Interactions with Matter Photons, Electrons and Neutrons
Ionizing Interactions
Jason Matney, MS, PhD Interactions of Ionizing Radiation
1. Photon Interactions Indirectly Ionizing
2. Charge Particle Interactions Directly Ionizing Electrons Protons Alpha Particles
3. Neutron Interactions Indirectly Ionizing PHOTON INTERACTIONS Attenuation
Attenuation – When photons are “attenuated” they are removed from the beam. This can be due to absorption or scatter . Linear Attenuation Coefficient = μ . Fraction of incident beam removed per unit path-length Units: 1/cm Measurement of Linear Attenuation Coefficient - “Narrow Beam”
No −µx Nx N(x) = N o e
Khan, x Figure 5.1
Narrow beam of mono-energetic photons directed toward absorbing slab of thickness x.
Small detector of size d placed at distance R >> d behind slab directly in beam line.
Only photons that transverse slab without interacting are detected. −µx N(x) = N o e −µx I(x) = I o e
Attenuation Equation(s) Mass Attenuation Coefficient
Linear attenuation coefficient often expressed as the ratio of µ to the density, ρ = mass attenuation coefficient
Know these 1 units! 3 2 µ cm 1 = cm = cm cm g g g ρ 3 cm Half Value Layer
HVL = Thickness of material that reduces the beam intensity to 50% of initial value.
For monoenergetic beam HVL1 = HVL2.
I −µ (HVL) 1 = ⇒ e 2 I o Take Ln of both sides
1 Ln2 − µ(HVL) = Ln HVL = Important 2 µ relationship! Half Value Layer Polychromatic Beams
After a polychromatic beam traverses the first HVL, it is Khan, Figure 5.3 hardened. low energy photons preferentially absorbed. Beam has higher effective energy after passing through first HVL. More penetrating
HVL2>HVL1 Note: Monochromatic beams
HVL1=HVL2 Tenth Value Layer - TVL
TVL = Thickness of absorber to reduce beam intensity to one tenth of original intensity Ln10 TVL = µ
TVL = (3.32)HVL (important relationship for board exams) Most shielding calculations and materials are specified in TVLs More Important Relationships
HVL TVL n n 1 1 N = N N = N o o 2 10 n = number of HVL n = number of TVL Fundamental Photon Interactions
1. Coherent Scatter
3. Compton Scatter
4. Pair Production 1. Photoelectric Effect
Photon interacts with a tightly bound orbital electron (K,L,M) and transfers ALL of its energy to the electron. The electron is ejected from the atom with Kinetic
Energy TP.E.
e- = hν − T P.E. E B e + K L M Photoelectric Effect Cross-sections i.e. probability of an interaction Probability 3 µ α z PE E3
Lower Energy P.E more likely P.E interactions are less likely at higher energy Higher Atomic Number: P.E. more likely Photoelectric effect
How is the interaction probability manipulated to achieve good contrast in diagnostic imaging? 3 µ α z PE E3 Use low Energy Radiation in imaging, so majority of interactions are photoelectric.
Radiation is preferentially absorbed in high Z material (bone) achieve good contrast between Bone and soft tissue Photoelectric Effect L-edge K and L edges Note: do not see K and L edge for H 0, occurs 2 at much lower energies A photon with E When E= B.E.L very high probability of L shell P.E interaction Spike in curve As energy increases E> B.E.L probability of L shell P.E decreases Dip in curve When E= B.E.K very high probability of K shell P.E interaction Spike in curve Khan, Figure 5.6 Photoelectric Effect Results . The fast moving photoelectron may participate in 1000s of interactions until it dissipates all of its energy. . Other Results • Characteristic X-rays • Auger Electrons Khan, Figure 5.5 Characteristic X-Ray Production Example (K-shell vacancy) 3. A photon with an energy equal 2. L shell e- fills vacancy the difference in the binding excess energy: E=Eb(K) energies is released. – Eb(L) 1. Incident photon ejects K shell electron. e K e + L M e Aujer Electrons When an electron displaces inner shell electron an outer shell electron fills the vacancy and rather than giving up the excess energy as characteristic X-Ray, the excess energy is given to a different outer shell electron, which is ejected. Aujer Electron Production Example (K-shell vacancy) 3. Excess Energy given to 2. L shell e- fills vacancy M shell e-, (auger e-), excess energy: E=Eb(K) which is ejected with – Eb(L) T=Eb(K) – Eb(L) - Eb(m) e 1. Incident photon ejects e k shell electron K e + L M e 1b. Coherent Scatter (Low Energy) Coherent scatter occurs when the interacting photon does not have enough energy to liberate the electron. Energy photon < binding energy of electron Photon energy is re-emitted by excited electron. The only change is a change of direction (scatter) of the photon, hence 'unmodified' scatter. Coherent scattering is not a major interaction process encountered in at the energies normally used in radiotherapy 2. The Compton Effect (E>100 KeV) A photon with energy, E=hv, incident on unbound stationary “FREE” electron (for purposes of easier calculation). The electron is scattered at an angle θ with energy T and the scattered photon with E=hν’ departs at angle f with energy, hv’. T = hν − hν ' hν hν '= hν 1+ (1− cosφ ) 2 mo c Khan, Figure 5.1 Compton Effect The incident photon can never transfer ALL of it’s energy to the electron, but it can transfer most of its energy. hν hν '= hν 1+ (1− cosφ ) 2 mo c The minimum energy of the scattered photon (max energy of scattered electron) occurs when ϕ=180o (backscattered photon). 