Detectors for particles and radiation Specialist course for Master students

1. Detectors for particles and radiation Specialist course for Master students Spring semester 2010 5 ECTS points Tuesday 10:15 to 12:00 - Lectures Tuesday 14:15 to 15:00 - Exercises Lecture 2: Particle-matter electromagnetic interactions

2. Detectors for particles and radiation

3. In the next lecture Particle-matter electromagnetic interactions Multiple scattering Specific energy loss Bethe-Bloch formalism Landau distribution Cerenkov radiation Transition radiation

4. Multiple Scattering • Particles don’t only loose energy …… they also change direction

5. Definitions and units Some important definitions and units • energy E: measure in eV • momentum p: measure in eV/c • mass mo: measure in eV/c2 1 eV is a tiny portion of energy. 1 eV = 1.6·10-19 J mbee = 1g = 5.8·1032 eV/c2 vbee= 1m/s  Ebee = 10-3 J = 6.25·1015 eV ELHC = 14·1012 eV To rehabilitate LHC… Total stored beam energy: 1014 protons * 14·1012 eV  1·108 J this corresponds to a mtruck = 100 T vtruck = 120 km/h

6. Definitions and units The concept of cross sections Cross sections sor differential cross sections ds/dW are used to express the probability of interactions between elementary particles. Example:2 colliding particle beams beam spot areaA F1= N1/t F2= N2/t What is the interaction rate Rint. ? Rint N1N2 / (A ·t) = s · L shas dimension area ! Practical unit: 1 barn (b) = 10-24 cm2 LuminosityL[cm-2 s-1] Example:Scattering from target scattered beam solid angle elementdW target q incident beam .nA= area density of scattering centers in target Nscat(q) Ninc·nA ·dW = ds/dW (q)·Ninc·nA·dW

7. Single (Rutherford) scattering z An incoming particle with charge z interacts elastically with a target of nuclear charge Z. The cross-section for this e.m. process is Rutherford formula • Approximation • Non-relativistic • No spins • Average scattering angle • Cross-section for infinite ! • Scattering does not lead to significant energy loss

8. MS Theory • Average scattering angle is roughly Gaussian for small deflection angles • With • Angular distributions are given by

9. Correlations • Multiple scattering and dE/dx are normally treated to be independent from each other • Not true • large scatter  large energy transfer • small scatter  small energy transfer • Detailed calculation is difficult but possible • Wade Allison & John Cobb are the experts

10. Interaction of charged particles Optical behaviour of medium is characterized by the complex dielectric constant e Refractive index Absorption parameter Instead of ionizing an atom or exciting the matter, under certain conditions the photon can also escape from the medium.  Emission of Cherenkov and Transition radiation. (See later). This emission of real photons contributes also to the energy loss.

11. Interaction of charged particles Particles can only be detected if they deposit energy in matter. How do they lose energy in matter ? Wade Allison & John Cobb: Discrete collisions with the atomic electrons of the absorber material. Collisions with nuclei not important (me<<mN) for energy loss. If are in the right range  ionization. e -

12. Energy Loss Function

13. The real Bethe-Bloch formula. Interaction of charged particles Average differential energy loss Energy loss at a single encounter with an electron e- b v z·e 2b Introduced classical electron radius How many encounters are there ? Should be proportional to electron density in medium

14. Bethe-Bloch Formula • Describes how heavy particles (m>>me) loose energy when travelling through material • Exact theoretical treatment difficult • Atomic excitations • Screening • Bulk effects • Simplified derivation • Phenomenological description

15. Bethe-Bloch (1) • Consider particle of charge ze, passing a stationary charge Ze • Assume • Target is non-relativistic • Target does not move • Calculate • Energy transferred to target (separate) ze b y r θ x Ze

16. Force on projectile Change of momentum of target/projectile Energy transferred Bethe-Bloch (2)

17. Bethe-Bloch (3) • Consider α-particle scattering off Atom • Mass of nucleus: M=A*mp • Mass of electron: M=me • But energy transfer is • Energy transfer to single electron is

18. Bethe-Bloch (4) • Energy transfer is determined by impact parameter b • Integration over all impact parameters b db ze

19. Bethe-Bloch (5) • Calculate average energy loss • There must be limit for Emin and Emax • All the physics and material dependence is in the calculation of this quantities

20. Bethe-Bloch (6) • Simple approximations for • From relativistic kinematics • Inelastic collision • Results in the following expression

21. Bethe-Bloch (7) • This was just a simplified derivation • Incomplete • Just to get an idea how it is done • The (approximated) true answer iswith • ε screening correction of inner electrons • δ density correction, because of polarisation in medium

22. Average Ionisation Energy

23. Density Correction • Density Correction does depend on materialwith • x = log10(p/M) • C, δ0, x0, x1 material dependant constants

24. Different Materials (1)

25. Different Materials (2)

26. Particle Range/Stopping Power

27. Application in Particle ID • Energy loss as measured in tracking chamber • Who is Who!

28. Bethe-Bloch overview Energy loss by Ionisation only  Bethe - Bloch formula • dE/dx in [MeV g-1 cm2] • valid for “heavy” particles (mmm). • First approximation: medium simply characterized by Z/A ~ electron density Z/A = 1 “Fermi plateau” Z/A~0.5 “relativistic rise”   3-4 minimum ionizing particles, MIPs “kinematical term”

