Interactions of Photons with
Matter – Photoelectric Effect
George Starkschall, Ph.D.
Lecture Objectives
• Identify and describe the photoelectric
effect
• Recall the dependence of the
photoelectric attenuation coefficient
on atomic number and energy
Systematic catalog of interactions
Kinds of
interaction
Effects of
interaction
1. Interaction with atomic
electrons
a. Complete absorption
2. Interaction with nucleons
b. Elastic scattering
(coherent)
3. Interaction with the electric c. Inelastic scattering
field surrounding nuclei or
(incoherent)
electrons
4. Interaction with the meson
field surrounding nucleons
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Systematic catalog of interactions
• 12 possible processes
• Only 5 are of significance in
radiological physics
5 interactions
• Classical scatter
– (1b) Atomic electrons/Elastic scatter
• Photoelectric effect
– (1a) Atomic electrons/Complete absorption
• Compton scatter
– (1c) Atomic electrons/Inelastic scatter
• Pair production
– (3a) Electric field/Complete absorption
• Photonuclear disintegration
– (2a) Nucleons/Complete absorption
Mass attenuation coefficient
• Mass attenuation coefficients for
each process add to obtain total
mass attenuation coefficient
/ = coh/ + / + C/ + /
– coh/
– /
– C/
– /
coefficient for classical scatter
coefficient for photoelectric effect
coefficient for Compton scatter
coefficient for pair production
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Qualitative description of effect
• Photon interacts with atom
– Transfers all of its energy h to atom
– Ejects orbital electron from atom
Energy of photoelectron
• Energy of photoelectron given by
Ee = h - Eb
• For soft tissue, Eb approximately 0.5 keV, so most
photon energy transferred to photoelectron
Energy of photoelectron
• Recoil energy of target atom nearly 0, so
essentially all kinetic energy goes into
photoelectron
3
Characteristic x-rays
• If inner-shell electron is ejected, filling
vacancy results in emission of
characteristic x-ray
Theoretical treatments
• Exact solutions difficult and tedious
– Need tools of relativistic quantum
mechanics
• Quantitative aspects largely
empirical
Energy dependence
• Plot / vs energy on log-log plot
• Straight line implies that /  (h)-n
4
Energy dependence
• In particular, / falls about 3 orders of magnitude per
order of magnitude of energy, so n approximately
equal to 3
Edges in energy dependence
• For Pb, note structure in behavior of attenuation
coefficient vs photon energy near 16 keV and near 90
keV
Edges in energy dependence
• Discontinuities near binding energies of various shells
– K shell
– L shell
88 keV
16 keV
• Just below shell binding energy – insufficient energy to ionize
electron
• Just above shell binding energy – sufficient energy to ionize
electron
• Attenuation coefficient increases by factor of around 5
5
Z dependence
• Attenuation coefficient much higher for Pb than for
water
– 3 orders of magnitude change in coefficient for 1 order of
magnitude change in Z (water Z=7.5, Pb Z = 82)
Z dependence
• Experimentally /  Zn, where n is approximately 3
for high Z materials and closer to 3.8 for low Z
materials
Summary of dependences
• Combining proportionalities, we get
/  Z3/(h)3
• Photoelectric absorption most
probable at low energies and high Z
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Angular dependence
• At low energies, photoelectron ejected
near 90º relative to incident photon
– Incident photon is electromagnetic wave
– Induced motion of electron is in direction of
electric field – transverse
• At higher energies, photoelectron ejected
in more forward direction
– Conservation of momentum
Angular dependence
Conservation of momentum
• Whenever h >> Eb, KE  h
• But, rest mass of electron is finite
• Electron momentum > photon
momentum
• Need recoil atom to achieve
momentum conservation
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Additional radiation
• Ejected photoelectron leaves
vacancy behind
– Auger electron – energy deposited in
immediate vicinity of interaction
– Characteristic x-ray – energy deposited
near, but not adjacent to interaction
• In tissue, characteristic x-ray has
very low energy, so energy deposited
locally
Summary
• Photoelectric effect involves bound
electrons
• Probability of ejection maximum if photon
has just enough energy to eject electron
from shell
• Mass attenuation coefficient varies
inversely as cube of photon energy
• Mass attenuation coefficient varies
directly as cube of atomic number
Summary
• In tissue, energy transferred is
approximately equal to energy
absorbed, i.e., very little energy
radiated
– Characteristic x-ray absorbed locally
– No scattered photons
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