07 chap 05 interactions of ionizing radiation

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07 chap 05 interactions of ionizing radiation

  1. 1. Chapter 5 Interactions of Ionizing Radiation scattered electron ionization and excitation knocked outincoming electron, photon secondary electron, -ray interact with the medium scattered photon with reduced energy 1
  2. 2. 5.1 Ionization scattered electron Ionization: The energy lost by the incident particle is sufficiently large to remove an electron from the atom, resulting in an ion pairincident (negative charged electron &electron positive charged atom). scattered electron Excitation: The energy lost by the incident particle is insufficient to cause ionization, but leaving the atom in an excited state. 2
  3. 3. 5.1 Ionization (cont’d)Directly ionizing radiation: charged particles (electrons,protons, -particles) produce large amount of ionization in itsenergy loss to the medium. (Example: it takes approx. 34 eVto produce 1 ion pair in air. Thus, for an electron to lose 1MeV of its energy, approx. 30,000 ion pairs are produced.)Indirectly ionizing radiation: neutral particles (photons,neutrons) themselves produce very little ion pairs. Instead,they eject directly ionizing particles from the medium.(Example: a 2-MeV photon, upon interacting with the medium,loses about 1-MeV of its energy, but producing only 1 pair ofions.) 3
  4. 4. 5.2 Photon Beam Description dNFluence ( ): The quotient of dNby da where dN is the number of daphotons that enter an imaginarysphere of cross-sectional area da: dN / daFluence rate or flux density ( ): The fluence per unit of time: d / dtEnergy Fluence ( ): The quotient of dEfl by da, where dEflis the energies of all photons that enter an imaginary sphereof cross-sectional area da: dE fl / da If all photonshave the same energy (monoenergetic), then: dE fl dN hEnergy fluence rate, energy flux density, or intensity ( ):The energy fluence per unit of time: d / dt 4
  5. 5. 5.3 Photon Beam Attenuation transmitted photon Incident fluence photon fluence detector collimator scattered photons dN Ndx dI Idx dN Ndx dI dx is the linear I x attenuation coefficient I ( x) I 0e 5
  6. 6. 5.3 Photon Beam Attenuation (mono-energetic photon beam) 100 100 1 n 0.693 transmission 2 50 HVL 50 Transmitted intensity (%) 10 10 HVL = 2cm 1 1 0 2 4 6 8 10 0 1 2 3 4 5 Absorber thickness (cm) Absorber thickness (HVL) 6
  7. 7. Example:Suppose the HVL for a 6-MV beam is 1.4 cm cerrobend,what is the transmission through a 7 cm cerrobend block?7 cm / 1.4 cm = 5, (that is, 5 HVLs)Transmission = (1/2)5 = 1/32 ~ 3.1% 7
  8. 8. 5.3 Photon Beam Attenuation (poly-energetic photon beam) 100 50 Transmitted intensity (%) 50 25 12.5 10 1st HVL 2nd HVL 3rd HVL 1 0 1 2 3 4 5 6 Absorber thickness (mm Al) 8
  9. 9. 5.4 Coefficients (attenuation coefficients)Linear attenuation coefficient: (cm-1) depends on photon energy and the nature of the material.Mass attenuation coefficient: / (cm2/g) 1Electronic attenuation coefficient: e = (cm2/electron) N0 N0 is the number of electrons per gram N 0 N A Z Aw Zatomic attenuation coefficient: a = (cm2/atom) N0 9
  10. 10. 5.4 Coefficients (energy transfer coefficients) EtrEnergy transfer coefficient: tr (cm-1) h Etr is the average energy transferred into kinetic energy ofcharged particle per interaction, hv is the original photonenergy.Mass Energy transfer coefficient: tr/ (cm2/g) 10
  11. 11. 5.4 Coefficients (energy absorption coefficients)Energy absorption coefficient: en = tr (1-g) (cm-1) ‘g’ is the fraction of the energy of secondary charged particlesthat is lost to bremsstrahlung in the material. Thus, en represents the energy absorbed locally in the material.Mass Energy absorption coefficient: en / (cm2/g)In soft tissues (low Z materials), g 0. Thus, en tr . 11
  12. 12. 5.5 Interactions of Photons with MatterIn the energy range of radiation therapy, 4 types ofinteraction of photons with matter are of interest:Coherent scattering, photoelectric effect, Comptonscattering, and pair production. coh c Incoming particle: 1 photon Outgoing particle(s): Pair coherent photoelectric compton production 1 electron + 1 electron + 1 photon 1 electron 1 photon 1 positron 12
  13. 13. 5.6 Coherent Scattering Lord Rayleigh (1842-1919)Also known as classical orRayleigh scattering.Scattered photon changedirection, but no energy loss.Only probable in high-Zmaterial and at low photonenergy.Not important for radiationtherapy. 13
