Part B. Radiation sources Radiation Safety 1. Interaction of electrons-e with the matter −31 me = 9.11×10 kg ; E = m ec2 = 0.511 MeV; qe = -e 2. Interaction of photons-γ with the matter mγ = 0 kg ; E γ = 0 eV; q γ = 0 3. Interaction of neutrons-n with the matter −27 mn = 1.68 × 10 kg ; En = 939.57 MeV; qn = 0 4. Interaction of protons-p with the matter −27 mp = 1.67 × 10 kg ; Ep = 938.27 MeV; qp = +e Note: for any nucleus A: mass number – nucleons number A = Z + N Z: atomic number – proton (charge) number N: neutron number 1 / 35 1. Interaction of electrons with the matter Radiation Safety The physical processes: 1. Ionization losses inelastic collisions with orbital electrons 2. Bremsstrahlung losses inelastic collisions with atomic nuclei 3. Rutherford scattering elastic collisions with atomic nuclei Positrons at nearly rest energy: annihilation emission of two 511 keV photons 2 / 35 1. Interaction of electrons with1.E+02 the matter Radiation Safety ) 1.E+03 -1 Graphite – Z = 6 .g 2 1.E+01 ) Lead – Z = 82 -1 .g 2 1.E+02 1.E+00 1.E+01 1.E-01 1.E+00 collision 1.E-02 radiative collision 1.E-01 stopping pow er (MeV.cm total radiative 1.E-03 stopping pow er (MeV.cm total 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E-02 energy (MeV) 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 Electrons – stopping power 1.E+02 energy (MeV) S 1 dE ) === -1 Copper – Z = 29 ρρρ ρρρ dl .g 2 1.E+01 S 1 dE 1 dE === +++ ρρρ ρρρ dl coll ρρρ dl rad 1 dE 1.E+00 : mass stopping power (MeV.cm 2 g. −−−1 ) ρρρ dl collision dE −−−1 1.E-01 : linear stopping power (MeV.cm ) radiative dl total stopping pow er (MeV.cm 1.E-02 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 3 / 35 energy (MeV) 1. Interaction of electrons with the matter Radiation Safety Continuous Slowing Down 1.E+03 Approximation range: 1.E+02 0 1 1.E+01 rCSDA === dE .g) -2 S E0 tot 1.E+00 graphite 1.E+00 copper 1.E-01 lead 1.E-01 1.E-02 CSDA range(cm graphite 1.E-03 1.E-02 copper 1.E-04 lead 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 radiation yield energy (MeV) 1.E-03 Radiation yield: 1.E-04 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 Fraction of the initial kinetic energy that energy (MeV) is converted to Bremsstrahlung energy as the electron slows down to rest. 4 / 35 1. Interaction of electrons with the matter Radiation Safety mbarn Differential Bremsstrahlung cross section: 12 10 MeV 1 dσ 100 MeV 10 2 k × 1 GeV Z dk 10 GeV 8 mbarn 6 25 10 MeV 100 MeV 4 20 1 GeV 10 GeV 2 15 lead – Z = 82 0 0 0.2 0.4 0.6 0.8 1 10 k/T k: photon energy T: electron kinetic energy 5 T = m γ c2 - m c 2 = m c 2 / {1 - v2/c 2}1/2 - m c 2 carbon – Z = 6 0 0 0.2 0.4 0.6 0.8 1 k/T 5 / 35 1. Interaction of electrons with the matter Radiation Safety Multiple scattering mean scattering angle 1.E+02 ) 2 -1 graphite .g 2 2 Es X 1.E+01 θθθ === copper .cm βββp X0 2 lead 1.E+00 mass scattering power S sc 1.E-01 1.E-02 2 1 d θθθ S === sc ρρρ dx 1.E-03 1.E-04 mass scattering power (radian Es = 21.2 MeV 1.E-05 1.E+00 1.E+01 1.E+02 1.E+03 X0: radiation length β: v/c energy (MeV) p: momentum 6 / 35 2. Interaction of electrons with the matter Radiation Safety • Particles involved: – Electrons / Positrons – Photons – Neutrons X0 X0: radiation length 7 / 35 2. Interaction of electrons with the matter Radiation Safety 4 Electromagnetic cascade 3 2 1 photon electron 0 cm positron -1 -2 -3 -4 -5 0 5cm 10 15 one 500 MeV electron interacting with lead target 8 / 35 2. Interaction