Chapter 3 - Photon Interactions with Matter (Part 2) PDF

Part 2: Types of X-ray Interaction (Chap. 3) Introduction to Types of X-ray Interaction with Matter X-rays are created by the interaction of energetic e-(s) with matter at the atomic level Photons (x-ray & γ-ray) end their lives by transferring their E to e-(s) contained in matter ✓ Low E x...

Part 2: Types of X-ray Interaction (Chap. 3) Introduction to Types of X-ray Interaction with Matter X-rays are created by the interaction of energetic e-(s) with matter at the atomic level Photons (x-ray & γ-ray) end their lives by transferring their E to e-(s) contained in matter ✓ Low E x-rays interact with whole atoms ✓ Moderate E x-rays interact with e-(s) ✓ High E x-rays interact with the nuclei As an x-ray beam passes through an object, 3 possible fates await each photon: It can penetrate the section of matter without interacting (transmitted) It can interact with the matter & be completely absorbed by depositing its E It can interact & be scattered @ deflected from its original direction & deposit part of its E For your info about SCATTERING: refers to the change in the direction of photons and it contributes to both attenuation and absorption At high photon E, scatter is in the forward direction & contributes to absorbed dose At low photon E, scatter occurs in all directions & may contribute to loss of image quality by increasing the overall density of the film Scattered x-ray photons contribute to exposure of staff, patient and public Info about Absorption: refers to the taking up of energy from the beam by the irradiated material It is the absorbed energy which is important in producing the radiobiological effects Info about Transmission: There are 5 interactions of x-ray with matter: Descriptions for each interaction 1. Coherent Scattering (Classic / Rayleigh Scattering) = elastic scattering of photon which usually occurs when a very low E photon interacts with an orbital e- → unable to eject this e- but being absorbed by it There are 3 main steps in coherent scatter: a) An incoming x ray photon with less than 10 keV (so a very low E x-ray photon) interacts with an outer orbital e- b) The incoming x ray photon transfers ALL of its E to the outer orbital e-. The incoming x-ray photon no longer exists after transferring its E. This makes the outer orbital e- excited c) The outer orbital e- gives off the excess E (in the form of an x-ray photon) in a different direction than the original incoming x-ray photon. The new x-ray photon has the same E as the incoming x-ray photon λi = λf Only probable in high-Z material & at low diagnostic x-rays, as used in mammography (which operates at E = 15 to 30 keV) Initial photon is scattered in a different direction without a change in its E, λ @ f 2. Photoelectric Effect = most likely to occur when E of incident photon exceeds but is relatively close to the B.E of the e- it will strikes usually occurs with e-(s) that are firmly bound to the atom (relatively high B.E) The inc. photon transfers ALL of its E to an e- There are 3 main steps in PE: a) A high E incoming x-ray photon knocks out an orbital e- (diagram below show K shell e- being knocked out). E of the x-ray photon must be ≥ than B.E of the orbital e- b) The e- knocked out of its orbit is called = photoelectron. It loses its E as heat in the object being imaged K.E of photoe- (T) = hv – EB where, hv = incident photon E EB = B.E of the orbital e- Fraction of energy transferred to all electrons 𝑇 ℎ𝑣 − 𝐸𝐵 = ℎ𝑣 ℎ𝑣 c) The atom now has an empty orbital e-- & is in excitation state. To de-excite, e- (s) from other orbitals will jump the shells (i.e. L shell to K shell @ M shell to K shell, etc.). This produces characteristic radiation