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Interactions of Photons with
Matter – Coherent Scatter (Part 1)
George Starkschall, Ph.D.
Lecture Objectives
• Identify and describe the process of
coherent scatter
• Calculate the cross sections for
coherent scatter
Description
• Classically: Electromagnetic wave passing
near atom excites electrons to oscillate
• Oscillating electrons accelerated, emitting
energy
• Angle of scatter is small
• Scatter interactions are with electrons –
scatter from nuclei relatively infrequent
1
Thomson scatter
• First theoretical treatment of
classical scatter
• Did not agree with experiment, but
Thomson scatter cross section
included in all scattering equations –
provides good start
Scatter cross section
• Look upon differential scatter cross
section as related to the probability
that an incident photon produces
scattered photon at specified solid
angle
• Units of cross section are [m2
electron(atom)-1 steradian-1]
Scatter cross section
• From differential scatter cross
section we can calculate fraction of
energy scattered in any direction
• Fraction of energy scattered =
scattering cross section ×
electron(atom) areal density × angle
subtended by detector
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Scatter cross section
• So, to calculate a scattering cross
section, we need to determine the
fraction of energy scattered per
electron (atom) areal density per
solid angle subtended by detector
Follow the energy!
Thomson scatter
• Start with classical description of
electromagnetic wave
– E and B at right angles moving with velocity c
– E unpolarized, components E1 and E2
• Interaction with atom: Electric field causes
electron to accelerate
• Electron acceleration induces electric field
• Fraction of energy scattered related to
induced electric field
Thomson scatter
• Consider electric field interacting with free
electron
• Force on free electron due to electric field
Fi = keEi
Where
– e:
– E:
– i:
– k:
electron charge
electric field (in same direction of force)
= 1 or 2
same constant as in Coulomb force
equation (8.988  109 Nt  m2/C2)
3
Thomson scatter
• The electron will accelerate in the same direction
of the force: F = ma
• Solve for the acceleration of an electron due to an
electric field
ai = keEi/m0
• From classical E & M, the accelerated charge will
radiate energy in an electromagnetic wave
• This is the scattered radiation whose intensity we
need to calculate
Thomson scatter
• Look at the electric field vector at
point Q due to accelerated charge at
origin
Thomson scatter
r – distance PQ
 - angle between
E1 and PQ
4
Thomson scatter
• Define the classical electron radius
by
• Note: This is a very small number. The diameter of a nucleus
is 10-13 m
• Then
Thomson scatter
• Similarly, the component E2 will give rise
to electric field component (note that
is
parallel to
• The electric vector of a radiated wave is a
very small fraction of the electric vector of
the incident wave (r0 very small)
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