X-ray Interactions Flashcards
What are the processes that happen to x-ray when it interacts with an object?
Absorption (caused by attenuation)
Scatter (caused my attenuation)
Transmission
What are the possible interactions of x-rays?
Compton scattering
Coherent scattering
Photoelectric absorption
Pair production
What happens in Compton scatter process?
Incident x-ray photon scattered by a loosely bound electron (free electron further from nucleus)
Energy is lost by photon and given to recoil electron
(frequency ∝ 1 / λ)
What type of scattering is Compton scattering?
Inelastic: energy of the scattering x-ray (hv) < energy of incident x-ray
Incoherent-scattering centres (electrons) scatter independently
What is α?
Scaling factor: the ratio between energy of photon and rest energy of electron (m_o c^2)
α = h v m_o c^2
What is the wavelength shift?
λ’ - λ = h/m_o c (1 - cosφ)
What is the scattered photon energy?
hv’ = m_o c^2 / (1 - cosφ) + 1/α
What is the energy equation?
E^2 = p^2c^2 + m_o^2c^4
What is the α of x-ray photon of 511 keV?
1
What happens as angle of scatter increases?
Forward scattering: not much energy lost
Backwards scattering: φ = 180, θ = 0 (max energy transfer to recoil electron and energy deposit in tissue)
as φ increases: more energy lost
What is Compton shift Δλ independent of?
Energy
φ = 90 degrees, Δλ = h/mc
What is attenuation and the attenuation coefficient?
The removal of photons from the primary beam (caused by absorption and scatter)
attenuation coefficient: probability of a process
μ_compton ∝ ρ
μ = μ_photoelectric + μ_compton + μ_coherent + μ_pairproduction
What is Beer’s law?
N = N_o e^ - μt
What does a high μ mean?
Greater probability for interaction (property of material)
What is the kinetic energy of the recoil electrons?
T_max = hv / 1 + (1/2α)
recoil electrons ionise the material until energy is lost
What is coherent scatter?
Elastic scattering from bound atomic electrons
Incident λ > electron spacing: interacts with entire atom so all electrons take up recoil (unlike Compton scatter)
Electron starts to oscillate with incoming wave and start to accelerating causes them to emit radiation
If the photon energy is high, how would it interact with the atom?
It is more likely to interact with single e- (as photon energy is greater than binding energy)
What is coherent scatter confined to?
Small angles
have small contribution to the total cross section especially at high x-ray energy
When do coherent or compton scatter occur?
All interactions are stochastic processes (occurs with probability that varies with energy)
Compton takes over after a certain energy which depends on material
What is the photoelectric effect?
Photons incident on bound electrons (inner shell) can be totally absorbed by atom as a whole takes up recoil momentum
The excited electron is then emitted with energy
T = hv - Be
The atom becomes excited
Be = binding energy of electron
When does photoelectric effect dominate?
At low energies («_space;0.1 MeV)
What is the energy of the photon absorbed in photoelectric effect close to?
It is close to the binding energy of e- in K shell
What happens when the ionised atom de-excites?
Characteristic x-ray:
Electron drops down from higher shell
Energy of x-ray depends on relative shell energies
More likely at higher Z
Auger electron:
Energy given to outer shell electron - emitted
More likely for low atomic number materials
(cascaded mechanisms)
What is the relationship between photoelectric effect and E?
proportional to 1/E^3
so it constantly decreases (as well as absorption) but there are exceptions at attenuation edges
What are absorption edges?
Discontinuities in energy spectrum at the positions of the binding energies of specific electron shells e.g. photon needs to be above binding energy of k shell to overcome K edge and kicks out K shell electrons
Where are the absorption edges in low z materials?
As binding energies are not in x-ray energy regime there aren’t significant edges
What is the probability of photoelectric absorption?
μ ∝ Z^3 ρ / E^3
(only exception to this is at absorption edges)
When does pair production occur?
At photon energies > 1.02 MeV leads to an interaction with the electrostatic field of the nucleus = positron and electron pair
When are two gamma rays produced?
When positron annihilates an electron giving two 0.511 MeV gamma rays
What does Compton scatter depend on?
On density of material alone
