Detectors in Nuclear Physics (40 hours)

Transcription

1 Detectors in Nuclear Physics (40 hours) Silvia Leoni, Complemetary material: Lectures Notes on γ-spectroscopy LAB

2 Application to Medicine (8 hours) Andrea Mairani,

3 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 -NOCoulomb 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

4 Importance for Radioprotection

5 Charged Particles A 10 / cm / A cm

6 Maximum energy transfered from charged particle to electron is 4Em 0 /m = 1/500 of the particle energy per nucleon loss of energy by many interactions, gradual process Penetration distance

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!!!

8 = def = def = Energy loss by the particle in path length dx

9 Stopping Power and Range tables SRIM & TRIM Ziegler et al.

10 1. Z p e = particle charge Z p e, M, v number of interacting electrons # electrons per unit volume

11 . r min corresponds to maximum kinetic energy T max gained by e - It corresponds to head-on-collision: Estimate of Radial Limits: T r 4 ( pmax ) p max = = = me mev rmin min = Z p e m v e 4 4 Z e m v r max corresponds to minimum kinetic energy T min gained by e - min IE ionization en. 4 Z pe min = IE = mev rmax e T = = 10 Z ev T r max = Z p e 4 ( IE) m v e

12 4πZ m v e e 4 p 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 ) Average energy loss de dx ρz Z p 1 / v T Large in dense material Large for heavy ions Large for slow particles

13 β

14 velocity Relativistic rise: part of the energy is subtracted by light (Cerenkov radiation) N.B. Bethe-Block is accurate for pions in the range 6 MeV-6 GeV

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16 (de/dx) min versus Z

17 Capture of low energy electrons decreass the particle charge [the ion may become neutral] de/dx on large scale Nuclear physics βγ < 1 Boundaries between different approximations

18 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

19 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

20 Examples for Nuclear Physics -de/dx Z p

21 E kin Z p [ex. Active area of detector ]

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23 de dx E mz E E = mz Application: Particle identification E E Very usefull method to separate ions up to more than A = 30

24 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 with E in MeV 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

25 In nuclear physics E e For typical electron energy the bremsstrahlung photon energy is quite low it is reabsorbed close to its point of origin

26 1/E Charge is reduced due to electrons pick up

27 it corresponds to thickness x where N(x) = N 0 /

28 Landau has shown that the asymmetric tail is due to great energy losses in close collisions The distribution is Gaussian only if x is large enough

29 - 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

30 Importance in application of Monte Carlo Simulation programs!!! ( See last Lectures)