Detectors in Nuclear Physics (48 hours)
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1 Detectors in Nuclear Physics (48 hours) Silvia Leoni, Complemetary material: Lectures Notes on γ-spectroscopy LAB
2 Application to Medicine (~ Lectures) Andrea Mairani,
3 Textbooks G.F. Knoll Radiation Detection and Measurements Wiley & Sons W.R. Leo Techniques for Nuclear and Particle Physics Experiments Springer-Verlag Additional Material:
4 Radiation Interaction 1. charged particles. γ-rays 3. neutrons Charged particle Radiations heavy charged particles (typical distance 10-5 m) Fast electrons (typical distance 10-3 m) Uncharged Radiations neutrons (typical distance 10-1 m) X- and γ-rays (typical distance 10-1 m) Continuous interaction via Coulomb force with electrons in the medium - NO Coulomb Interaction - catastrophic interaction which alters the particle properties in a single hit [often it involves the nucleus] - Full/partial transfer of energy to atomic electrons or nuclei
5 Importance for Radioprotection
6 Charged Particles A 10 / cm / A cm R nucl = 1. A 1/3 fm =1. A 1/ cm a Z = 1 A = 10-8 cm
7 From elastic collisions between incoming particle m 1, v i,1 and electron at rest Maximum energy transfer To atomic electron Example: proton transfer 1/500 E p in a single collision!!! m p = 1836 m e 000 m e
8 Maximum energy transfered from charged particle to electron is 4Em 0 /m = 1/500 of the particle energy per nucleon à loss of energy by many interactions, gradual process Penetration distance
9 = def = def = Energy loss by the particle in path length dx
10 Stopping Power and Range tables SRIM & TRIM Ziegler et al.
11 1. Z p e = particle charge Z p e, M, v number of interacting electrons # electrons per unit volume
12 . r min corresponds to maximum kinetic energy T max It corresponds to head-on-collision: gained by e- T max = (Δp max ) m e r min = Z pe 4 m e v 4 = Z pe 4 = m m e v e v r min Estimate of Radial Limits: r max corresponds to minimum kinetic energy T min T = T r min IE ionization en. 4 Z pe min = IE = mev rmax max gained by e- = 10 Z ev = Z p e 4 ( IE) m v e
13 4πZ m v e 4 p e N e 1 mev ln IE 3. 1 de 4πZ pe ρ dx m v e 4 Z T 1 mev ln IE Phenomenological model Bethe-Bloch Quantum Mechanical Equation (for heavy particles M >> m e, β = v/c) Average energy loss de dx ρz Z p T 1/ v Large in dense material Large for heavy ions Large for slow particles
14 β Additional corrections: Wide minimum for v c; β 1
15 Near Constant Broad Minimum for v à c At the minimum: very similar behaviour for different light particles at E > 100 MeV minimum ionizing particles Electrons are at the minimum of ionization at E > 1 MeV!!! very different de/dx behaviour for different particles at E < E min: Technique used for particle identification E=mc = m 0 c + E kin
16 (de/dx) min versus Z
17 velocity Relativistic rise: part of the energy is also Subtracted by light (Cerenkov radiation) N.B. Bethe-Block is accurate for pions in the range 6 MeV-6 GeV
18 Strong correlation θ à β: Cerenkov effect is used to identify particles (Cerenkov counters: photomultipliers)
19 Corrections to Bethe-Bloch formula Average energy loss Corrections - δ - C/Z Density correction (importat for high energy): - Atoms are polarized by electric field of the particle - Far electrons are shieldedà less contribution to de/dx Shell correction (important for low energy): - Velocity of incident particle comparable to orbital velocity of bound electrons - electrons are NOT stationary with respect to incoming particle à Picking up of electrons to the charged particle à Reduced charge
20 Equilibrium charge state distribution for 110 MeV 17 I ions stripped in various materials Average charge depends on Energy E, and for solid absorbers is q Z = 0.708( x 0.058) for 0.05 < x < 0.5 x= Z (E/A) 1/ 1/ 0.04 average charge decreases with decreasing energy (see Ziegler et al. ) de/dx decreases
21 Capture of low energy electrons decreases the particle charge [the ion may become neutral] de/dx on large scale Nuclear physics βγ < 1 Boundaries between different approximations
22 Exception to Bethe-Block formula: Channeling Effects importat for material with spatially symmetric atomic structure: Series of correlated scattering guiding the particle down an open channel of the lattice à Less electrons encounterd as compared to amorphous material (assumed by Bethe- Block) à Importance of crystal orientation Critical angle for channeling is small ( 1 for β 0.1) a 0 = Bohr radius d = interatomic spacing For φ > φ c channeling does NOT occurn à the material can be treated as amourphous
23 the particle charge changes at the end of the path due to electrons pick up 4. Z p f ( v) unique function for particle with velocity v R a Aa Z b ( v) = A Z b a R ( v) b
24 Examples for Nuclear Physics - de/dx Z p
25 E kin Z p [ex. Active area of detector ]
26
27 de dx E mz E E = mz Application: Particle identification E E Very useful method to separate ions up to more than A = 30
28 Bethe-Bloch Quantum Mechanical Equation for FAST electrons FAST electrons can loose energy by - Ionization/collisions - Radiation (bremsstrahung) Trajectories are complex: mass is small and equal to orbital electrons rad with E in MeV Coll de dx coll πe m v e 4 e ρz T ln m v E e ( IE) ( 1 β ) (ln ) ( ) ( ) ( ) 1 1 β 1+ β + 1 β β 8 Similar to heavy-ions relativistic terms de dx r ρez ( Z + 1) e 4 137m c EρZ e 4 E 4ln m c e 4 3 large for energetic electrons in heavy materials
29 In nuclear physics E γ For typical electron energy bremsstrahlung photon energy is quite small it is reabsorbed close to its point of origin
30 The Bragg Peak energy deposited per mass unit Absorbed dose (also known as total ionizing dose, TID) : energy deposited in a medium by a ionizing radiation per unit mass Unit of measurements: Joules/Kilogram = 1 gray (Gy) in SI or rad in GGS N.B. The absorbed DOSE depends on: Incident particle and Absorbing material Example: an X-rays can deposit up to 4 times more energy in a bone than in air and none at all in vacuum!
31 1/E Charge is reduced due to electrons pick up
32 it corresponds to thickness x where N(x) = N 0 /
33 After absorber The distribution is Gaussian only if Δx is large enough Landau has shown that the asymmetric tail is due to great energy losses in close collisions Important in Nuclear Rections with Thick Targets
34 After absorber - mean distance over which a high-energy e - reduces to 1/e of its energy by bremsstrahlung - 7/9 of the mean free path for pair production by a high-energy photon - appropriate scale length for high-energy electromagnetic cascades Important in Nuclear Rections with Thick Targets
35 Importance in application of Monte Carlo Simulation programs!!! ( See last Lectures)
Detectors in Nuclear Physics (40 hours)
Detectors in Nuclear Physics (40 hours) Silvia Leoni, Silvia.Leoni@mi.infn.it http://www.mi.infn.it/~sleoni Complemetary material: Lectures Notes on γ-spectroscopy LAB http://www.mi.infn.it/~bracco Application
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