within the object being imaged. This cascade of e-(s) continues until the atom has filled all its empty shells  Probability PE to occur: 𝑍3 𝑃𝐸 ∝ 3 𝐸 Example: A K-shell e- with a B.E = 68.5 keV. PE interaction is more likely to occur when the incident photon is 70 keV than if it were 120 keV. Energy range: 0.01 MeV – 1.0 MeV PE interactions result in increased patient dose, contributing to biological damage De-excitation mechanisms: Some info. during the de-excitation of the atom: What is characteristic x-ray? If e- in the K shell is ejected from atom by inc. photon, an orbital e- vacancy is created e- from L or M shell will “jumps in” to fill the vacancy. In the process, it emits a characteristic x-ray and in turn, produces a vacancy in the L or M shell When a vacancy is created in the L shell by either the inc. photon or by the previous event, e- from the M or N shell will “jumps in” to occupy the vacancy. In this process, it emits a characteristic x-ray and in turn, produces a vacancy in the M or N shell The characteristic X-rays are labeled as K, L, M or N to denote the shells they originated from  What is Auger electron? Sometimes, as the atom returns to its stable condition, instead of emitting a characteristic x-ray it transfers the excitation E directly to one of the outer e-, causing it to be ejected from the atom (Auger e-) Auger e-(s) are more probable in low Z elements than in high Z elements 3. Compton Scattering (Compton Effect ,CE) **also known as incoherent scattering = inelastic scattering of photon which incident x-ray loses some of its E to the scattering e- E of the incident photon must be large compared to the B.E of the electron it will strikes (B.E is comparatively small and can be ignored) There are 3 main steps in CE: a) An incoming x-ray photon interacts with an outer orbital e- (free e-) b) The incoming x-ray photon knocks the orbital e- out of it orbit (becoming a recoil e-) at angle ϕ. The recoil e- loses E as heat or creates bremsstrahlung radiation within the object being imaged c) The x-ray photon is deflected in a different direction at angle θ with less E (determined by subtracting the binding energy of the orbital electron). The higher the E of the incoming x-ray photon, the smaller angle of deflection (meaning the x-ray photon will continue closer to its original path) higher E x-ray photon stays closer to its original path Laws of conservation of E & momentum place limits on both scattering angle and E transfer Energy of scattered photon Compton shift λf – λi = Energy of recoil e- Maximal E transfer to recoil e- occurs with a 180o photon backscatter (θ = 180o) 2ℎ𝑣 𝑇𝑚𝑎𝑥 = 𝑚𝑜 𝑐 2 2+ ℎ𝑣 Where, v = frequency of incident photon v' = frequency of scattered photon h = Planck’s constant and its numerical value is 6.625 × 10-34 Js mo = mass of electron, its numerical value is 9.11 × 10 -31 kg c = speed of light and its value is 3 × 108 m/s moc2 = e- rest energy = 0.511 MeV θ = scattering angle of incident rays ϕ = angle of the recoil e- λi = initial wavelength of the incident rays λf = final wavelength of incident rays after scattering Δλ = Compton shift T = E of recoil e- Example: A 3 MeV photon is scattered by a Compton interaction. What is the maximum energy transferred to the recoil electron? Answer: Maximum energy transferred to recoil e- is when the photon is backscattered at θ = 180o 2ℎ𝑣 𝑇𝑚𝑎𝑥 = 𝑚 𝑐2 2+ 𝑜 ℎ𝑣 So, 2(3𝑀𝑒𝑉) 𝑇𝑚𝑎𝑥 = 0.511𝑀𝑒𝑉 2+ 3𝑀𝑒𝑉 = 2.76 MeV Energy transferred to recoil e- ≈ 92 % The rest is the energy of scattered photon Since scattered photon has less E, so it has a longer λ & less penetrating than the inc. photon Although photon may be scattered at any θ with respect to its original direction, the recoil e- is confined to an