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## Interaction Ionizing Radiation with Matter

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**Interaction Ionizing Radiation with Matter**BNEN 2012-2013 Intro William D’haeseleer**Ionizing particles**• Directly ionizing particles alpha (He-4++) & beta (e-/e+) • Indirectly ionizing particles Gamma or X rays/photons & neutrons**Ionizations**Energetic ionizing particles move around in sea of electrons, ions & nuclei • Leads to ionizations i.e., creation of i/e pairs Excitations in atoms and nuclei**Ionization - alphas**• Alpha particles4He++(~ 4-8 MeV) • Very massive and ++ • Create ample i/e pairs per unit distance • Loose on ave 34 eV per e/i pair in air 38 eV per e/i pair in water • Create ample local damage • Are very easily stopped in air & matter • E.g., in air ~ Range 3 to 7 cm water ~ Range 0.03 to 0.09 mm**Ionization - betas**• Beta particlese- / e+(~ keV …10 MeV) • Very light and + (elect) or + (posit) • Create “some” i/e pairs per unit distance • Create some local damage • Are quite easily stopped in air & matter • Range less precisely defined (straggling)**Ionization - betas**• Beta particlese- / e+(~ keV …10 MeV) • … • E.g., 3 MeV particles • Alpha in air R ~ 3 cm … 4000 i/e pairs/mm • Beta in air R ~ 10 m … 4 i/e pairs/mm • Beta 1.0 keV in water Range ~ μm • Beta 1.7 MeV in water Range 6cm in air Range 4.5 m**Ionization - Gammas**• X & Gamma / Photon interactions (~ eV …10 MeV) • Photoelectric effect • Compton scattering • Pair formation**Photons / Gammas**Consider beam of impinging photons with intensity I0 Intensity (2) detector (1) (3) (1) detected; not yet interacted(2) & (3) disappear from original beam as a consequence of interactions**Photons / Gammas**Impinging intensity (or flux) = I0particles/(m2s) At location x still I particles/(m2s) remaining from original beam Between 0 and x, some of the particles have deviated from the original path due to interactions**Photons / Gammas**Call:μ the probability for an interaction per m Hypothesis: μ = uniform ≠ f(x) a particle at location x has the same probability to undergo an interaction within the next 1 cm as a particle at the location 0 would have between 0 and 1 cm.**Photons / Gammas**Probability for interaction of a particle within the interval dx = μ dx Suppose at place x I particles/(m2s), then the number of particles that undergoes an interaction (on average) per m2s is = I μ dx**Photons / Gammas**Hence, the decrease in number of particles (from originally parallel beam): dI = -I μ dx So that: I = I0 e-μx or**Photons / Gammas**Or, alternatively μ≡ linear attenuation coefficient [1/m](=probability for interaction per m) μ/ρ≡ mass attenuation coefficient [m²/kg]**Photons / Gammas**Hence, the attenuation coefficient is a measure for attenuation of the originally parallel beam = fraction that has not yet interacted**Ionization - Gammas**Half length for attenuation X1/2 = ln2 / μ After 3 X1/2 factor 8 attenuation After 10 X1/2 factor 1024 attenuation**Photons / Gammasa. Photo-electric effect**Fig. 3.1. Photoelectric effect in lead -- Ref: Schaeffer**Ionization - Gammas**Photoelectric effect**Photons / Gammasb. Compton effect**Microscopic cross section Ref: Lamarsh & Baratta**Photons / Gammasc. Pair Formation**Ref: Schaeffer**Photons / Gammasc. Pair Formation**Ref: Lamarsch & Baratta**Ionization - Gammas**Pair formation**Ionization - Gammas**Sum of all processes**Photons / Gammas**Dose Rate Assume that upon interaction, an amount of energy E of the impinging particle will be transferred to the target material: deposited energy per interaction x RR E**Photons / Gammas**Dose Rate Dose rate expressed per kg**Photons / Gammas**Dose Rate In case of the Compton effect (see later for definition), not the total impinging energy will be deposited; only the fraction E = hv = energy of incoming photon E’ = hv’ = energy of scattered photon**Photons / Gammas**Dose Rate Therefore, one writes: Note: actually, μa must be obtained through averaging over all angles mass absorption coefficient**Photons / Gammas**Dose Rate If one takes this μasystematically, one no longer has to bother about the actually absorbed energy!**Ionization - Gammas**Total attn coeff metals**Ionization - Gammas**Total abs coeff metals**Ionization - Gammas**Total attn coeff low-Z materials**Ionization - Gammas**Total abs coeff low-Z materials**Ionization - Neutrons**• Interactions with neutrons (~ eV …8 MeV) • Elastic scattering • Inelastic scattering • Absorption (n,γ) Billiard ball collision Collision with nucleus left in excited state - recoil nucleus - gamma from de-excitation Neutron absorbed in nucleus which becomes highly excited - recoil nucleus - gamma from de-excitation - extra n moves nucleus up one step in N,Z plot new nucleus may be radioactive**Ionization - Neutrons**with Macroscopic cross section fcn (target material, En)**Ionization - Neutrons**Half length for attenuation X1/2 = ln2 / Σ After 3 X1/2 factor 8 attenuation After 10 X1/2 factor 1024 attenuation**Ionization - Neutrons**Neutron attenuation**Ionization - Neutrons**• Interactions with neutrons (~ eV …8 MeV) • Elastic scattering • Inelastic scattering • Absorption (n,γ) Neuton absorbed in nucleus which becomes highly excited - some absorption in U-233 U-235 and Pu-239 can lead to fission**Ionization**Summary Ionizations & Range in tissue/water Ref. J. Shapiro**Ionization - Summary**Ref. J. Shapiro**References**• Some examples (a.o.)