Particle-Matter Interactions

Transcription

1 Particle-Matter Interactions to best detect radiations and particles we must know how they behave inside the materials 8/30/2010 PHYS6314 Prof. Lou 1

2 Stable Particles Visible to a Detector Hadrons (Baryon/Meson) strong interaction/em Proton, antiproton, Helium nucleus (α rays) Photon or Leptons EM/Weak infinity C τ (µm) neutron, antineutron π ± π 0 ( γγ 98.8%) K ± K 0 (short, long) , e ± (β rays) infinity µ ± ν l γ (g rays) close to infinity infinity 8/30/2010 PHYS6314 Prof. Lou 2

3 PART II Physics of Particle-Matter Interactions Chapter 2 Energy Loss of Charged Particles Chapter 3 Photons and Neutrons 8/30/2010 PHYS6314 Prof. Lou 3

4 PART II Physics of Particle-Matter Interactions Reading 8/30/2010 PHYS6314 Prof. Lou 4

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9 Chapter 2 Energy Loss of Charged Particles Energy loss of charged particles Ionization of charged particles, de/dx, Bethe-Bloch formula Stopping power, range, radiation length Collision loss, multiple scattering, Bremsstrahlung Cherenkov radiation Electromagnetic and hadronic showers 8/30/2010 PHYS6314 Prof. Lou 9

10 Energy Loss of Charged Particles The passage of charged particles (e ±, µ ±, π ±, K ±,p, ap, ) through matter undergoes energy loss and deflection as the result of these processes: Inelastic collisions with atomic electrons excitation, ionization Elastic scattering from nuclei Cherenkov radiation Nuclear reactions Bremmstralung rare frequent 8/30/2010 PHYS6314 Prof. Lou 10

11 Energy Loss of Charged Particles Inelastic collisions with atomic electrons (µ ±, π ±, K ±,p, ap) lose energy primarily through this interaction: ionization (soft) or excitation (hard)of atoms (on-shell electrons, not much with the nuclei) in the material the energy loss can be very large: 10 MeVproton loses all its energy in 0.25mm of copper high energy recoil electrons: δ-rays, knock-on electrons Elastic scattering from nuclei 8/30/2010 PHYS6314 Prof. Lou 11

12 Energy Loss of Charged Particles Inelastic collisions with atomic electrons (µ ±, π ±, K ±,p, ap) lose energy primarily through this interaction: ionization (soft) or excitation (hard)of atoms (on-shell electrons, not much with the nuclei) in the material the energy loss can be very large: 10 MeVproton loses all its energy in 0.25mm of copper high energy recoil electrons: δ-rays, knock-on electrons Elastic scattering from nuclei Compton scattering causing deflection of flights 8/30/2010 PHYS6314 Prof. Lou 12

13 Energy Loss of Charged Particles Electron traversing a medium 8/30/2010 Source: Leo PHYS6314 Prof. Lou 13

14 Energy Loss of Charged Particles Bethe-Bloch Formula for energy loss calculation de 2 2 Z z 2meγ v W max 2 = 2π Nare mec ρ ln 2β 2 2 dx A β I 8/30/2010 PHYS6314 Prof. Lou 14

15 Energy Loss of Charged Particles Rutherford differential cross section for scatterringby electrons: by free electrons by atomic electrons 8/30/2010 PHYS6314 Prof. Lou 15

16 Energy Loss of Charged Particles Bethe-Bloch Formula (modified) for energy loss calculation de 2 2 Z z 2meγ v W max 2 C = 2π Nare mec ρ ln 2β δ dx A β I Z δ: density correction C: shell correction 8/30/2010 PHYS6314 Prof. Lou 16

17 Energy Loss of Charged Particles 8/30/2010 PHYS6314 Prof. Lou 17

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19 Bethe-bolch formula with and without shell/density corrections Source: Leo 8/30/2010 PHYS6314 Prof. Lou 19

20 de/dx vs particle species Source: Leo 8/30/2010 PHYS6314 Prof. Lou 20

21 de/dxfor the muonvse 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 21

22 de/dx in air vs particle species de/dx for α-particle vs E 300 MeVp in water 8/30/2010 PHYS6314 Prof. Lou Source: Tavernier 22

23 Energy Loss of Charged Particles Energy loss by charged particles -- Multiple scatering: Charged particles interacting with the Coulomb field of the nuclei can be deflected by a series of multiple scattering. 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 23

24 Energy Loss of Charged Particles Energy loss by charged particles -- Multiple scatering: The distribution of the scattering angles is described by the Moliere s theory: 13.6MeV βcp proj 2 Θ rms = Θ = + x z ( ln( x / X 0) Z p momentum in MeV, β c velocity, x thickness, X radiation length(to be defined later) 0 with z=1, the approximation is held: proj 2 Θ rms = Θ = 13.6MeV βcp 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 24 x X 0

25 Energy Loss of Charged Particles Energy loss by charged particles -- Bremsstrahlung: Charged particles interacting with the Coulomb field of the nuclei can be slowed down and thus emit photons (bremsstrahlung), losing a fraction of their energies: 2 de Z 2 2 e α N A z ( 2 ) E ln 4πε 1 0mc dx pair prod. A 3 Z Z, A atomic number, mass of the medium z, m, E charge number, mass and energy of incidnt particle For electrons, E m : de Z dx A pair prod. e 2 2 4α N A re E ln 183 Z 1 3 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 25

26 Energy Loss of Charged Particles Energy loss by charged particles -- Bremsstrahlung: Radiation Length X 0 : de dx E X brems. 0 approximately X 1 Z 0 2 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 26

27 Energy Loss of Charged Particles Energy loss by charged particles -- Bremsstrahlung: Numerical approximateion for Radiation Length X 0 : X 0 = A( g / mol) Z( Z + 1)ln(287 / Z ) g / cm 2 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 27

28 Energy Loss of Charged Particles Energy loss by charged particles -- Direct electron-pair production: At high energies electron-positron pairs can be produced by virtual photons in the Coulomb field of the nuclei: de = bpair prod ( Z, A, E) E dx pair prod. 6 2 For 100 GeV muons in iron b pair prod 3 10 cm / g : 100 GeV µ de MeV = 0.3 dx g / cm pair prod 2 = 8/30/2010 PHYS6314 Prof. Lou Source: Grupen 28