Interaction of charged particles and photons with matter

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1 Interaction of charged particles and photons with matter Robert Miyaoka, Ph.D. Old Fisheries Center, Room 200 Passage of radiation through matter depends on Type of radiation charged particles (e.g., electrons, protons, etc.) high energy photons or x-rays Energy of radiation (e.g., kev or MeV) Nature of matter being traversed (atomic number and density) Types of charged particle radiation relevant to Nuclear Medicine Passage of charged particles through matter Particle Symbol Mass Charge Electron e-, β kev/c 2-1 Gradual loss of particle s energy Energy transferred to nearby atoms and molecules Positron e+, β+ 511 kev/c 2 +1 Alpha α 3700 MeV/c 2 +2 Charged particle interaction mechanisms Ionization Interaction between charged particle and orbital electron Energy transferred from passing particle to electron Ionization Excitation Bremsstrahlung If E > ionization potential, electron is freed ionization potential for gases are in the range of ev. Ejected electrons energetic enough to cause secondary ionizations are called δ rays 1

2 Excitation Energy is transferred to an orbital electron, but not enough to free it. Electron is left in an excited state and energy is dissipated in molecular vibrations, atomic emission of infrared, visible or uv radiation, etc. Bremsstrahlung Some particles will interact with the nucleus. The particle will be deflected by the strong electrical forces exerted on it by the nucleus. The particle is rapidly decelerated and loses energy in the collision. The energy appears as a photon of electromagnetic radiation. Collisonal versus radiation losses Ionization and excitation are collisonal losses. Bremsstrahlung production is called a radiation loss. Radiation losses increase with increasing particle energy and increasing atomic number of the absorbing material. Even though high-energy electrons (β ) in nuclear medicine dissipate most of their energy in collisional losses. Bremsstrahlung production can be important when shielding large quantities of energetic β- emitters (e.g., tens of mci of 32 P). Energy deposition along a chargedparticle track Linear stopping power (S l ): ΔE / Δx total expressed in MeV/cm (total energy loss rate) Linear energy transfer (L): only includes energy lost "locally", does not include radiation losses. Specific ionization (SI): total number of ion pairs produced (both primary and secondary ionization events) Energy deposition along a chargedparticle track (cont.) Bragg Peak Average energy expended per ionization (W): W = L / SI Ionization potential (I): average energy required to cause an ionization Note: W = I Difference between W and I is the energy dissipated in nonionizing excitation events. Specific ionization increases as particle slows down. This gives rise to the Bragg ionization peak. 2

3 Tracks Charged particle ranges (α particles) Loses energy in a more or less continuous slowing down process as it travels through matter. The distance it travels (range) depend only upon its initial energy and its average energy loss rate in the medium. The range for an α particle emitted in tissue is on the order of µm s. Charged particle ranges (β particles) Electrons or β particles have ranges that are quite variable from one electron to the next, even for electrons of exactly the same energy in a specific absorbing material. Charged particle ranges (β particles) This is because of the different types of scattering events the β particle can encounter (i.e., scattering events, bremsstrahlung-producing collisions, etc.). The β range is often given as the maximum distance the most energetic β can travel in the medium. The range for β particles emitted in tissue is on the order of mm s. II. Interactions of high energy photons with matter Interaction mechanisms Photoelectric effect Compton scattering (photoelectric effect) An atomic absorption process in which an atom absorbs all the energy of an incident photon. PE" Z 3 E 3 # Z is atomic number of the material, E is energy of the incident photon, and ρ is the density of the material. Pair production Coherent (Rayleigh) scattering 3

4 (photoelectric effect) Photons are preferentially absorbed by more tightly bound electrons. Collision between a photon and a loosely bound outer shell orbital electron. Interaction looks like a collision between the photon and a free electron. The probability of Compton scatter is a slowly varying function of energy. It is proportional to the density of the material (ρ) but independent of Z. The scattering angle is determined by the amount of energy transferred in the collision. CS " # ρ is the density of the material. As energy is increased scatter is forward peaked. 4