of photons with the matter Radiation10 Safety Electromagnetic cascade 8 6 4 2 photon 0 electron cm -2 positron -4 -6 -8 -10 0 5 10 15 20 cm one 6 GeV electron interacting with lead target 9 / 35 2. Interaction of photons with the matter Radiation Safety The physical processes: 1. Photo-electric effect removal of an orbital electron of the inner shells (K,L,M) 2. Compton scattering inelastic scattering on loosely bound electrons 3. Pair production production of e -/e + pair essentially with nuclei 4. Rayleigh (coherent) scattering elastic scattering not important for radiation physics 10 / 35 2. Interaction of photons with the matter Radiation Safety 1.E+04 Photon cross sections Graphite - Z = 6 1.E+03 ) -1 coherent .g 1.E+02 2 com pton photoelectric 1.E+01 pair production 1.E+00 total 1.E-01 cross section (cm 1.E-02 1.E-03 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 energy (MeV) 11 / 35 2. Interaction of photons with the matter Radiation Safety 1.E+04 Photon cross sections Lead - Z = 82 1.E+03 ) -1 coherent .g 1.E+02 2 com pton photoelectric 1.E+01 pair production 1.E+00 total 1.E-01 cross section (cm 1.E-02 1.E-03 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 energy (MeV) 12 / 35 2. Interaction of photons with the matter 1.E+04 1.E+03 Radiation Safety ) -1 coherent .g 1.E+02 2 com pton photoelectric 1.E+01 pair production Photo-electric effect: 1.E+00 total 1.E-01 photo-electron cross section (cm 1.E-02 ΔE = E 0 –E1 = K a 1.E-03 ΔE = E – E 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 0 energy (MeV) ΔE = E 0 –E2 = K b E2 E E E0 1 0 E KLMN KLMN incoming X-ray The K lines Auger electron ΔE = E 1 –E2 = L a E1 Auger-electron E1 ΔE = E 1 –E2 –E3 E2 E2 ΔE = E –E 1 3 KLMN KLMN = L b E3 E3 The L lines 13 / 35 2. Interaction of photons with the matter 1.E+04 1.E+03 Radiation Safety ) -1 coherent .g 1.E+02 2 com pton photoelectric Compton scattering: 1.E+01 scattered photon pair production 1.E+00 total energy E c 1.E-01 θ cross section (cm E0 1.E-02 Ec === 1.E-03 E0 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 primary photon Compton electron 1 +++ ((()(1 −−− cos θθθ))) energy (MeV) m c 2 energy = E -E 0 energy E 0 0 c 2 2 dσ/dW (r e x cm / electron) E (MeV) 1.E+02 c 1.E+00 50 keV 100 keV 500 keV 1.E+01 1 MeV 1.E-01 10 MeV 50 keV 100 MeV 100 keV 500 keV 1.E+00 1 MeV 1.E-02 10 MeV 100 MeV 1.E-01 1.E-03 0 30 60 90 120 150 180 θθθ (degrees) 1.E-02 0 30 60 90 120 150 180 θθθ (degrees) 14 / 35 2. Interaction of photons with the matter 1.E+04 Radiation Safety 1.E+03 ) -1 coherent .g 1.E+02 2 com pton photoelectric 1.E+01 Pair production: pair production 1.E+00 total 1.E-01 cross section (cm 1.E-02 1.E-03 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 2 energy (MeV) σnucleus ∝ Z threshold: 1.022 MeV 1 σ ∝ Z 0.9 electron 0.8 threshold: 2.044 MeV 0.7 0.6 0.5 0.4 0.3 relative probability 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 E/k 15 / 35 2. Interaction of photons with the matter Radiation Safety Interaction of photons with matter Macroscopic description - Attenuation factors The mass attenuation coefficient μ/ρ: 1 −µ d (cm ) 0 .9 N = N 0 × e µ 1 dN 0 .8 µµ N µ === − d ( g⋅cm −2 ) ρρρ ρρρN dl 0 .7 ρ 0 .6 N = N 0 × e units: cm 2.g -1 0 .5 The linear attenuation coefficient μ: 0 .4 1 dN 0 .3 µµµ === 0 .2 N dl 0 .1 0 units: cm -1 0 1 2 3 4 5 6 7 8 9 1 0 d (cm) d (g.cm -2) The conversion factor from σ (barns.atom -1) to μ/r (cm 2.g -1): µµµ N === 10 −−−24 A σσσ ρρρ A 16 / 35 2.