880.A20 Winter 2002 Richard Kass Particle Detection In order to detect a particle it must interact with matter! The most important processes are electromagnetic: Energy loss due to ionization (e.g. charged track in drift chamber) heavy particles (not electrons!) electrons and positrons Energy loss due to photon emission (electrons, positrons) bremsstrahlung Interaction of photons with matter (e.g. EM calorimetry) photoelectric effect Compton effect pair production Coulomb Scattering (multiple scattering) Other electromagnetic processes cerenkov light (e.g. RICH counters) scintillation light (e.g. trigger and TOF systems) transition radiation (e.g. particle id at high momentum) Can calculate the above effects with a combo of classical E&M and QED. In most cases calculate approximate results, exact calculations very difficult. 880.A20 Winter 2002 Richard Kass Incident particle z=charge of incident particle =v/c of incident particle =(1- 2 ) -1/2 W max =max. energy transfer in one collision Bethe-Bloch Formula for Energy Loss Fundamental constants r e =classical radius of electron m e =mass of electron N a =Avogadros number c=speed of light =0.1535MeV-cm 2 /g Average energy loss for heavy charged particles Energy loss due to ionization and excitation Early 1930s Quantum mechanics (spin 0) Valid for energies >z ( z/137) heavy= m incident >>m e proton, k, , Absorber medium I=mean ionization potential Z= atomic number of absorber A=atomic weight of absorber =density of absorber =density correction C=shell correction 880.A20 Winter 2002 Richard Kass Corrected Bethe-Bloch Energy Loss =parameter which describes how transverse electric field of incident particle is screened by the charge density of the electrons in the medium. 2ln + , with a material dependent constant (e.g. Table 2.1of Leo) C is the shell correction for the case where the velocity of the incident particle is comparable (or less) to the orbital velocity of the bound electrons ( z ). Typically, a small correction (see Table 2.1 of Leo) Other corrections due to spin, higher order diagrams, etc are small, typically 137 m e c 2 Z 1/3. For this case we have: Thus the total energy lost by an electron traveling dx due to radiation is: We can rearrange the energy loss equation to read: Since rad is independent of E we can integrate this equation to get: L r is the radiation length, the distance the electron travels to lose all but 1/e of its original energy. 880.A20 Winter 2002 Richard Kass Radiation Length (L r ) The radiation length is a very important quantity describing energy loss of electrons traveling through material. We will also see L r when we discuss the mean free path for pair production (i.e. e + e - ) and multiple scattering. There are several expressions for L r in the literature, differing in their complexity. The simplest expression is: Leo and the PDG have more complicated expressions: Leo, P41 PDG L rad1 is approximately the simplest expression and L rad2 uses 1194Z -2/3 instead of 183Z -1/3, f(z) is an infinite sum. Both Leo and PDG give an expression that fits the data to a few %: The PDG lists the radiation length of lots of materials including: Air: 30420cm, 36.66g/cm 2 teflon: 15.8cm, 34.8g/cm 2 H 2 O: 36.1cm, 36.1g/cm 2 CsI: 1.85cm, 8.39g/cm 2 Pb: 0.56cm, 6.37g/cm 2 Be: 35.3cm, 65.2g/cm 2 Leo also has a table of radiation lengths on P42 but the PDG list is more up to date and larger. 880.A20 Winter 2002 Richard Kass Interaction of photons ( s) with matter There are three main contributions to photon interactions: Photoelectric effect (E < few MeV) Compton scattering Pair production (dominates at energies > few MeV) Contributions to photon interaction cross section for lead including photoelectric effect ( ), rayleigh scattering ( coh ), Compton scattering ( incoh ), photonuclear absorbtion ( ph,n ), pair production off nucleus (K n ), and pair production off electrons (K e ). Rayleigh scattering ( coh ) is the classical physics process where s are scattered by an atom as a whole. All electrons in the atom contribute in a coherent fashion. The s energy remains the same before and after the scattering. A beam of s with initial intensity N 0 passing through a medium is attenuated in number (but not energy) according to: dN=- Ndx or N(x)=N 0 e - x With = linear attenuation coefficient which depends on the total interaction cross section ( total = coh + incoh + + ). 