5 Klein-Nishina How likely is scattering to occur at different angles? At low energies scattering happens at all angles with - equal probabilities. At high energies, forward angle scatter is favored. Polar plot of relative frequency of scattering angles From: Bruno, UC Berkeley masters thesis (pair production) Pair production occurs when a photon interacts with the electric field of a charged particle. Usually the interaction is with an atomic nucleus but occasionally it is with an electron. Photon energy is converted into an electron-positron pair and kinetic energy. Initial photon must have an energy of greater than MeV. Positron will eventually interact with a free electron and produce a pair of 511 kev annihilation photons. (Coherent or Rayleigh scatter) Scattering interactions that occur between a photon and an atom as a whole. Because of the great mass of an atom very little recoil energy is absorbed by the atom. The photon is therefore deflected with essentially no loss of energy. Coherent scattering is only important at energies <50 kev. Attenuation When a photon passes through a thickness of absorber material, the probability that it will experience an interaction (i.e., photoelectric, Compton scatter, or pair production) depends on the energy of the photon and on the composition and thickness of the absorber. Attenuation Under conditions of narrow beam geometry the transmission of a monoenergetic photon beam through an absorber is described by an exponential equation: I(x) =I(0)e "µx, where I(0) is the initial beam intensity, I(x) is the beam intensity transmitted through a thickness x of absorber, and µ is the total linear attenuation coefficient of the absorber at the photon energy of interest. The linear attenuation coefficient is expressed in units of cm -1. 5

6 Attenuation coefficients Relative magnitudes There are three basic components to the linear attenuation coefficient: µ τ due to the photoelectric effect; µ σ due to Compton scattering; and µ κ due to pair production. The exponential equation can also be written as: or I(x ) = I(0)e "(µ # +µ $ +µ % )x I(x ) = I(0)e "µ # x e "µ $ x e "µ % x NaI(Tl) and BGO linear attenuation coefficients Narrow beam vs broad beam attenuation Without collimation, scattered photons cause artificially high counts to be measured, resulting in smaller measured values for the attenuation coefficients. From: Bicron (Harshaw) Scintillator catalog Attenuation Attenuation Coefficient Under conditions of narrow beam geometry the transmission of a monoenergetic photon beam through an absorber is described by an exponential equation: I(x) = I(0) e -µx, where I(0) is the initial beam intensity, I(x) is the beam intensity transmitted through a thickness x of absorber, and µ is the linear attenuation coefficient of the absorber at the photon energy of interest. Linear attenuation coefficient µ l depends on photon energy depends on material composition depends on material density dimensions are 1/length (e.g., 1/cm, cm -1 ) Mass attenuation coefficient µ m µ m = µ l /ρ (ρ = density of material yielding µ l ) does not depend on material density dimensions are length 2 /mass (e.g., cm 2 /g) 6

7 Half and tenth value thicknesses Half-value thickness is the amount of material needed to attenuate a photon flux by 1/2 (attenuation factor = 0.5). Half and tenth value thicknesses (values for lead and water) Material (energy) µ (cm -1 ) HVT (cm) TVT (cm) 0.5 = I/I 0 = e -µhvt µhvt = -ln(0.5) HVT = 0.693/µ Tenth value thickness is given by 0.1 = I/I 0 = e -µtvt TVT = 2.30/µ Lead (140 kev) Lead (511 kev) Water (140 kev) Water (511 kev) Example Calculation What thickness of lead is required to attenuate 99% of 511 kev photons? Example Calculation What fraction of 140 kev photons will escape unscattered from the middle of a 30 cm cylinder? 99% attenuated = 1% surviving Using the exponential attenuation formula 0.01 = I/I 0 = e -µd = e -(1.7/cm)d ln(0.01) = -(0.17/cm)d d = -ln(0.01)/(1.7/cm) = 2.7 cm Alternatively, if the TVT is known (1.35 cm), doubling the TVT results in two consecutive layers which each transmit 1/10 of photons, or a total transmission of 1/100 or 1%. 2 * 1.35 cm = 2.7 cm. The photons must travel through 15 cm of water. I/I 0 = e -µd = e -(0.15/cm)(15cm) = = 10.5% Buildup Factors (broad beam versus narrow beam values) Buildup Factors (broad beam versus narrow beam values) The transmission factor for 511-keV photons in 1 cm of lead was found to be 18% for narrow-beam conditions. Estimate the actual transmission for broad-beam conditions. HVT for lead is 0.4 cm. Therefore, µ l = 0.693/0.4 cm = 1.73 cm-1. For 1 cm µ l x = Using values from buildup factor table for lead and linear interpolation: B = * ( ) B = 1.37 T = Be -µ l x T = 1.37 * 18% = 25% 7

8 Beam Hardening A polychromatic beam (multiple energies) (e.g., from x- ray tube, Ga-67, In-111, I-131) has complex attenuation properties. Since lower energies are attenuated more than higher energies, the higher energy photons are increasingly more prevalent in the attenuated beam. Summary of interaction of charged particles and photons with matter Charged particles have a very short range in tissue ~ mm for beta particles ~ µm for alpha particles Alphas have a predictable, continuously slowing path Betas have a more sporatic path Photons have a longer range interact very infrequently, depositing much or all of their energy in each interaction: range ~cm. Compton scatter is the dominant process in tissue equivalent materials for the energy range of photons for Nuclear Medicine imaging 8