29. Straggling (1) • So far we have only discussed the mean energy loss • Actual energy loss will scatter around the mean value • Difficult to calculate • parameterization exist in GEANT and some standalone software libraries • Form of distribution is important as energy loss distribution is often used for calibrating the detector

30. δ-Rays • Energy loss distribution is not Gaussian around mean. • In rare cases a lot of energy is transferred to a single electron • If one excludes δ-rays, the average energy loss changes • Equivalent of changing Emax δ-Ray

31. Straggling (2) • Simple parameterisation • Landau function

32. Landau in thin layers Real detector (limited granularity) can not measure <dE/dx> ! It measures the energy DE deposited in a layer of finite thickness dx. For thin layers or low density materials:  Few collisions, some with high energy transfer.  Energy loss distributions show large fluctuations towards high losses: ”Landau tails” DEmost probable<DE> e- d electron DE Example: Si sensor: 300 mm thick. DEm.p ~ 82 keV<DE> ~ 115 keV DEm.p.<DE> For thick layers and high density materials:  Many collisions.  Central Limit Theorem  Gaussian shaped distributions. e- DE

33. Landau in thin layers

34. Landau in thin layers “Theory” 300 mm Si DEm.p. ~ 82 keV <DE> ~ 115 keV charge collection is not 100%  = 26 keV L. Alexander et al., CLEO III test beam results 300 mm Si Includes a Gaussian electronics noise contribution of 2.3 keV Landau’s theory J. Phys (USSR) 8, 201 (1944) DEm.p. ~ 56.5 keV x (300 mm Si) = 69 mg/cm2 energy loss (keV)

35. Restricted dE/dx • Some detector only measure energy loss up to a certain upper limit Ecut • Truncated mean measurement • δ-rays leaving the detector

36. Bremsstrahlung • Energy loss by Bremsstrahlung Radiation of real photons in the Coulomb field of the nuclei of the absorber medium Effect plays a role only for e± and ultra-relativistic m (>1000 GeV) For electrons: e- radiation length [g/cm2] (divide by specific density to get X0 in cm)

37. Critical energy energy loss (radiative + ionization) of electrons and protons in copper • Critical energy Ec For electrons one finds approximately: Ec(e-) in Cu(Z=29) = 20 MeV For muons Ec(m) in Cu  1 TeV Unlike electrons, muons in multi-GeV range can traverse thick layers of dense matter. Find charged particles traversing the calorimeter ?  most likely a muon  Particle ID

38. Electrons • Electrons are different light • Bremsstrahlung • Pair production

39. Interaction of photons In order to be detected, a photon has to create charged particles and / or transfer energy to charged particles • Photo-electric effect: (already met in photocathodes of photodetectors) Only possible in the close neighborhood of a third collision partner - photo effect releases mainly electrons from the K-shell. Cross section shows strong modulation if Eg ≈Eshell At high energies

40. Interaction of photons • Compton scattering: e- Compton cross-section (Klein-Nishina) Assume electron as quasi-free. Klein-Nishina At high energies approximately qC Eg (keV) Atomic Compton cross-section:

41. Interaction of photons Typical energy spectrum of Compton electrons So called Compton edge! Example for 137Cs : gamma 662 keV

42. Interaction of photons Pair production Only possible in the Coulomb field of a nucleus (or an electron) if Cross-section (high energy approximation) independent of energy ! Energy sharing between e+ and e- becomes asymmetric at high energies.

43. Interaction of photons In summary: m: mass attenuation coefficient Part. Data Group Part. Data Group photo effect Rayleigh scattering (no energy loss !) pair production Compton scattering

44. Reminder: basic electromagnetic interactions e+ / e- g Photoelectric effect Compton effect Pair production Ionisation Bremsstrahlung s dE/dx E E s E dE/dx E s E

45. Compton electron What is Vavilov-Cherenkov radiation? The History. 1888 predicted by O. Heaviside 1936(re)Discovered by P.A. Cherenkov 1937 Explanation by I.E. Tamm and I.M. Frank In two papers of 1888 and 1889, Heaviside calculated the deformations of electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser medium. This included a prediction of what is now known as Cherenkov radiation, and inspired Fitzgerald to suggest what now is known as the Lorentz-Fitzgerald contraction. 1901 Lord Kelvin predicted it 1904 Sommerfeld predicted it Pierre and Marie Curie saw it M.L. Mallet (1926) saw it p: silver mirror A: radiator liquid D: aperture Ø3 mm K: neutral grey wedge L: ocular lens E: colour filter N: polarisation prism • The existence of an energy threshold • The light is directional • The photons are polarised

46. q n=n(l) Cherenkov Radiation with a classic twist (I.M. Frank on the basis of Huygen's principle): A charged particle with velocity bb=v/c in a medium with refractive index n n=n(l) may emit light along a conical wave front. The angle of emission is given by: and the number of photons by: For some missing steps: see J.D. Jackson, Classical Electrodynamics, Section 13 or equivalent

47. A beautiful picture (which has next to nothing to do with) Cherenkov radiation ABB.com

48. Cherenkov Radiation • How many Cherenkov photons are detected?

49. q Conservation of energy and momentum The behavior of a photon in a medium is described by the dispersion relation If: then: The same, but let us consider how a charged particle interacts with the medium

50. The Cherenkov radiation condition: e real and 0cos()1 Argon at normal density Argon still at normal density where n is the refractive index W.W.M. Allison and P.R.S. Wright, RD/606-2000-January 1984