1 2 0.511MeV hν '= m = = 0.255MeV 2 0 c 2 Compton Effect The direction of scattered photon depends on the incident photon energy\ Higher Energy is “forward” scattered hν hν '= hν 1+ (1− cosφ ) 2 mo c Compton Probability of an Interaction Compton effect is independent of Z Compton effect does depend on e- density Let’s consider these statements in more detail….. Compton Probability of an Interaction Because the Compton interaction involves essentially free electrons in the absorbing material, it is independent of atomic number Z. It follows that the Compton mass attenuation coefficient (σ/r) is independent of Z and depends only on the number of electrons per gram. Although the number of electrons per gram of elements decreases slowly but systemically with atomic number, most materials except hydrogen can be considered as having approximately the same number of electrons per gram. Electrons per Gram Density Electrons per Z • most materials (g/cm3) eff gram1023 (e-/g) except hydrogen have approx. the Fat 0.916 5.92 3.48 same number of electrons per gram. Muscle 1.00 7.42 3.36 Water 1.00 7.42 3.34 N A Z Air 0.001293 7.64 3.01 AW Bone 1.85 13.8 3.0 Compton Scatter Interactions If the energy of the beam is in the region where the Compton effect is the most common mode of interaction (i.e. megavoltage therapy beams) get same attenuation in any material of equal density thickness (density (ρ) times thicknes (x)). g g ρx = ×(cm) = 3 2 cm cm For example, in the case of a beam that interacts by Compton effect, the attenuation per g/cm2 for bone is nearly the same as that for soft tissue. However, 1 cm of bone will attenuate more than 1 cm of soft tissue, because bone has a higher electron density. Electron density = number of electrons per cubic centimeter = density times the number of electrons per gram. N AZ Electron Density (ρ) AW Density Electron per gram Electron density Z (g/cm3) eff 1023 (e-/g) 1023 (e/cm3) Example (ρ ) 5.55 e bone = = Fat 0.916 5.92 3.48 3.19 1.65 (ρe )muscle 3.36 per cm of absorber Muscle 1.00 7.42 3.36 3.36 • attenuation Water 1.00 7.42 3.34 3.34 produced by 1 cm of bone will Air 0.001293 7.64 3.01 0.0039 be equivalent to that produced by 1.65 cm of soft Bone 1.85 13.8 3.0 5.55 tissue. 3. Pair Production Absorption process in which photon disappears and gives rise to an electron/positron pair. e- hν >1.02 MeV e+ e- Nucleus Positron only exists for an occurs in the coulomb instant, combines with force field of the near free e- nucleus Two photons created at annihilation, each with 0.511 MeV and separated by 180o Pair Production: Threshold Energy The incident photon must have sufficient energy to “create” a positron and an and electron (need rest mass of each, 0.511 MeV), any extra energy is kinetic energy for the positron and electron (hν = 2mc2 + KE+ + KE-). Energy Threshold = 1.022MeV Pair Production Kinematics The incident photon must have sufficient Energy 2 + − hν = + + 2mo c T T Average KE of positron/electron hν −1.022MeV T = 2 Average angle of departure of positron/electron 2 Units are in radians mo c θ = to convert to degree multiply by 360o/2p T Pair Production X-Sections Probability of an interaction Because the pair production results from an interaction with the electromagnetic field of the nucleus, the probability of this process increases rapidly with atomic number. The attenuation coefficient for Khan, Figure 5.11 pair production varies with: Z2 per atom, For a given material, above the threshold energy, the probability of interaction increases as Ln(E). Probability of Interaction Three photon interactions dominate at the energies we use in radiotherapy Energy Z Increases Increases Photoelectric Effect ↓ ( ) ↑ (Z3) 1 3 ⁄𝐸𝐸 Compton Scatter ↓ ( ) No change 1 ⁄𝐸𝐸 Pair Production ↑ (E > 1.02 MeV) ↑ Z Let’s Test our knowledge… Photon Interactions Which of the following is FALSE? A photon can undergo a ______followed by a ______interaction. 