X-ray Interactions

Question 1

What are the processes that happen to x-ray when it interacts with an object?

Answer 1

Absorption (caused by attenuation)
Scatter (caused my attenuation)
Transmission

Question 2

What are the possible interactions of x-rays?

Answer 2

Compton scattering
Coherent scattering
Photoelectric absorption
Pair production

Question 3

What happens in Compton scatter process?

Answer 3

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)

Question 4

What type of scattering is Compton scattering?

Answer 4

Inelastic: energy of the scattering x-ray (hv) < energy of incident x-ray

Incoherent-scattering centres (electrons) scatter independently

Question 5

What is α?

Answer 5

Scaling factor: the ratio between energy of photon and rest energy of electron (m_o c^2)

α = h v m_o c^2

Question 6

What is the wavelength shift?

Answer 6

λ’ - λ = h/m_o c (1 - cosφ)

Question 7

What is the scattered photon energy?

Answer 7

hv’ = m_o c^2 / (1 - cosφ) + 1/α

Question 8

What is the energy equation?

Answer 8

E^2 = p^2c^2 + m_o^2c^4

Question 9

What is the α of x-ray photon of 511 keV?

Answer 9

1

Question 10

What happens as angle of scatter increases?

Answer 10

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

Question 11

What is Compton shift Δλ independent of?

Answer 11

Energy

φ = 90 degrees, Δλ = h/mc

Question 12

What is attenuation and the attenuation coefficient?

Answer 12

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

Question 13

What is Beer’s law?

Answer 13

N = N_o e^ - μt

Question 14

What does a high μ mean?

Answer 14

Greater probability for interaction (property of material)

Question 15

What is the kinetic energy of the recoil electrons?

Answer 15

T_max = hv / 1 + (1/2α)

recoil electrons ionise the material until energy is lost

Question 16

What is coherent scatter?

Answer 16

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

Question 17

If the photon energy is high, how would it interact with the atom?

Answer 17

It is more likely to interact with single e- (as photon energy is greater than binding energy)

Question 18

What is coherent scatter confined to?

Answer 18

Small angles

have small contribution to the total cross section especially at high x-ray energy

Question 19

When do coherent or compton scatter occur?

Answer 19

All interactions are stochastic processes (occurs with probability that varies with energy)

Compton takes over after a certain energy which depends on material

Question 20

What is the photoelectric effect?

Answer 20

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

Question 21

When does photoelectric effect dominate?

Answer 21

At low energies (&laquo_space;0.1 MeV)

Question 22

What is the energy of the photon absorbed in photoelectric effect close to?

Answer 22

It is close to the binding energy of e- in K shell

Question 23

What happens when the ionised atom de-excites?

Answer 23

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)

Question 24

What is the relationship between photoelectric effect and E?

Answer 24

proportional to 1/E^3

so it constantly decreases (as well as absorption) but there are exceptions at attenuation edges

Question 25

What are absorption edges?

Answer 25

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

Question 26

Where are the absorption edges in low z materials?

Answer 26

As binding energies are not in x-ray energy regime there aren't significant edges

Question 27

What is the probability of photoelectric absorption?

Answer 27

μ ∝ Z^3 ρ / E^3 (only exception to this is at absorption edges)

Question 28

When does pair production occur?

Answer 28

At photon energies > 1.02 MeV leads to an interaction with the electrostatic field of the nucleus = positron and electron pair

Question 29

When are two gamma rays produced?

Answer 29

When positron annihilates an electron giving two 0.511 MeV gamma rays

Question 30

What does Compton scatter depend on?

Answer 30

On density of material alone