2 The Interaction of Radiation with Matter
9
sections (both for discrete excitations as well as transitions to the continuum) for
many commonly used gases are given in the book by Berkowitz [25, 26].
At energies sufficiently above the ionisation threshold, the molecular photoabsorption cross section is, to a good approximation, given by the sum of the
photoabsorption cross sections of the constituent atoms. A comprehensive compilation of atomic photoabsorption data (in the energy range between ∼30 eV and
30 keV) can be found in Ref. [27]. Calculations for energies between 1 and 100 GeV
are available in the NIST XCOM database [24]. Calculated photoionisation cross
sections for individual shells can be found in Refs. [28–30]. At high energies, i.e.
above the respective absorption edges, photons interact preferentially with innershell electrons. The subsequent relaxation processes (emission of fluorescence
photons and Auger electrons) are discussed in Sect. 2.6.
The response of a solid with atomic number Z to an incident photon of energy
E = ¯
hω is customarily described in terms of the complex dielectric function ε(ω) =
ε 1 (ω) + iε 2 (ω). The oscillator strength density is related to ε(ω) by
df (E)
dE
= E
2Z
π
¯
hh p
2
ε 2 (E)
ε 2
1 (E) + ε 2
2 (E)
= E
2Z
π
¯
hh p
2 Im
−1
ε (E)
,
(2.6)
where
¯
hh p =
4πα ( ¯
hc)
3 NZ
mc 2
(2.7)
is the plasma energy of the material, which depends only on the electron density
NZ. In terms of the dielectric loss function Im (−1/ε), the TRK sum rule reads
dE Im
−1
ε (E)
E =
π
2
¯
hh p
2 .
(2.8)
Compilations of evaluated optical data for semiconductors are available in
Ref. [32], and for solids in general in Ref. [31]. As an example, Fig. 2.3 shows
the dielectric loss function of silicon, a prominent feature of which is the peak at
∼17 eV, corresponding to the plasma energy of the four valence (M-shell) electrons.
2.2.2 Compton Scattering
Compton scattering refers to the collision of a photon with a weakly bound electron,
whereby the photon transfers part of its energy to the electron and is deflected with
respect to its original direction of propagation. We assume in the following that
the target electron is free and initially at rest, which is a good approximation if
the photon energy E is large compared to the electron’s binding energy. Due to
9
sections (both for discrete excitations as well as transitions to the continuum) for
many commonly used gases are given in the book by Berkowitz [25, 26].
At energies sufficiently above the ionisation threshold, the molecular photoabsorption cross section is, to a good approximation, given by the sum of the
photoabsorption cross sections of the constituent atoms. A comprehensive compilation of atomic photoabsorption data (in the energy range between ∼30 eV and
30 keV) can be found in Ref. [27]. Calculations for energies between 1 and 100 GeV
are available in the NIST XCOM database [24]. Calculated photoionisation cross
sections for individual shells can be found in Refs. [28–30]. At high energies, i.e.
above the respective absorption edges, photons interact preferentially with innershell electrons. The subsequent relaxation processes (emission of fluorescence
photons and Auger electrons) are discussed in Sect. 2.6.
The response of a solid with atomic number Z to an incident photon of energy
E = ¯
hω is customarily described in terms of the complex dielectric function ε(ω) =
ε 1 (ω) + iε 2 (ω). The oscillator strength density is related to ε(ω) by
df (E)
dE
= E
2Z
π
¯
hh p
2
ε 2 (E)
ε 2
1 (E) + ε 2
2 (E)
= E
2Z
π
¯
hh p
2 Im
−1
ε (E)
,
(2.6)
where
¯
hh p =
4πα ( ¯
hc)
3 NZ
mc 2
(2.7)
is the plasma energy of the material, which depends only on the electron density
NZ. In terms of the dielectric loss function Im (−1/ε), the TRK sum rule reads
dE Im
−1
ε (E)
E =
π
2
¯
hh p
2 .
(2.8)
Compilations of evaluated optical data for semiconductors are available in
Ref. [32], and for solids in general in Ref. [31]. As an example, Fig. 2.3 shows
the dielectric loss function of silicon, a prominent feature of which is the peak at
∼17 eV, corresponding to the plasma energy of the four valence (M-shell) electrons.
2.2.2 Compton Scattering
Compton scattering refers to the collision of a photon with a weakly bound electron,
whereby the photon transfers part of its energy to the electron and is deflected with
respect to its original direction of propagation. We assume in the following that
the target electron is free and initially at rest, which is a good approximation if
the photon energy E is large compared to the electron’s binding energy. Due to