  14. 14. 5.7 Photoelectric Effect discovered by Einstein in 1905 Characteristic Auger x-ray electron Albert Einstein (1879-1955)Incident photon absorbed by the K L Matom, an electron is ejected with akinetic energy equal to hv – EB.The vacancy is filled by an outer photonshell electron, thereby emitting a hvcharacteristic x-ray.The characteristic x-ray itself may photo-be absorbed, and ejects an Auger (hv – EB) electronelectron. 14
  15. 15. 5.7 Photoelectric Effect (cont’d) L-shell binding energy ~15 keV Mass photoelectric attenuation coefficient 100 3 10 K-shell binding energy ~88 keV 1E 3 Z ( , cm2/g) 1 3 3 0.1 lead Z E 0.01 water 0.01 0.1 1 10 Photon energy (MeV) 15
  16. 16. 5.8 Compton Effect Arthur Compton (1892-1962) e- (Compton electron)Incident photon interacts with a‘free’ electron. hv0The electron is ejected at angle hv’ with energy E.The photon is scattered at angle with a reduced energy hv’. 1h hv0 1 (1 cos ) hv0 / m0 c 2 hv0 ( MeV ) / 0.511 16
  17. 17. 5.8 Compton Effect (special cases)Direct hit, =0 , = 180 : h 1 2 min h 0 , Emax h 0 1 2 1 2 Grazing hit, = 90 , =0 : h min h 0 , Emax 0Low energy incident photons: hv0<<m0c2, then 0, hv’ hvHigh energy incident photons: hv0>>m0c2, then >> 1, 90 photon scatter ( = 90 ): hv’ 0.511 MeV 180 photon scatter ( = 180 ): hv’ 0.255 MeV 17
  18. 18. 5.8 Compton Effect (Dependence of Compton Effect on Energy and Atomic Number)Compton effect involvesinteraction of photon with Compton effect decreases withindividual electrons, 1 increasing photon energy. Compton coefficienttherefore its coefficientdepends on the number ofelectrons per gram. 0.1 Z NA/ASince Z/A is nearlyconstant (1/2) for low-Zmaterials, it follows that 0.01 0.1 1 10 is also nearly the same Photon energy (MeV)for all such materials. 18
  19. 19. Carl D Anderson 5.9 Pair Production (1905-1991) The photon interacts with the e- (electron) electromagnetic field of the nucleus and gives up all its energy in the process of creating a pair of electron (e-) and positron (e+). hv>1.02 MeVSince the rest mass energy of each particle is0.51 MeV, the photon energy must be greaterthan 1.02 MeV for this interaction to happen. e+ (positron)The total kinetic energy carried by the pair is(hv – 1.02) MeV. 19
  20. 20. 5.9 Pair Production (cont’d)Annihilation: The positron loses itsenergy as it traverses through the hv=0.51 MeVmedium. Near the end of its track,with almost no energy left, thepositron combines with an electron e+and the total mass of these two e-particles is converted into twophotons, each with 0.511 MeV,ejected in opposite directions. hv=0.51 MeV(This is the principle on whichPET works.) 20
  21. 21. 5.9 Pair Production (cont’d) Pair production coefficient 1 a Z2 Pair production coefficient 0.1 increases with photon energy. 0.1 1 10 100 Photon energy (MeV) 21
  22. 22. 5.10 Relative Importance of Various Types of Interations L-shell binding energy ~15 keV 10 Mass attenuation coefficient (cm2/g) K-shell binding energy ~88 keV 1 (for illustration only) lead water 0.1 0.01 0.1 1 10 Photon energy (MeV) 22
  23. 23. 5.11 Interactions of Charged ParticlesInteraction between the incident charged particle and: atomic electrons ionization and excitation; nucleus bremsstrahlung photons.Electrons suffer much greater scattering than heavy particles.Heavy charged particles may also cause nuclear reactions.Stopping power S = dE/dx, defined as energy loss per unitpath length (MeV/cm). For example, water’s stopping powerfor electrons is approx. 2 MeV/cm.Mass stopping power is S/ . (MeV cm2/g) 23
  24. 24. 5.12 Interactions of NeutronsNeutrons interacts in two processes:• collision with the nucleus - protons from hydrogen &heavy nuclei from other elements.• Nuclear disintegration.Energy transfer is most efficient if the medium has lightatomic weight. (e.g. paraffin is used for neutron shielding,water is used to slow down neutrons in nuclear reactor.)Nuclear disintegration results in emission of heavycharged particles, neutrons, -rays. 24
  25. 25. 5.13 Comparative Beam Characteristics (neutrons and Co-60)Depth dose distribution for neutron beams is similar to thatof Co-60. 25
  26. 26. 5.13 Comparative Beam Characteristics (heavy charged particles)Heavy charged particle beam is characterized by the Bragg peak,which may be modulated using filters to form a flat dose distributionat the peak region, followed by a sharp dropoff beyond the range. 26
  27. 27. 5.13 Comparative Beam Characteristics (protons and electrons)Electron beams also show constant dose region up to about half ofthe range, followed by a falloff, normally not as sharp as that ofprotons due to excessive scattering. 27

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