6
H. Bichsel and H. Schindler
dσ/dE and its moments. The integral cross section (zeroth moment), multiplied
by the atomic density N, corresponds to the charged particle’s inverse mean free
path λ −1 or, in other words, the average number of collisions per unit track length,
λ
−1
= M 0 = N
E max
E min
dσ
dE
dE.
(2.1)
The stopping power dE/dx, i.e. the average energy loss per unit track length, is
given by the first moment,
−
dE
dx
= M 1 = N
E max
E min
E
dσ
dE
dE.
(2.2)
The integration limits E min, max are determined by kinematics. Due to the stochastic
nature of the interaction process, the number of collisions and the sum of energy
losses along a particle track are subject to fluctuations. Section 2.5 deals with
methods for calculating the probability density distribution f (, x) for different
track lengths x. The energy transfer from the incident particle to the electrons of
the medium typically results in excitation and ionisation of the target atoms. These
observable effects are discussed in Sect. 2.6.
As a prologue to the discussion of charged-particle collisions, Sect. 2.2 briefly
reviews the principal photon interaction mechanisms in the X-ray and gamma ray
energy range.
Throughout this chapter, we attempt to write all expressions in a way independent
of the system of units (cgs or SI), by using the fine structure constant α ∼ 1/137.
Other physical constants used occasionally in this chapter include the Rydberg
energy Ry = α 2 mc 2 /2 ∼ 13.6 eV, and the Bohr radius a 0 = ¯
hc/
αmc 2 ∼
0.529 Å. Cross-sections are quoted in barn (1 b = 10 −24 cm 2 ).
2.2 Photon Interactions
Photons interact with matter via a range of mechanisms, which can be classified
according to the type of target, and the effect of the interaction on the photon
(absorption or scattering) [9, 21]. At energies beyond the ultraviolet range, the
dominant processes are photoelectric absorption (Sect. 2.2.1), Compton scattering
(Sect. 2.2.2), and pair production (Sect. 2.2.3). As illustrated in Fig. 2.1, photoabsorption constitutes the largest contribution to the total cross section at low photon
energies, pair production is the most frequent interaction at high energies, and
Compton scattering dominates in the intermediate energy range.
H. Bichsel and H. Schindler
dσ/dE and its moments. The integral cross section (zeroth moment), multiplied
by the atomic density N, corresponds to the charged particle’s inverse mean free
path λ −1 or, in other words, the average number of collisions per unit track length,
λ
−1
= M 0 = N
E max
E min
dσ
dE
dE.
(2.1)
The stopping power dE/dx, i.e. the average energy loss per unit track length, is
given by the first moment,
−
dE
dx
= M 1 = N
E max
E min
E
dσ
dE
dE.
(2.2)
The integration limits E min, max are determined by kinematics. Due to the stochastic
nature of the interaction process, the number of collisions and the sum of energy
losses along a particle track are subject to fluctuations. Section 2.5 deals with
methods for calculating the probability density distribution f (, x) for different
track lengths x. The energy transfer from the incident particle to the electrons of
the medium typically results in excitation and ionisation of the target atoms. These
observable effects are discussed in Sect. 2.6.
As a prologue to the discussion of charged-particle collisions, Sect. 2.2 briefly
reviews the principal photon interaction mechanisms in the X-ray and gamma ray
energy range.
Throughout this chapter, we attempt to write all expressions in a way independent
of the system of units (cgs or SI), by using the fine structure constant α ∼ 1/137.
Other physical constants used occasionally in this chapter include the Rydberg
energy Ry = α 2 mc 2 /2 ∼ 13.6 eV, and the Bohr radius a 0 = ¯
hc/
αmc 2 ∼
0.529 Å. Cross-sections are quoted in barn (1 b = 10 −24 cm 2 ).
2.2 Photon Interactions
Photons interact with matter via a range of mechanisms, which can be classified
according to the type of target, and the effect of the interaction on the photon
(absorption or scattering) [9, 21]. At energies beyond the ultraviolet range, the
dominant processes are photoelectric absorption (Sect. 2.2.1), Compton scattering
(Sect. 2.2.2), and pair production (Sect. 2.2.3). As illustrated in Fig. 2.1, photoabsorption constitutes the largest contribution to the total cross section at low photon
energies, pair production is the most frequent interaction at high energies, and
Compton scattering dominates in the intermediate energy range.