1. Compton, Pair Production 2. Compton, another Compton 3. Compton, photoelectric 4. Photoelectric, Compton Photon Interactions Which of the following is FALSE? A photon can undergo a ______followed by a ______interaction. 1. Compton, Pair Production 2. Compton, another Compton 3. Compton, photoelectric 4. Photoelectric, Compton No photon remains after photoelectric interaction! KEY: So long as incident photon has sufficient energy following first interaction, can undergo another interaction Photoelectric Effect Which of the following statements regarding Photoelectric Interactions is FALSE? 1. They are mainly responsible for differential attenuation in radiographs 2. The incident photon is absorbed 3. Bound electrons are involved 4. The probability increases rapidly with increasing energy Photoelectric Effect Which of the following statements regarding Photoelectric Interactions is FALSE? 1. They are mainly responsible for differential attenuation in radiographs 2. The incident photon is absorbed 3. Bound electrons are involved 4. The probability increases rapidly with increasing energy decreasing Photoelectric Effect Two materials are irradiated by the same energy photons. Material A has an atomic number of 14 and B has an atomic number of 7. The photoelectric interaction cross-section (probability) of A is _____ times that of B? Photoelectric Effect Two materials are irradiated by the same energy photons. Material A has an atomic number of 14 and B has an atomic number of 7. The photoelectric interaction cross-section (probability) of A is _____ times that of B? 3 µ α Z 3 PE 3 A (14) E = , A = 8B B (7)3 Using above equation, set up a ratio and solve (energy cancels out). Photoelectric Effect A photon detected following a photoelectric interaction is most likely to be: 1. The scattered incident photon 2. A gamma ray 3. An annihilation photon 4. Crenkov Radiation 5. A characteristic X-Ray Photoelectric Effect A photon detected following a photoelectric interaction is most likely to be: 1. The scattered incident photon 2. A gamma ray 3. An annihilation photon 4. Crenkov Radiation 5. A characteristic X-Ray Trivia: Cherenkov Radiation Cherenkov radiation is EM The characteristic blue glow of radiationemitted when a charged nuclear reactors is due to particle (such as an electron) passes Cherenkov radiation. through an insulator at a constant speed greater than the speed of light in that medium. It is named after Russian scientist Pavel Cherenkov, the 1958 Nobel Prize winner who was the first to characterize it rigorously. http://en.wikipedia.org/wiki/Cherenkov_radiation Photoelectric, Compton Scatter & Pair Production What is the overall effect of “Photon Beam”? “Total” Attenuation Coefficient Mass attenuation coefficient for photons of a given, relevant energy in a given material composed of the individual contributions from the physical processes that can remove photons from the narrow beam. µ µ µ µ = + + ρ ρ ρ ρ PE CS PP Photon Interactions in Water as a function of energy Some important Energies: 26 keV, 150 keV, and 24 MeV Nomenclature: T = Photoelectric, s = Compton, P = Pair Production PE most likely at Low E 1:1 PE:Compton All Compton 1:1 Compton:PP PE most likely at very High E Photon Interactions (m/r) Two materials: H20 and Pb Photoelectric effect Higher for Pb than H20. Pair Production Higher for Pb than H20. PE Compton effect Similar for both materials. Compton Pair Production Khan, figure 5.12 “Total” Attenuation Coefficient Rule of Thumb: Compton scattering interaction dominates from ~25 keV to ~25 MeV in water ELECTRON INTERACTIONS Electron Interactions As electrons travel through a medium they interact with atoms through a variety of processes due to COULOMB interactions. Directly ionizing Through these collisions the electron may Lose kinetic energy (collision and radiative loss) Change direction (scatter) Electron Interactions Two Types of Electron Interactions Collisional Interactions: Radiative Interactions: Incident electron interacts Incident electron interacts with atomic electrons in the with atomic nuclei in the absorbing medium absorbing medium. e- e- Electron Interactions - Distance of electron e - e passes atom at from atom in relation to some distance, b size of the atom will b determine the type of a=radius e- interaction of atom Three Possibilities a 1. b>>a Collision Interactions 2. b=a Radiative 3. b< Two types of collision interactions: 1. Hard collisions 2. Soft Collisions Collision Interactions Soft Collision (b>>a) Soft Collision: when an e- (primary e-) passes an atom at a considerable distance, the e-’s coulomb force affects the atom as a whole. Result excite and sometimes ionize