Interaction radiation-matter M. Cobal, G. Panizzo

1. Interaction radiation-matter M. Cobal, G. Panizzo

2. Particles – matter interactions • Processes at the base of particle detector’s operations • The energy lost by the particles is converted in electrical signal to measure the various observables (positions, energy, momentum…) • Any observable is measured with a specific detector • Different particles, different interactions • Heavychargedparticles • Electrons • Photons

3. Charged Particles Main phenomena Energy loss Anelasticcollisions with electrons or atomicnuclea Deflection Elasticdiffusion from nuclea Ioniation Bremsstrahlung Negligible for heavy charged particles Coulombian multiple scattering Other phenomena Cherenkov emission, Transition radiation

4. Heavy charged particles energy loss: Ionization • If the followinghypotheses are true • Mass M>>me • Atomic e- free and in quiet • Small transferredmomentum One can evaluate (-dE/dx) = average rate for the energy loss through ionization of a charged particle Bohr (classical) Bethe-Bloch (relativistic)

5. Bethe-Bloch formula Valid for β>0.1 I = average ionization potential Z, A, ρ= characteristics of the material z, β, γ = characteristics of the incident particles Wmax = max energy transferred in one collision re = classical radius of the electron me = electron mass Na = Avogadro number C = shell correction δ = density effect

6. Comments • Zone A: fast decrease proportional to 1/β² • Point B: minimum of the energy loss • Zone C: slow relativistic increase proportional to ln • Zone D: constant energy loss per unit lenght , ionization limited by density effects

7. Comments (ρ/A) Na=N (numerical atomic density) -(dE/dX)~ZN A material dense and with high atomic number gain more energy from the incident particle) The energy released does not depends from the mass of the incident particle • A fast particle releases less energy • A particle with higher charge, releases more energy

8. Comments • Density effects (important at high energies): the atoms polarization screen the electrical field for the electrons which are far away, so that the collisions wirth these electrons contribute less to the total energy loss. • Shell corrections(inportant at low energies): quando v(particella)~v(orbitale elettrone) non vale l’assunzione di elettrone stazionario • Channeling in materials with a symmetric atomic structure: the energy loss is smaller if the particles move through a channel. This happens when the angle is smaller than a critical value.

9. Comments Relativistic limit: v=0.96c Ionization minimum: dE/dx~2Mev*cm2/g First part of the curve • Small ß and ~1 • Non relativistic particle E~ mc2+mv2/2, p=mv • The term 1/ß2 is dominant • dE/dx as a function of energy and momentum particle discrimination • Secondpart of the curve • Largeß~1 and  • Relativisticparticle: E~pc E=mc2>>mc2 • Thetermln(2ß2) isdominant • Logarothmicgrowth as a function of energy • equalforallthparticles

10. Minimum Ionization • The energywhichcorresponds to the ionization minimum depends from the mass of the incidentparticle. • Heavierparticlesreach the minimum athigherenergies • The relativisticraiseis the same for all the particles.

11. Dependency from the material • Energy loss increases as Z/A increases • Particles with the same velocity have about the same energy loss in different materials • Linear absorbing power: (dE/dx)*(1/ρ) normalize materials with different mass density ρ=mass density, l=thickness, ρ*l= mass thickness Different materials with the same mass thickness have the same effect in the same radiation

12. Mass thickness

13. Bethe-Bloch

14. Bragg Curve Bragg curve • When the particle slow down it looses more energy • Most of the energy is deposited at the end: this is important for medical application • The curve goes to zero for the electrons pick up (particle becomes neural) dE/dx(Mev*cm2/g) Pick up Profondità di penetrazione Penetration depth

15. Penetration Depth (or Range) Range: distance crossed by the particle in the material Heavy charged particles • Beam degraded in energy • Many collisions • No large deflections: • range defined Outgoing/ingoing particlei as a function of the material thickness straggling ma 1,0 Extrapolated range Particle-matter interaction: statistical process 0,5 Range straggling Average range NB: In general the rangedoesnot coincide excatly with the thickness of the materialneeded to stop the particle, due to the presence of the scattering.

16. Statistical Fluctuations Bethe-Bloch: <dE/dx> = averagevalue of the energyloss in a material via ionization Statistical fluctuations on: • Number of collisions • Energy transfer in each collision Thickabsorbers Large number of collisions Gauss distribution Thinabsorbers Large energy transfer are possible in one single collision Landau distribution Large tails at high energy

17. Electrons-matter interaction • Coulomb interactions with: • Nuclea (elastic collisions, deflession) • Atomic electrons (anelastic collisions, energy losses) • Energy transfers in a single collision larger than in the case of heavy charged particles. • Electrons less penetrating than heavy charged particles since they loose energy in a smaller number of collisions • Trajectories perturbed -> can just extrapolate the range • Backscatteringfor low energy electrons and materials with a large atomic number.

18. Ionization via electrons Modifications to the Bethe-Bloch formula: smallme Large deviations possible scattering between identical particles Quantum-mechanics rules τ = kinetic energy of the particle in mec2 units Flat behaviour

19. Bremsstrahlung • Radiation emission for diffusion in the electrical field of the nucleus (bremmstrahlung = breaking) • The energy is not transferred to the material but to the emitted photons. Below few hundreds of Gev only electrons undergo this loss of energy σ ~ 1/m2 Negligible effect for heavy particles • It depends from the strenght of the electrical field «seen» by the incoming electronimportanza dello • screening from atomic electrons

20. Electron energy loss (dE/dx)tot = (dE/dx)rad + (dE/dx)coll IONIZATION up to fewMeV BREMSSTRAHLUNGfrom tenths of MeV Itexists a criticalenergyabovewhich Bremsstrahlung dominates The critical energy strongly depends from the absorbing material For each material, one defines a critical energy Ec at which the energy loss by raiation is equal to the energy loss due to colllisions. (dE/dx)rad = (dE/dx)coll

21. Comparison electron-proton Ec