ϕ, which is ≤ 90o w.r.t the motion of the incident photon Both θ & ϕ decrease with increasing E of the incident photon As E of inc. photon increases, scattered photons & e-(s) are scattered more toward forward direction → This means that higher photon E allow greater absorption (better dose distribution) of the dose in the body with less scattering of E  By products of CE: Recoiled / Scattered electron Scattered photon with lower energy Possesses kinetic energy and is Continues on its way, but in a different capable of ionizing atoms direction Finally recombines with an atom It can interact with other atoms, either that has an electron deficiency by photoelectric or Compton scattering - It may emerge from the patient as scatter - Contributes to radiographer dose and film fog Almost independence on photon E 4. Pair Production = can only occur if E of incident photon is at least 1.022 MeV (rest mass E of e- = 0.511 MeV, so need ≥ 2 rest mass E of e- for PP to happen) Occurs with the atomic nucleus & produced e-–positron pair (particle – antiparticle) → process of conservation of momentum (PP cannot occur in empty space) The inc. photon transfers ALL of its E to the atomic nucleus it strikes There are 4 main steps in PP: a) A high E (≥ 1.022 MeV) incoming x-ray photon being absorbed by heavy atomic nucleus it interacts b) This attenuation results in the production of e-–positron pair moving in opposite direction (if E of inc. photon is > 1.022 MeV, the excess E is shared between the pair as K.E) c) The e- will eventually loss all its E to medium d) However the fate of the positron is not so straight forward. As it comes to a rest, it combines with a neighbouring e- & 2 particles neutralize each other in a phenomenon known as annihilation radiation. Here, these 2 particles are converted back into 2 photons, each of E = 0.511 MeV travelling at 180o to each other. These photons are then absorbed or scattered within the medium (annihilation also need to occur inside a solid, which provides e- which is needed) PP can be represented by an equation which represents the conservation of total energy (or mass-energy): hv = 2moc2 + T- + T+ where, hv = E of incident photon moc2 = 0.511 MeV = rest energy of an e-, which is equal to that of the positron, so the factor of 2 represents the fact that two particles of identical rest mass are created T & T = represent K.E of e- & positron, immediately after their creation - + ***If the photon E were exactly 2moc2 = 1.02 MeV → the two particles would be created at rest (with zero K.E) & this would be an example of the complete conversion of energy into mass *** e- & positron do not necessarily receive equal E, but their average (𝑇̅): ℎ𝑣 − 1.022𝑚𝑒𝑉 𝑇̅ = 2 For annihilation: 2moc2 + T- + T+ = 2 hv Where, moc2 = 0.511 MeV rest energy of both particles, T- & T+ = K.E of e- & positron just before the collision 2 hv = two photons created, each having a the same frequency f & E Probability for PP to occur: 𝑃𝑃 ∝ 𝐸𝑍 2 2 cases for PP: 1) PP in NUCLEAR COULOMB FORCE FIELD → produce e- - positron 2) PP in e- FIELD → production of TRIPLET (e- - positron & host e-) → hv = 1.022 meV + T+ + T1- + T2- Dependence of PE, CE & PP on Z of target material & E of the X-rays: Which Z?? 5. Photonuclear Interactions Photon with E exceeding few MeV excites nucleus, which emits proton @ neutron Contributes to kerma & dose Relative amount less than 5% of pair production Usually not included in dosimetry consideration Important for shielding design (neutrons) Attenuation Coefficient = parameter indication fraction of radiation attenuated by a given absorber thickness 1. Linear Attenuation Coefficient (μ) = a constant that describes the unique properties of a material that attenuates