880.A20 Winter 2002 Richard Kass Photoelectric effect The photoelectric effect is an interaction where the incoming photon (energy E hv)is absorbed by an atom and an electron (energy=E e ) is ejected from the material: E e = E -BE Here BE is the binding energy of the material (typically a few eV). Discontinuities in photoelectric cross section due to discrete binding energies of atomic electrons (L-edge, K-edge, etc). Photoelectric effect dominates at low energies (< MeV) and hence gives low energy es. Exact cross section calculations are difficult due to atomic effects. Cross section falls like E -7/2 Cross section grows like Z 4 or Z 5 for E > few MeV Einstein wins Nobel prize in 1921 for his work on explaining the photoelectric effect. Energy of emitted electron depends on energy of and NOT intensity of beam. 880.A20 Winter 2002 Richard Kass Compton Scattering Compton scattering is the interaction of a real with an atomic electron. in ou t electron The result of the scattering is a new with less energy and a different direction. Solve for energies and angles using conservation of energy and momentum The Compton scattering cross section was one of the first (1929!) scattering cross sections to be calculated using QED. The result is known as the Klein-Nishima cross section. At high energies, >>1, photons are scattered mostly in the forward direction ( ) At very low energies, 0, K-N reduces to the classical result: Not the usual ! 880.A20 Winter 2002 Richard Kass Compton Scattering At high energies the total Compton scattering cross section can be approximated by: (8/3) r e 2 =Thomson cross section From classical E&M=0.67 barn We can also calculate the recoil kinetic energy (T) spectrum of the electron: This cross section is strongly peaked around T max : T max is known as the Compton Edge Kinetic energy distribution of Compton recoil electrons 880.A20 Winter 2002 Richard Kass Pair Production ( e + e - ) This is a pure QED process. A way of producing anti-matter (positrons). inin vv e-e- e+e+ Nucleus or electron Z Z inin vv e+e+ e-e- Z Z + First calculations done by Bethe and Heitler using Born approximation (1934). Threshold energy for pair production in field of nucleus is 2m e c 2, in field of electron 4m e c 2. At high energies (E >>137m e c 2 Z -1/3 ) the pair production cross sections is constant. pair =4Z 2 r e 2 [7/9{ln(183Z -1/3 )-f(Z)}-1/54] Neglecting some small correction terms (like 1/54, 1/18) we find: pair = (7/9) brem The mean free path for pair production ( pair ) is related to the radiation length (L r ): pair =(9/7) L r Consider again a mono-energetic beam of s with initial intensity N 0 passing through a medium. The number of photons in the beam decreases as: N(x)=N 0 e - x The linear attenuation coefficient ( ) is given by: = (N a /A)( photo + comp + pair ). For compound mixtures, is given by Braggs rule: ( )=w 1 ( )++ w n ( n n ) with w i the weight fraction of each element in the compound. 880.A20 Winter 2002 Richard Kass Multiple Scattering A charged particle traversing a medium is deflected by many small angle scatterings. These scattering are due to the coulomb field of atoms and are assumed to be elastic. In each scattering the energy of the particle is constant but the particle direction changes. In the simplest model of multiple scattering we ignore large angle scatters. In this approximation, the distribution of scattering angle plane after traveling a distance x through a material with radiation length =L r is approximately gaussian: with In the above equation =v/c, and p=momentum of incident particle The space angle = plane The average scattering angle =0, but the RMS scattering angle 1/2 = 0 Some other quantities of interest are given in The PDG: The variables s, y, are correlated, e.g. y = 3/2 880.A20 Winter 2002 Richard Kass Why we hate Multiple Scattering Multiple scattering changes the trajectory of a charged particle. This places a limit on how well we can measure the momentum of a charged particle (charge=z) in a magnetic field. s=sagitta r=radius of curvature L/2 Trajectory of charged particle in transverse B field. The apparent sagitta due to MS is: The sagitta due to bending in B field is: GeV/c, m GeV/c, m, Tesla The momentum resolution p/p is just the ratio of the two sigattas: Independent of p As an example let L/L r =1%, B=1T, L=0.5m then p/p 0.01/ . Thus for this example MS puts a limit of 1% on the momentum measurement Typical values 880.A20 Winter 2002 Richard Kass Scintillation Devices As a charged particle traverses a medium it excites the atoms (or molecules) in the the medium. In certain materials called scintillators a small fraction energy released when the atoms or molecules de-excite goes into light. ENERGY IN LIGHT OUT The use of materials that scintillate is one of the most common experimental techniques in physics. Used by Rutherford in his scattering experiments Scintillation light can be used to: Signal the presence of a charged particle Measure energy since the amount of light is proportional to energy deposition Measure the time it takes for a charged particle to travel a known distance (time of flight technique) There are