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Putting it all together - Particle Detectors. Writeup for 3 rd section: http://yeti.phy.bris.ac.uk/Level3/phys30800/CourseMaterials/Part_3.pdf. Measurements. Destructive Initial particle absorbed or significantly scattered

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Putting it all together - Particle Detectors

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Putting it all together- Particle Detectors

Writeup for 3rd section:



  • Destructive

  • Initial particle absorbed or significantly scattered

  • Detection generally by energy deposited by charged particles produced

  • Can detect neutral particles

  • Non-Destructive

  • Particle only minimally perturbed

  • Generally involves electrically charged particles depositing energy through many soft scatters

  • Aim for low mass detector

Types of Measurement




Time of flight

Event separation


Cerenkov/Transition radiation


Total energy


Position measurement

  • All detectors give some indication of particle position

    • ( even if it is only that the particle passed through the detector )

  • Most detectors have better resolution in one (or two) directions than the other two (or three).

    • Hodoscope ~ cm (2D)

    • Silicon strip detector ~5mm (1D)

    • Silicon pixel detector ~5mm (2D)

    • Photographic emulsion ~1mm (3D)

Position Measurement - Tracking

  • Measuring two (or more) points along the path of a particle allows its direction as well as is position to be measured.

  • Measuring a number of points along the path of a particle allows any curvature to be measured.

     Radius of curvature in a magnetic field gives the momentum

Position Measurement – Tracking

Pattern recognition can be tricky….

Timing Measurement

  • The time at which a particle passed through a detector can be measured to better than 1ns (10-9s)

    • Scintillator tends to be good ( 100ps )

  • Can measure velocity of particle

    • “time-of-flight” (ToF ) from interaction to detector.

    • Measuring b and p or E gives particle mass ( E=bm, p=bgm) and hence (usually) identity

    • ToF only useful for fairly low energy particles ( “slightly relativistic” ) since highly relativistic particles all have b=1 within the bounds of error.

Timing Measurement

  • Distinguish particles from different “events”

    • The interval between interactions generating the particles being measured is is often short. Need good timing resolution to separate tracks from different events.

  • Measure start time for drift chambers.

    • … and other devices that rely on measuring signal propagation times.

Timing Measurement – Particle ID

Timing Measurement – Particle ID

Timing Measurement – Particle ID

  • Hermes experiment uses TOF as one means of particle identification.

  • Bunches of electrons hit fixed target.

  • Measure time between collision and particles reaching scintillation detectors.

  • m2 = (1/2 – 1) p2

Dead Time

  • Most detectors take a finite time to produce a signal and recover before they can detect another. This is the dead-time

    • Dead time varies with detector e.g. Si-strip detector ~ ns , Geiger-Muller tube ~ ms

  • If the dead-time is Tdand particles arrive at a mean rate of r per unit-time then probability that the detector is “dead” is ~ rTd

    • I.e. efficiency is e = e0(1 – rTd )

Timing Coincidence

  • Where a detector has a high background it is common to use two or more detectors in coincidence

    • Output from combined detector only if all parts detect a particle. ( or 3 of 4, ….. etc.)

  • If two detectors have a background rate of B1, B2 and a signal is produced if both detectors “fire” within the coincidence time,Dt then the background rate from the combined detector is B = B1 B2 Dt

Energy Measurement

Rate of energy loss – dE/dx

Total energy - Calorimetry

Energy Measurement – dE/dx

  • Measure the rate of energy loss of a charged particle through detector by ionization - dE/dx

    • dE/dx Depends on bg

    • ( particles with same bg but different masses give ~ same dE/dx )

    • Measuring bg and one of E,p, gives particle mass.

dE/dx Data

dE/dx (keV/cm)





  • Data from gaseous track detector.