a photon beam Unit: cm-1 𝑁 = 𝑁𝑜 𝑒 −𝜇𝑥 𝜇 2. Mass Attenuation Coefficient ( ) 𝜌 obtained by dividing μ by ρ of the material It removes the density of the material from determining attenuation, instead basing attenuation off the atomic properties of the substance can be used instead of μ: 𝜇 −( )𝑥𝜌 𝑁 = 𝑁𝑜 𝑒 𝜌 3. Energy Transfer Coefficient (μtr) It is useful to consider the amount of E that is transferred by attenuated photons to e-(s) within the material Most photons will interact through incoherent scattering, losing some E & continuing through the material e-(s) are responsible for most of the dose deposition within the tissue is found by multiplying μ by the average E transferred through photon interactions (𝐸̅𝑡𝑟 ) & dividing this value by the photon E (hν) 𝐸̅𝑡𝑟 𝜇𝑡𝑟 = 𝜇 ℎ𝑣 4. Energy Absorption Coefficient (μen) e-(s) lose their E in a material through collisional @ radiative processes Collisions (excitation/ionization) occur when an e- interacts with orbital e-(s), & usually deposit E locally Radiative events (bremsstrahlung) occur when e-(s) interact with the nucleus of an atom, generating an x-ray These x-rays usually travel outside of the volume of interest  The average amount of E lost through bremss. in a material is referred to as g (average fraction of 2o e- E that is lost in radiative int. → bremss. @ in-filght annihilation), giving the formula for μen: 𝜇𝑒𝑛 = 𝜇𝑡𝑟 (1 − 𝑔) In tissues where Z is low @ generated e-(s) have low E → g is very low It becomes more important in materials such as lead which may give rise to a significant amount of bremsstrahlung Calculation of μ & μ/ρ o The attenuation of photons within a material is due to the photon interactions o Each interaction is dependent on the physical structure of the material & E of the photon o For a particular material, the total attenuation (linear attenuation coefficient) is due to the attenuation from each of these processes: Coherent scattering (Rayleigh) - σcoh Photoelectric Effect - τ Incoherent scattering (Compton) - σinc Pair and Triplet Production - π Photodisintegration Giving: 𝜇 = 𝜎𝑐𝑜ℎ + 𝜏 + 𝜎𝑖𝑛𝑐 + 𝜋 o Given that photon interactions are dependent on the atomic properties of a material rather than its density, the attenuation coefficients for individual processes are often given as μ/ρ: 𝜇 𝜎𝑐𝑜ℎ 𝜏 𝜎𝑖𝑛𝑐 𝜋 = + + + 𝜌 𝜌 𝜌 𝜌 𝜌 Where, 𝜎 𝑁𝐴 𝑍 CE: = ∙𝑒 𝜎 𝜌 𝐴 𝜏 𝑍 3 PE: = (ℎ𝑣) 𝜌 𝜅 𝜅 𝜅 PP: (𝜌) =( ) +( ) (combination of 2 cases) 𝑝𝑎𝑖𝑟 𝜌 𝑛𝑢𝑐𝑙𝑒𝑎𝑟 𝜌 𝑒− Explanation: Attenuation from Coherent Scattering Coherent scattering is important for low kilovoltage photons, and increases with increasing Z Attenuation from Photoelectric effect The mass photoelectric attenuation coefficient is proportional to Z3 & inversely proportional to E3 beam E Attenuation from Incoherent Scattering The mass incoherent scattering attenuation coefficient is similar for most values of Z, but decreases slowly with increasing beam E. It is most dependent on the e- density Attenuation from Pair Production Pair production only occurs with higher beam energies (over 1.02 MeV). The mass attenuation coefficient for pair production is linearly related to Z. Increasing beam E also increases the attenuation from pair production in a logarithmic fashion. Coefficient for compounds & mixtures 1) Linear attenuation coeff. 𝜇𝑚𝑖𝑥 = 𝜇𝐴 𝑓𝐴 + 𝜇𝐵 𝑓𝐵 + ⋯ 2) Mass attenuation coeff. 𝜇 𝜇 𝜇 ( ) = ( ) 𝑓𝐴 + ( ) 𝑓𝐵 + ⋯ 𝜌 𝑚𝑖𝑥 𝜌 𝐴 𝜌 𝐵 3) Energy-transfer coeff. 𝜇𝑡𝑟 = (𝜇𝑡𝑟 )𝐴 𝑓𝐴 + (𝜇𝑡𝑟 )𝐵 𝑓𝐵 + ⋯ 4) Energy-absorption coeff. (𝜇𝑒𝑛 )𝑚𝑖𝑥 = (𝜇𝑒𝑛 )𝐴 𝑓𝐴 + (𝜇𝑒𝑛 )𝐵 𝑓𝐵 + ⋯ = (𝜇𝑡𝑟 )𝐴 (1 − 𝑔𝐴 )𝑓𝐴 + (𝜇𝑡𝑟 )𝐵 (1 − 𝑔𝐵 )𝑓𝐵 + ⋯ Where, fA, fB,…. = weight fraction of the separate elements (A, B, …) gA, gB = radiation yield fraction for elements (A, B, …) = can be obtained from tables of μtr/ρ & μen/ρ