lots of different types of materials that scintillate: non-organic crystals (NaI, CsI) organic crystals (Anthracene) Organic plastics (see Table on next page) Organic liquids (toluene, xylene) 880.A20 Winter 2002 Richard Kass Scintillators A typical plastic Scintillator system violet blue Emission spectrum of NE102A Plastic scintillator Properties of common plastic scintillators Typical cost 1$/in 2 880.A20 Winter 2002 Richard Kass Photomultiplier tubes We need a way to convert the scintillation photons into an electrical signal. Photons photoelectric effect electrons Use a photomultiplier tube to convert scintillation light into electrical current Properties of phototubes: very high gain, low noise current amplifier gains 10 6 possible possible to count single photons Off the shelf item, buy from a company wide variety to choose from (size, gain, sensitivity) tube costs range from $10 2 -$10 3 Sensitive to magnetic fields (shield against earths): use mu-metal In situations where a lot of light is produced (>10 3 photons) a photodiode can be used in place of a phototube, e.g. CLEOs calorimeter Quantum efficiency of bialkali cathode vs wavelength violet blue green Electric field accelerates electrons Electrons crash into dynodes create more electrons light es 880.A20 Winter 2002 Richard Kass Scintillation Counter Example Some typical parameters for a plastic scintillation counter are: energy loss in plastic scintillator:2MeV/cm scintillation efficiency of plastic:1 photon/100 eV collection efficiency (# photons reaching PMT):0.1 quantum efficiency of PMT0.25 What size electrical signal can we get from a plastic scintillator 1 cm thick? A charged particle passing perpendicular through this counter: deposits 2MeV which produces 2x10 4 s of which 2x10 3 s reach PMT which produce 500 photo-electrons Assume the PMT and related electronics have the following properties: PMT gain=10 6 so 500 photo-electrons produces 5x10 8 electrons =8x C Assume charge is collected in 50nsec (5x10 -8 s) current=dq/dt=(8x coulombs)/(5x10 -8 s)=1.6x10 -3 A Assume this current goes through a 50 resistor V=IR=(50 )(1.6x10 -3 A)=80mV (big enough to see with Oscope) So a minimum ionizing particle produces an 80mV signal. What is the efficiency of the counter? How often do we get no signal (zero PEs)? The prob. of getting n PEs when on average expect is a Poisson process: The prob. of getting 0 photons is e - =e -500 0. So this counter is 100% efficient. Note: a counter that is 90% efficient has =2.3 PEs 880.A20 Winter 2002 Richard Kass Time of flight with Scintillators Time of Flight (TOF) is a particle identification technique. measure particle speed and momentum determine mass t=x/v=x/( c) with =pc/E=pc/[(mc 2 ) 2 +(pc) 2 ] 1/2 Consider two particles with different masses but same momentum: For high momentum (e.g. p>1 GeV/c for s): t 1 +t 2 =2t and x/t c Actually, we measure the time it takes for the particle to travel a known distance. x 880.A20 Winter 2002 Richard Kass Time of Flight with Scintillators As an example, assume m 1 =m (140MeV), m 2 =m k (494MeV), and x=10m t=3.8 nsec for p=1 GeV t=0.95 nsec for p=2GeV Time resolution of a good TOF system is 150ps (0.15 ns) Scintillator+phototubes are capable of measuring such small time differences In colliding beam experiments, 0.5 2.25x10 10 cm/s No radiation radiation ct (c/n)t In a time t wavefront moves (c/n)t but particle moves ct. Huyghens wavefronts 880.A20 Winter 2002 Richard Kass Threshold Momentum for Cerenkov Radiation Example: Threshold momentum for Cerenkov light: For gases it is convenient to let =n-1. Then we have: The momentum (p t ) at which we get Cerenkov radiation is: For a gas +2 so the threshold momentum can be approximated by: For helium =3.3x10 -5 so we find the following thresholds: electrons63 MeV/ckaons61 GeV/c pions17 GeV/cprotons115GeV/c Medium =n-1 t helium3.3x CO 2 4.3x H 2 O glass 880.A20 Winter 2002 Richard Kass Number of photons from Cerenkov Radiation From classical electrodynamics (Frank&Tamm 1937, Nobel Prize 1958) we find the following for the energy loss per wavelength ( ) per dx for charge=1, n>1: With =fine structure constant, n( ) the index of refraction which in general depends on the wavelength ( ) of light. We can re-write the above in terms of the number of photons (N) using: dN=dE/E For example see Jackson section 13.5 We can simplify the above by considering a region were n( ) is a constant=n: We can calculate the number of photons/dx by integrating over the wavelengths that can be detected by our phototube ( 1, 2 ): Note: if we are using a phototube with a photocathode efficiency that varies as a function of then we have: 880.A20 Winter 2002 Richard Kass Number of photons from Cerenkov Radiation For a typical phototube the range of wavelengths ( 1, 2 ) is (350nm, 500nm). We can simplify using: For a highly relativistic particle going through a gas the above reduces to: For He we find:2-3 photons/meter (not a lot!) For CO 2 we find:~33 photons/meter For H 2 Owe find:~34000 photons/meter GAS Photons are preferentially emitted at small s (blue) For most Cerenkov counters the photon yield is limited (small) due to space limitations, the index of refraction of the medium, and the phototube quantum efficiency. 