2 − IE . (3.46)
For E ≫ I we have σ(E) → σ T (all scatterings lead in that case to ionisation) and
further for θ c → π we have σ(E) → 0. Because for most ions I ≪ m e c 2 , this last
condition occurs for E ≃ √ Im e c 2 /2 ≫ I. See Fig. 3.21 for an example of some
cross sections. In general, Compton ionisation is important if the ionising spectrum
contains a significant hard X-ray contribution, for which the Compton cross section
is larger than the steeply falling photoionisation cross section.
One sees immediately that for E ≫ I we have σ(E) → σ T (all scatterings lead
in that case to ionisation) and further that for θ c → π we have σ(E) → 0. Because
for most ions I ≪ m e c 2 , this last condition occurs for E ≃ √ Im e c 2 /2 ≫ I. See
Fig. 3.21 for an example of some cross sections.
exercise 3.9. Estimate for which energy Compton ionisation becomes more important
than photoionisation for neutral iron.
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