    • Each point from a single particle

    • Several energy loss samples for each point

    • “Averaged” to get energy loss

    • Fluctuations easily seen


p (GeV/c)

Energy Measurement – Calorimetry

  • Measure total energy of a particle by stopping the particle in a medium and arranging for the energy to produce a detectable signal. This process is called calorimetry

    • Detector needs to be thick enough to stop the particle

    • Can measure energy of neutral particles using calorimetry

Energy Measurement – Regions of Applicability

Measuring Velocity

  • Use a process such as Cerenkov radiation or transition radiation where the threshold/intensity of the radiation depends on the velocity of the particle

    • Cerenkov radiation: angle and intensity are functions of b

    • Transition radiation: intensity is a function of g (useful for highly relativistic particles)

  • dE/dx by ionization ( already mentioned)

Sources of measurement error

  • Fluctuations of underlying physical processes

    • “Statistical” fluctuations of numbers of quanta or interactions

    • Variation in the gain process

  • Noise from electronics etc.

Fluctuation in dE/dx by Ionization

Fluctuation in dE/dx by Ionization

  • Up to now we have discussed the mean energy lost by a charged particle due to ionization.

  • The actual energy lost by a particular particle will not in general be the same as the mean.

    • dE/dx due to a large number of random interactions

    • Distribution is not Gaussian.

Fluctuation in dE/dx by Ionization

  • Distribution of dE/dx usually called the “Landau Distribution”

Fluctuation in dE/dx – Gaussian Peak

  • Most interactions involve little energy exchange and there are many of them.

  • The total energy loss from these interactions is a Gaussian (central limit theorem)

Fluctuation in dE/dx – Gaussian Peak

  • For a Gaussian distribution resulting from N random events the ratio of the width/mean  1/N

  • Increasing the thickness of the detector decreases the relative width of the Gaussian peak:

    • (from Bethe)

Fluctuation in dE/dx – High Energy Tail

  • The probability of a interaction that involves a significant fraction of the particles energy is low. However such interactions produce a large signal in the medium.

Fluctuation in dE/dx – High Energy Tail

  • Energy loss is in the form of “d-rays” –scattered electrons with appreciable energy.

  • Energy deposited in a thin detector can be different from the energy lost by the particle – the d-electron can have enough energy to leave the detector.

  • Depending on the thickness of the detector there may not be any d-electrons produced.

dE/dx – High Energy Tail

  • Because of the high energy tail increasing the thickness of the detector does not improve the dE/dx resolution much.

    • Relative width of Gaussian peak reduces, so would expect to get better estimate of mean dE/dx, but….

    • Probability of high energy interaction rises, so tail gets bigger.

  • Usual method of measuring dE/dx is to take several samples and fit distribution (or just discard values far from Gaussian peak)

Multiple Scattering

Deflection of a charged particle by large numbers of small angle scatters.

Multiple Scattering

  • Looking at dE/dx from ionization, ignore nuclei.

    • Energy transfer small compared to scattering from (lighter) electrons.

  • However, scattering from nuclei does change the direction of the particles momentum, if not its magnitude.

    • Deflection of particle’s path limits the accuracy with which the curvature in a magnetic field can be determined, and hence the momentum measured.

“Single Scattering”

  • Deflections are in random directions

    • “Drunkards Walk”

  • Total deflection from N collisions  N

  • The angular deflection caused by a single collision is well modelled by the Rutherford Scattering formula:

    ds/dW  1/q4  ds/dq  1/q3

    Most probable scatter is at small angle

Multiple Scattering

  • RMS angular deflection, projected onto some plane:

    • RMS deflection  x

    • Length scale is the radiation length X0

Multiple Scattering – Probability Distribution

  • Small scattering angles - many small scatters. Gaussian

  • Large scattering angles from single large scatters. Probability  1/q3

Quantum Fluctuations

  • A signal consists of a finite number of quanta (electrons, photons,….)

  • If at some stage in detection chain the number of quanta drops to N then the relative fluctuation in the signal will be:

  • NB. Any subsequent amplification of the signal will not reduce this relative fluctuation

Quantum Fluctuations – Poisson Distribution

  • If the number of quanta is small then the probability of producing m quanta when the average is n is:

  • Probability of producing no signal:

    Efficiency of detector reduced by (1- e-n)

Quantum Fluctuations –Fano Factor

  • If the energy deposited by a particle is distributed between many different modes, only a small fraction of which give a detectable signal then the Poisson distribution is applicable.

