278
Chapter 4. Particle scattering
total cross section σ i for inelastic scattering divided by the total
cross section σ e for elastic scattering is given [24] by
σ i
20
≈ .
(4.177)
σ e
Z
Following Bethe [5], the momentum transfer q is related to the
scattering angle θ by
q
2 ≈ θ
2 + θ
2
(4.178)
E ,
where θ E is defined as
m ΔE ¯
θ E =
,
(4.179)
h
2 k
2
¯ 0
and Δ E ¯ is the average energy loss per collision, and is in the range
of a few eV to a few tens of eV, depending on the target material.
Given that the scattering is from the electron cloud of the target
atom, the predominant scattering angles for a fast incident particle
are small, in the range of 1 mrad.
4.8 Slowing of a charged particle in a
dielectric medium
When a fast charged particle passes through a solid, it interacts
electromagnetically with many atoms simultaneously. In addition
conduction band electrons are delocalized, with nonzero probability density over a region many atomic diameters in size. The
incident particle interacts collectively with the electrons of the
target material. It is worthwhile to consider the interaction in a
classical approximation. This section closely follows the analysis
by Landau and Lifshitz [56]. This material is described in more
detail, and placed in the context of the earlier work of others by
Egerton [24].
Chapter 4. Particle scattering
total cross section σ i for inelastic scattering divided by the total
cross section σ e for elastic scattering is given [24] by
σ i
20
≈ .
(4.177)
σ e
Z
Following Bethe [5], the momentum transfer q is related to the
scattering angle θ by
q
2 ≈ θ
2 + θ
2
(4.178)
E ,
where θ E is defined as
m ΔE ¯
θ E =
,
(4.179)
h
2 k
2
¯ 0
and Δ E ¯ is the average energy loss per collision, and is in the range
of a few eV to a few tens of eV, depending on the target material.
Given that the scattering is from the electron cloud of the target
atom, the predominant scattering angles for a fast incident particle
are small, in the range of 1 mrad.
4.8 Slowing of a charged particle in a
dielectric medium
When a fast charged particle passes through a solid, it interacts
electromagnetically with many atoms simultaneously. In addition
conduction band electrons are delocalized, with nonzero probability density over a region many atomic diameters in size. The
incident particle interacts collectively with the electrons of the
target material. It is worthwhile to consider the interaction in a
classical approximation. This section closely follows the analysis
by Landau and Lifshitz [56]. This material is described in more
detail, and placed in the context of the earlier work of others by
Egerton [24].