(1) Photoelectric effect
(2) Compton scattering

(3) Pair Production

A. What is the fluence of photons?

B. What is its symbol?

C. Give the formula for photon fluence.

A. The fluence of photons is the number of photons entering per unit cross-sectional area.

B. Photon fluence, Φ

C. Φ = dN/da,

where dN = number of photons, da = cross-sectional area

A. What is fluence rate?  What is another name for fluence rate?

B. What is its symbol?

C. Give the formula for fluence rate.

A. Fluence rate is the photon fluence per unit time, also called flux density.

B. Fluence rate, φ

C. φ = dΦ/dt

A. What is energy fluence?

B. What is its symbol?

C. Give the formula for energy fluence.

D. How can this formula be simplified for a monoenergetic beam?

A. Energy fluence is the ratio of energy entering (here, in the form of photons) per unit cross-sectional area.

B. Energy fluence, Ψ

C. Ψ = dE_fl / da,

where dE_fl = the sum of all photons that enter a cross-sectional area

D. In the case of a monoenergetic photon beam:

Ψ = dN*hν / da 

A. What is energy fluence rate?  What is another name for it?

B. What is its symbol?

C. Give the formula for energy fluence rate.

A. Energy fluence rate is the measure of energy fluence per unit time.  It is also known as energy flux density.

B. Energy fluence rate, ψ

C. ψ = Ψ/dt

dN is proportional to Ndx,

where dN is the number of photons absorbed, N is the number of incident photons, and dx is the thickness of absorbing material

dN = -μNdx,

where μ is a proportionality constant called the attenuation coefficient.

dI = -μIdx

dI/I = -μdx

Solving the differential equation,

I(x) = I₀e^-μx

Note: This formula only applies to monoenergetic beams.

A. What is the half-value layer (HVL)?

B. Give the formula relating HVL to attenuation coefficient.

A. The half-value layer, HVL, is the thickness of absorber required to attenuate the intensity of a photon beam to half its initial value.  It is analagous to half-life.

B. HVL = 0.693/μ

For a heterogeneous photon beam, place the following in order from least to greatest:

HVL₁
HVL₂
HVL₃

HVL₁ < HVL₂ < HVL₃

This is due to the hardening of the beam by filtration.

A. What is the mass attenuation coefficient?

B. What is its symbol?

C. What are its units?

D. What units are its corresponding 'thickness' expressed in?

E. Why is it used?

A. The mass attenuation coefficient relates the absorption of a photon beam to the thickness of material independent of its density.

B. Mass attenuation coefficient, μ/ρ

C. μ/ρ = cm^-1 / (g/^cm3) = cm²/g

D. ρx is given in g/cm²

E. The mass attenuation coefficient is more fundamental than the linear attenuation coefficient because it depends not on the density of the absorbing material but only on its atomic composition.

A. One coefficient used in describing photon beam attenuation is the electronic attenuation coefficient.  What is its symbol? 

B. What are its units?

C. What units are its corresponding 'thickness' expressed in?

A. Electronic attenuation coefficient, _eμ 

B. _eμ = μ/ρ * 1/N₀ cm²/electron,

where N₀ is the number of electrons per gram:

N₀ = NA * Z / A_W

C. electrons / cm²

A. One coefficient used in describing photon beam attenuation is the atomic attenuation coefficient.  What is its symbol? 

B. What are its units?

C. What units are its corresponding 'thickness' expressed in?

A. Atomic attenuation coefficient, _aμ 

B. _aμ = μ/ρ * Z/N₀ = μ/ρ * A_W/N_A cm²/atom,

where N₀ is the number of electrons per gram:

N₀ = NA * Z / A_W

C. atoms / cm²

A. What is the energy transfer coefficient?

B. What is its symbol?

C. Give the formula that describes energy transfer coefficient.

A. The energy transfer coefficient is the fraction of photon energy transferred into kinetic energy of charged particles per unit thickness of absorber.

B. Energy transfer coefficient, μ_tr

C. μ_tr = (E_tr/hν)μ,

where E_tr is the average energy transferred per interaction

A. What is the energy absorption coefficient?

B. What is its symbol?

C. Give the formula that describes energy absorption coefficient.

A. The energy absorption coefficient is the fraction of photon energy transferred into kinetic energy of locally-interacting (i.e., ionization and excitation) charged particles per unit thickness of absorber.  Energy absorption coefficient ignores interactions in which produced charged particles suffer bremsstrahlung interactions and do not deposit their energy locally.

B. Energy absorption coefficient, μ_en

C. μ_en = μ_tr(1-g),

where g is the fraction of energy of secondary particles lost to bremsstrahlung interactions

Coherent scattering: σ_coh

Compton scattering: σ_c

Photoelectric effect: τ

Pair production: Π

A. Describe the process of coherent scattering.

B. What are two other names for it?

C. Describe the probability of coherent scattering as it relates to photon beam energy and atomic number of the absorbing material.

A. In coherent scattering, a passing electromagnetic wave is absorbed by an electron which then begins to oscillate (is excited).  The oscillating electron re-emits the energy as an electromagnetic wave of the same frequency, but at a slightly different angle.  No energy is absorbed in the medium.

B.

(1) Rayleigh scattering
(2) Classical scattering

C. Coherent scattering increases with Z, decreases with energy.

A. Describe the process of the photoelectric effect.

B. Describe the kinetic energy of the ejected electron.

C. What two types of emissions can occur following a photoelectric interaction?

D. Describe the probability of photoelectric effect as it relates to photon beam energy and atomic number of the absorbing material.

A. In a photoelectric interaction, the entire energy of an incident photon is absorbed by an atom, ejecting an orbital electron.

B. K.E. = hv - E_B

C.
(1) Characteristic x-rays
(2) Auger electrons, which are monoenergetic electrons produced by the internal absorption of characteristic x-rays

D. Photoelectric effect is proportional to Z³/E³

As the energy of an incident photon beam increases past the K-shell binding energy of the absorbing material, the photoelectric effect decreases drastically and the Compton effect becomes more important.  Its probability, however, also decreases with photon energy.

Because the electrons are essentially "free" (relatively low binding energy compared to incident photon energy), the probability of Compton scattering is independent of Z.

Compton scattering is proportional to electron density, ρ_e, which is a measure of the number of electrons per volume.

To find electron density, simply multiply density by electrons per gram.

g/cm³ * electrons/g = electrons/cm³

A. Describe the process of pair production.

B. What is the threshold energy of the incident photon beam required for pair production to occur.  Why?

C. What is the reverse of this process called?

A. In pair production, an incident photon interacts with the electromagnetic field of an atomic nucleus, giving up all of its energy in the creation of an electron and positron.  The electron and positron tend to be emitted in the forward direction. 

B. The threshold energy for pair production to occur is ~1.022 MeV.  This is because the rest mass energy of the electron (and positron) is 0.511 MeV.

C. The reverse of pair production is annihilation radiation, where a positron and electron combine to form two photons, each with energy = 0.511 MeV, travelling in opposite directions.