    • E.g. scintillation detector: small fraction of deposited energy goes into photons. Only few photons reach light detector.

Quantum Fluctuations: Fano Factor

  • If most of deposited energy goes into the signal then Poisson statistics are not applicable.

    • E.g. Silicon detector – energy can either cause an electron-hole pair (signal detection and most likely process) or phonons.

  • In this case the fractional standard deviation:

    • F is the “Fano factor” (F ~ 0.12 for Si detector)

Electronic Noise

  • Most modern detectors produce and electrical signal, which is then recorded.

  • Electronic circuits produce noise – with careful design this can be minimized.

  • Consider different sources of intrinsic noise:

    • Johnson noise

    • Shot noise

    • Excess noise.

Johnson Noise

  • Appears across and resistor due to random thermal motion of charge carriers.

    • k : Boltzmanns constant

    • T : Temperature above absolute zero

    • B : Bandwidth ( range of frequency considered)

  • White noise spectrum (same noise power per root Hz at all frequencies)

Shot Noise

  • Fluctuation in the density of charge carriers ( “rain on a tin roof” )

  • White noise spectrum

Excess Noise

  • Anything other than Johnson and shot noise.

  • Depends on details of electronic devices (e.g. transistors)

  • Often has a 1/f spectrum ( same power per decade of frequency )

“Typical” Detector Front-End

Equivalent Circuit:

Noise: Dependence on Amplifier Capacitance.

  • The input resistance and capacitance of a detector “front end” form a low-pass filter which filters the Johnson noise from the input resistance:

Noise: Dependence on Amplifier Capacitance.

  • “Filtered” noise:

  • Noise spectrum :

  • Integrate over all frequencies to get total noise energy:

Noise: Dependence on Amplifier Capacitance.

  • Amplifier noise often expressed in terms of the number of electrons, DN, that would generate the same output.

  • Q = CV = e DN

  • Hence:

  • Johnson noise increases with the input capacitance of the pre-amplifier.

Overall Statistical Error

  • Depends on detector and the quantity measured, but…

  • For quantity like dE/dx which is estimated from the signal size:

  • S = A E

    • S=measured signal

    • E=primary signal , A=amplification

Overall Statistical Error

  • First term is fluctuation in production of interaction process ( e.g. Landau distribution of –dE/dx)


Overall Statistical Error

  • Signal is made up of a number of quanta ( electrons, photons, ions, … ).

  • Second terms comes from the fluctuation in the number of quanta, ns , ( F is the Fano factor)


Overall Statistical Error

  • In general, not all the quanta in the signal are collected – there is a “statistical bottle-neck” where the number of quanta, nh , is a minimum.

  • The contribution to the error due from this bottleneck is approximated by the third term:


Overall Statistical Error

  • Many detectors have an amplification stage (e.g. drift chambers have gain due to avalanche near the anode wire)

  • The gain process will have some fluctuation, represented by the fourth term

    • Each quanta produces on average A quanta after amplification.


Overall Statistical Error

  • There is a contribution to the uncertainty in the signal from the noise in the readout electronics. The noise tends to have the same amplitude regardless of the size of the signal, so contributes to ss/S like D/S

  • Described by the fifth term.


Energy Measurement Fluctuations

  • As already remarked:

    • Precision of momentum measurement (tracking) deteriorates at large momentum

    • Energy measurement precision (calorimeter) generally improves as energy increases.

Response of PbWO4 calo

to 120GeV e-

Energy Measurement fluctuations

  • Statistical fluctuations (n.quanta)1/2

  • Contributions from noise ~ constant

  • “systematics”  signal

  • (Fluctuations much smaller for EM than hadronic showers)

The “general purpose” detector

Often a detector has to cope with many different types of particle of many different energies.

 Construct a system of detectors allowing measurement of different aspects of different particles.

The “General Purpose” Detector

Typically a general purpose detector will have three main parts:

Tracking (charged particles, magnetic field)

Calorimeter (electrons, photons, hadrons)

Muon tracking (generally only muons get this far)

The “General Purpose” Detector

Tracking - will generally cross the tracking detector without leaving a signal.

