Interaction Ionizing Radiation with Matter BNEN Intro William D’haeseleer BNEN - Nuclear Energy Intro W. D'haeseleer

Ionizing particles Directly ionizing particles alpha (He-4 ++ ) & beta (e - /e + ) Indirectly ionizing particles Gamma or X rays/photons & neutrons BNEN - Nuclear Energy Intro W. D'haeseleer

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 BNEN - Nuclear Energy Intro W. D'haeseleer

Ionizations BNEN - Nuclear Energy Intro W. D'haeseleer

Directly ionizing particles BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - alphas Alpha particles 4 He ++ (~ 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 BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - alphas Range of alphas in air

Ionization - betas Beta particles e - / 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) BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - betas Beta particles e - / 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 BNEN - Nuclear Energy Intro W. D'haeseleer

Indirectly ionizing particles BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas X & Gamma / Photon interactions (~ eV …10 MeV) –Photoelectric effect –Compton scattering –Pair formation BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Consider beam of impinging photons with intensity I 0 detector (1) detected; not yet interacted (2) & (3) disappear from original beam as a consequence of interactions (2) (1) (3) Intensity BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Impinging intensity (or flux) = I 0 particles/(m 2 s) At location x still I particles/(m 2 s) remaining from original beam Between 0 and x, some of the particles have deviated from the original path due to interactions BNEN - Nuclear Energy Intro W. D'haeseleer

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. BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Probability for interaction of a particle within the interval dx = μ dx Suppose at place x I particles/(m 2 s), then the number of particles that undergoes an interaction (on average) per m 2 s is = I μ dx BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Hence, the decrease in number of particles (from originally parallel beam): dI = -I μ dx So that: I = I 0 e -μx or BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Or, alternatively μ ≡ linear attenuation coefficient[1/m] (=probability for interaction per m) μ/ρ ≡ mass attenuation coefficient[m²/kg] BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Hence, the attenuation coefficient is a measure for attenuation of the originally parallel beam = fraction that has not yet interacted BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Define μ ≡ N σ microscopic cross section actually μ = macroscopic cross section σ is measure for the probability of an interaction

BNEN - Nuclear Energy Intro W. D'haeseleer Intermezzo Cross Section Thickness dx Incoming beam I 0 Number of Interactions ~ I 0 A dx N proportionality constant ≡ σ

BNEN - Nuclear Energy Intro W. D'haeseleer Intermezzo Cross Section Alternatively:assume a very thin “sheet” of thickness dx, of material with particle density N → number of atoms per m² = N dx Impinging intensity I 0 /m²s Assume C = number of interactions per m²s fraction of the total area of 1 m² that has undergone an interaction σ = the effective area (“cross section”) of a single scattering center

BNEN - Nuclear Energy Intro W. D'haeseleer Intermezzo Cross Section Unit forσ = [ m² ] or,barn = m²

BNEN - Nuclear Energy Intro W. D'haeseleer Photons / Gammas Reaction Rate or Interaction Rate At location x : Iparticles in beam per m² and s μ = probability for interaction per m → μ I = number of interactions per m³ and s μ I ≡ RRReaction Rate [#/m 3 s] μ I ≡ RR Reaction Rate [#/m 3 s]

Photons / Gammas a. Photo-electric effect Fig Photoelectric effect in lead -- Ref: Schaeffer BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Photoelectric effect BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas b. Compton effect Microscopic cross section Ref: Lamarsh & Baratta BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas c. Pair Formation Ref: Schaeffer BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas c. Pair Formation Ref: Lamarsch & Baratta BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Pair formation BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Ref: Krane Aluminum - Al Lead - Pb

Ionization - Gammas Sum of all processes

BNEN - Nuclear Energy Intro W. D'haeseleer Ionization - Gammas Ref: Lamarsh & Baratta Comparison for different materials

BNEN - Nuclear Energy Intro W. D'haeseleer Ionization - Gammas Ref: Petzold & Krieger Fig Comparison for different materials

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 expressed per kg Dose Rate BNEN - Nuclear Energy Intro W. D'haeseleer

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 BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas Dose Rate Therefore, one writes: mass absorption coefficient Note: actually, μ a must be obtained through averaging over all angles BNEN - Nuclear Energy Intro W. D'haeseleer

Photons / Gammas If one takes this μ a systematically, one no longer has to bother about the actually absorbed energy! Dose Rate BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Total attn coeff metals BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Total abs coeff metals BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Total attn coeff low-Z materials BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Gammas Total abs coeff low-Z materials BNEN - Nuclear Energy Intro W. D'haeseleer

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 BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Neutrons with Macroscopic cross section fcn (target material, E n ) BNEN - Nuclear Energy Intro W. D'haeseleer

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 BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization Summary Ionizations & Range in tissue/water Ref. J. Shapiro BNEN - Nuclear Energy Intro W. D'haeseleer

Ionization - Summary Ref. J. Shapiro

Shielding BNEN - Nuclear Energy Intro W. D'haeseleer

Shielding BNEN - Nuclear Energy Intro W. D'haeseleer

References Some examples (a.o.) BNEN - Nuclear Energy Intro W. D'haeseleer