valence electrons. Energy of transition Transfer a small amount of energy (few eV) to atom of abs medium. Probability Very Likely, Most numerous type of collision interaction. Net Effect accounts for about ½ of total energy transferred to absorbing medium from collision interactions. Collision Interactions Hard Collision (b=a) Hard Collision (knock-on) b=a, incident e- (primary e-) interacts with atomic e-. Result d-Ray = atomic electron ejected with considerable kinetic energy (deposits its energy along separate track from 1o e-). Energy of transition considerable amount of energy to atom of abs medium. Probability Less Likely. Net effect accounts for about ½ of total energy transferred to absorbing medium from coulomb interactions. Radiative Interaction b< e- passes in close proximity to nucleus and interacts with coulomb force of nucleus. Two types of radiative interactions possible: 1. Elastic Interaction – No Energy change 2. Inelastic – Bremsstrahlung photons produced Elastic Radiative Interaction e- is scattered with NO change in energy No energy Transferred to absorbing Medium. Probability increases with Z2, (Z = atomic number of medium). Thin High Z foil can be used to elastically scatter electrons (e.g. scattering foil). Note: foil must be thin or too much Bremsstrahlung production. Accounts for 97 – 98% of radiative interactions Inelastic Radiative Interaction e- interacts with coulomb field of nucleus: Bremsstrahlung Radiation Energy carried away via photon emission Accounts for 2 - 3% of radiative interactions (for electrons). NEUTRON INTERACTIONS Why do we care about neutrons? Neutrons in Radiation Therapy Neutron Therapy (very few centers exist) Contamination Neutrons in X-Ray Therapy Contamination Neutrons in Proton Therapy Neutron Shielding Neutron Interactions with Tissue Neutrons are indirectly ionizing Neutrons interact by setting charged particles in motion i.e. give rise to densely ionizing (high LET) particles: recoil protons, a-particles, and heavier nuclear fragments. These particles then deposit dose in tissue. The type of interaction and the amount of dose deposited in the body is strongly dependent on neutron energy. Exponential Attenuation similar concept to photon attenuation Neutrons are removed −Σ t exponentially from a total I = Ioe collimated neutron beam stotalN by absorbing material. where N = number of absorber atoms 3 Io I per cm (atomic density) s = the microscopic cross section for the absorber, cm2 t = the absorber thickness, cm Classification of Neutrons by Energy Category Energy Range Fast > 500 keV Intermediate 10 keV – 500 keV Epithermal 0.5 eV – 10 keV Thermal < 0.5 eV The classification of neutrons by energy is somewhat dependent on the reference text. Some sources may include an epithermal category while others only include fast and slow (thermal). Fast Neutron Interactions in Tissue Higher energy neutrons result in the release of charged particles, spallation products, from nuclear disintegrations, [(n, D), (n,T), (n,alpha), etc]. These charged particles then deliver dose to tissue. Examples of (n,alpha) Oxygen Carbon Fast Neutron Interactions with Oxygen and Carbon Recoil alpha-particles A neutron interacts with a Carbon A neutron interacts with an Oxygen atom (6 protons and 6 neutrons), atom (8 protons and 8 neutrons) , resulting in three a-particles. resulting in four a-particles. (Hall, Fig 1.10) (Hall, Fig 1.10) Intermediate Neutron Interactions in Tissue Interact primarily with Hydrogen in Soft Tissue For intermediate energy neutrons, the interaction between neutrons and hydrogen nuclei is the dominant process of energy transfer in soft tissues. 3 Reasons 1.Hydrogen is the most abundant atom in tissue. 2.A proton and a neutron have similar mass, 938 MeV/cm2 versus 940 MeV/cm2. 3.Hydrogen has a large collision Hall, Figure 1.9 cross-section for neutrons. Thermal Neutron Interactions in Tissue The major component of dose from thermal neutrons is a consequence of the 14N(n,p) into 14C + 0.62 MeV photon Dominant energy transfer mechanism in thermal and epithermal region in body Another thermal neutron interaction of some consequence is the 1H(n,γ) into 2H + 2.2 MeV photon 2.2 MeV to gamma (non-local absorption) Small amount of energy to deuterium recoil (local absorption) *This 2.2 MeV photon interaction is important in shielding high energy accelerators* References The Physics of Radiation Therapy 3rd edition, Faiz Khan, Ch 5 Herman Cember. Introduction to Health Physics 3rd Ed. (1996) Eric J. Hall. Radiobiology for the Radiologist 5th Ed. (2000) Frank H. Attix. Introduction to Radiological Physics and Radiation Dosimetry. (1986)