880.A20 Winter 2002 Richard Kass Types of Cerenkov Counters There are three different types of Cerenkov counters used to identify particles. Listed in order of their sophistication they are: Threshold counter (on/off device) Differential counter (makes use of the angle of the Cerenkov radiation) Ring imaging counter (makes use of the cone of light) Each of the above counter is designed to work in a certain momentum range. Threshold counter: Identify the particle(s) which give off light. Can use to separate electrons from heavier particles ( , K, p) since electrons will give off light at a much lower momentum (e.g. 68 MeV/c vs 17 GeV/c for He) Problems with device: above a certain momentum several particles will give light. usually threshold counters use gas which implies low light levels (n-1 small) low light levels leads to inefficiency, e.g. =3, the prob. of zero photons: P(0)=e -3 =5%! Phototubes must be shielded from magnetic fields above a few tenths of a gauss. 880.A20 Winter 2002 Richard Kass Types of Cerenkov Counters Differential Cerenkov Counter: Makes use of the angle of Cerenkov radiation and only samples light at certain angles. For fixed momentum cos is a function of mass: Not all light will make it to phototube Differential cerenkov counters typically on work over a fixed momentum range (good for beam monitors, e.g. measure or K content of beam). Problems with differential Cerenkov counters: Optics are usually complicated. Have problems in magnetic fields since phototubes must be shielded from B-fields above a few tenths of a gauss. 880.A20 Winter 2002 Richard Kass Ring Imaging Cerenkov Counters (RICH) RICH counters use the cone of the Cerenkov light. The angle ( ) of the cone is given by: The radius of the cone is: r=Ltan , with L the distance to the where the ring is imaged. L r For a particle with p=1GeV/c, L=1 m, and LiF as the medium (n=1.392) we find: deg r(m) K P Thus by measuring p and r we can identify what type of particle we have. Problems with RICH: optics very complicated (projections are not usually circles) readout system very complicated (e.g. wire chamber readout, channels) elaborate gas system photon yield usually small (10-20), only a few points on circle Great /K/p separation! 880.A20 Winter 2002 Richard Kass CLEOs Ring imaging Cerenkov Counter The figures below show the CLEO III RICH structure. The radiator is LiF, 1 cm thick, followed by a 15.7 cm expansion volume and photon detector consisting of a wire chamber filled with a mixture of TEA and CH4 gas. TEA is photosensitive. The resulting photoelectrons are multiplied by the HV on the wires and the resulting signals are sensed by a rectangular array of pads coupled with highly sensitive electronics. 880.A20 Winter 2002 Richard Kass CLEOs Ring imaging Cerenkov Counter Lithium Floride (LiF) radiator Assembled radiators. They are guarded by Ray Mountain. Without Ray livingat the factory that produced the LiF radiators we would still be waiting for the order to be completed. A photodetector: CaF 2 window+cathode pads Assembled photodetectors 880.A20 Winter 2002 Richard Kass Performance of CLEOs RICH Number of detected photons on 5 GeV electrons A track in the RICH D*s without/with RICH information Preliminary data on /K separation 880.A20 Winter 2002 Richard Kass SuperK 481 MeV muon neutrino produces 394 MeV muon which later decays at rest into 52 MeV electron. The ring fit to the muon is outlined. Electron ring is seen in yellow-green in lower right corner. This is perspective projection with 110 degrees opening angle, looking from a corner of the Super-K detector (not from the event vertex). Color corresponds to time PMT was hit by Cerenkov photon from the ring. Color scale is time from 830 to 1816 ns with 15.9 ns step. In the charge weighted time histogram to the right two peaks are clearly seen, one from the muon, and second one from the delayed electron from the muon decay. Size of PMT corresponds to amount of light seen by the PMT. From:SuperK is a water RICH. It uses phototubes to measure the Cerenkov ring. Phototubes give time and pulse height information From SuperK site SuperK has: 50 ktons of H 2 O Inner PMTS: 1748 (top and bottom) and 7650 (barrel) outer PMTs: 302 (top), 308 (bottom) and 1275(barrel) For water n=1.33 For =1 particle cos =1/1.33, =41 o