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 c2 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. Interaction of photons with the matter Radiation Safety 1.E-02 Photonuclear reactions: photonuclear reactions ) -1 1.E-03 Neutron production Photo-pion 1.E-04
1.E-05 cross-section (cm cross-section
1.E-06 10 100 1000 energy (MeV) 1.E+04 80 (A − Z )× Z N Av ΣQD = × × ρ ×σ d 70 Giant resonance 1.E+03 γ(d,p)n A A Quasi-deuteron 60 1.E+02 50 1.E+01 40 -60/E 30 55 Mn( γ, n) 54 Mn 1.E+00 e 20 1.E-01 cross-section (mbarn) sγ(d,p)n 10 Cross-section [mbarn] 1.E-02 0 1 10 100 1000 10 20 30 40 energy (MeV) Energy [MeV]
17 / 35 2. Interaction of photons with the matter Radiation Safety 1.E+01 Photonuclear reactions: 1.E+00 Neutron production 1.E-01 Giant resonance
1.E-02 Quasi-deuteron numberneutrons of Photo-pion 1.E-03 0 5 10 15 20 1.E+02 energy (MeV) 1.E+01 1.E+00 1.E-01 Example: neutron spectrum 1.E-02 produced by 600 MeV electrons 1.E-03 on Cu target 1.E-04 number of neutrons 1.E-05 1.E-06 1.E+00 1.E+01 1.E+02 1.E+03 energy (MeV) 18 / 35 3. Interaction of neutrons with the matter Radiation Safety
The physical processes: 1. Elastic scattering • compound elastic scattering • potential scattering 2. Inelastic scattering (n,n’) 3. Other inelastic reactions: (n,p), (n, α), … 4. Absorption reactions • radioactive capture • charged particle reactions
5. Direct reactions: spallation
19 / 35 3. Interaction of neutrons with the matter Radiation Safety
Compound etc. inelastic scattering etc.
Compound nucleus formation Compound elastic scattering
EC
Compound Inelastic gamma-ray nucleus virtual formation energy
ZA + neutron
Capture gamma-rays B target nucleus Z A
A+1 neutron Z
energy = E C
20 / 35 3. Interaction of neutrons with the matter
Compound Radiation Safety etc. inelastic scattering etc. Compound elastic scattering
EC
Inelastic Compound gamma-ray nucleus virtual formation energy Neutron cross sections ZA + neutron Capture gamma-rays B
ZA+1 1.E+03 total elastic 1.E+02 capture
1.E+01 inelastic
1.E+00
1.E-01
1.E-02 cross section (barn)
1.E-03
1.E-04 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 energy (eV)
Example 1: iron 21 / 35 3. Interaction of neutrons with the matter
Compound Radiation Safety etc. inelastic scattering etc. Compound elastic scattering
EC
Inelastic Compound gamma-ray nucleus virtual Neutron cross sections formation energy ZA + neutron
Capture gamma-rays B 1.E+05
ZA+1
1.E+04 total elastic 1.E+03 capture 1.E+02 inelastic
1.E+01
1.E+00
1.E-01
cross section (barn) 1.E-02
1.E-03
1.E-04 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 energy (eV)
Example 2: cadmium 22 / 35 3. Interaction of neutrons with the matter
Compound Radiation Safety etc. inelastic scattering etc. Compound elastic scattering
EC
Inelastic Compound gamma-ray nucleus virtual formation energy Neutron cross sections ZA + neutron Capture gamma-rays B
1.E+04 ZA+1
1.E+03 total elastic 1.E+02 capture 1.E+01
1.E+00
1.E-01
1.E-02
cross section (barn) 1.E-03
1.E-04
1.E-05 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 energy (eV)
Example 3: hydrogen 23 / 35 3. Interaction of neutrons with the matter
Compound Radiation Safety etc. inelastic scattering etc. Compound elastic scattering
EC
Inelastic Compound gamma-ray nucleus virtual formation energy Neutron cross sections ZA + neutron Capture gamma-rays B
ZA+1 1.E+04
1.E+03 total elastic 1.E+02 capture 1.E+01 inelastic 1.E+00 (n,alpha)
1.E-01
1.E-02
cross section (barn) 1.E-03
1.E-04
1.E-05 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 energy (eV)
Example 4: boron 24 / 35 3. Interaction of neutrons with the matter
Radiation Safety 1.E+03 total elastic 1.E+02 Neutron cross sections capture
1.E+01 inelastic
1.E+00
1.E-01
1.E-02 cross section (barn)
1.E-03 inelastic cross section (barn) 2.2 1.E-04 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 2.0 Pb energy (eV) 1.8 1.6 W 1.4 Example: iron 1.2 1.0 0.8 Cu 0.6 Fe 0.4 Al
nonelasticcross section (b) 0.2 C 0.0 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 proton energy (GeV) neutron energy (GeV) 25 / 35 3. Interaction of neutrons with the matter Radiation Safety Elastic scattering target nucleus scattered neutron energy = E 1
initial neutron
energy = E 0 recoiling nucleus
target E −−− Minimum energy of scattered neutron: 1,minimum ∆∆∆E 2 A −−− 1 Hydrogen E ,1 min imum === E0 === αααE0 0 0.5 E 0 A +++ 1 (A=1) Iron Average energy loss per collision: 0.93 E 0 0.034 E 0 −−− 1 (A=56) ∆∆∆E === ((()(1 −−− ααα)))E0 Lead 2 0.98 E 0 0.0096 E 0 (A=207)
26 / 35 4. Interaction of protons with the matter Radiation Safety
The physical processes: 1. ionization 2. inelastic proton-nucleus scattering spallation
27 / 35 4. Interaction of protons with the matter Radiation Safety Proton ionization loss – Stopping power
stopping power (MeV.g -1.cm 2) 1.E+02 Al Fe minimum ionizing Pb particle
1.E+01
1.E+00 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 proton energy (MeV)
28 / 35 4. Interaction of protons with the matter Radiation Safety Comparison CSDA range of protons and electrons in iron
1,E+04
1,E+03 electron
) proton 1,E+02 -2
1,E+01
1,E+00
1,E-01
1,E-02
1,E-03 CSDA range (g.cm
1,E-04
1,E-05 1,E-03 1,E-02 1,E-01 1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 energy (MeV)
29 / 35 4. Interaction of protons with the matter Radiation Safety Inelastic proton – nucleus scattering: Spallation reaction
n
n p Δ π incident proton π (GeV range) n p intra-nuclear cascade
α d
n
γ evaporation
30 / 35 4. Interaction of protons with the matter Radiation Safety Inelastic proton – nucleus scattering Spallation reaction Inelastic cross section
2.2 2.0 Pb 1.8 1.6 W 1.4 E > 1 GeV 1.2 7.0 1.0 σ inel = .0 042 × A barn . 0.8 Cu 0.6 Fe 0.4 Al
nonelasticcross section (b) 0.2 C 0.0 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 proton energy (GeV)
31 / 35 4. Interaction of protons with the matter Radiation Safety Inelastic proton – nucleus scattering 1.E+02 1.E+03 Comparison ionization Pb Fe energy loss and inelastic Cu scattering 1.E+01 1.E+02 C concrete Al W
1.E+00 1.E+01 range(cm)
C
inelasticprobabilty (%) 1.E-01 concrete 1.E+00 Al W P Fe Cu
1.E-02 1.E-01 E > 1 GeV: 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 100 % probability proton energy (MeV) for spallation reaction
32 / 35 4. Interaction of protons with the matter Radiation Safety n inter-nuclear cascades Spallation n p D π incident proton π (GeV range) n p intra-nuclear cascade evaporation α D α spallation product n fast induced α, β, γ decay fission γ p γ n n n fission n n n fission products γ fission products (n,n’), (n,xn), γ (n, γ) ,… reactions . At ISIS: 1 proton produces 15-20 neutrons
33 / 35 4. Interaction of protons with the matter Radiation Safety Spallation
34 / 35 Radiation Safety Summary: Interaction of the radiation with the matter
From https://www.mirion.com/introduction-to-radiation-safety/types-of-ionizing-radiation/
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