Desirable – don’t want to scatter the photon or convert to charged particles. minimize material.

But, some will pair convert.

Calorimeter -will produce an EM shower.

Length scale X0.

Contained in EM portion of calo.

Muon tracking – won’t reach

General Purpose Detector: Photons

Tracking – will leave a trail of ionization.

Measure curvature to measure momentum.

Some will undergo Bremsstrahlung.

Calorimeter -will produce an EM shower.

Same as for photons.

Muon tracking – won’t reach

General Purpose Detector: Electrons

Tracking – charged hadrons will leave a trail of ionization.

Calorimeter -will produce an hadronic shower.

Length scale l0

Energy in both EM and hadronic parts of calo.

Muon tracking – won’t reach

General Purpose Detector: Hadrons

Tracking –will leave a trail of ionization.

Bremsstrahlung not a problem.

Calorimeter –X0for muons so long that no shower takes place.

Still deposits energy by ionization.

Muon tracking – crosses, leaving track of ionization

General Purpose Detector: Muons

Tracking – Decay close to interaction point. If daughters are charged may be able to reconstruct decay vertex.

Calorimeter, Muon tracking- primary particle never reaches, but daughters may.

General Purpose Detector: Tau, B-mesons, D-mesons

CMS (Compact Muon Solenoid)

CMS Cryostat Vacuum Tank

CMS – Transverse Slice

CMS “Event Display”

Zeus (800GeV p, 30GeV e+)

Zeus (800GeV p, 30GeV e+)

ZEUS “Compensating Calorimeter”

  • Response to hadrons and electrons of equal energy is not the same ( for hadrons energy lost in nuclear binding energy and nuclear fragments

Compensating Calorimeter

  • Can produce e/h ~ 1 by making absorber out of Uranium – hadronic shower induces fission, and emission of gamma-rays which deposit energy “compensating” for loss in binding energy etc. ( ZEUS calo)

  • Can also compensate by having fine-grained calorimeter, and trying to separate out EM and hadronic parts of shower ( e.g. H1 liquid argon calo )

Compensating Calo

Produce visible light

Transport to a light detector

Total internal reflection

Wavelength shifting fibres.

Convert to an electrical signal

Total Internal Reflection













Light Detector



















Scintillation detectors

Total Internal Reflection

  • A ray of light is incident on a boundary between two refractive indices is deflected.

  • If the angle of incidence, qi , is greater than the “critical angle” , qc , the light is totally internally reflected.

  • Sin(qc)= n2/n1

Total Internal Reflection – Fraction of Light Trapped

  • Estimate the fraction of light trapped by TIR by integrating over the solid angle

  • E.g. light trapped in a scintillating fibre:

TIR – Fraction of Light Trapped

  • Fraction trapped , f =

    (solid-angle, qi>qc)/(total solid-angle)

  • Put q = p- qi

  • dW= df d(Cosq) = Sinq df dq

Typically only get a few photons at light detector due to passage of particle

 Need a detector sensitive at the single-photon level.

Photomultiplier tube

Avalanche photo-diode

Hybrid photodiode

Light Detectors

Light falls on a photocathode in an evacuated tube and electrons emitted (photoelectric effect)

Quantum Efficiency depends on cathode material and wavelength ( QE ~ 25% )

Photoelectrons focused and accelerated towards the first dynode by electric field.

Photomultiplier Tube

When photoelectron strikes dynode several electrons emitted (on average) n ~ 5

Several dynodes ( ~ 10 ) give high gain ( 107)

PMT sensitive to magnetic field – need screening in many applications

Photomultiplier Tube


  • If a photon falls on a semiconductor an electron/hole pair can be created if the photon energy is greater than the band-gap  photodiode.

Avalanche Photodiode

  • Light output from scintillator normally too low to allow the use of photodiodes

    • No gain  output signal lost in noise of readout.

  • Increase bias to a point where electrons/holes collide with lattice with sufficient energy to generate new electron/hole pairs  avalanche photodiode (APD)

Avalanche Photodiode

  • Gain ~ 100 in linear mode ( can be operated in “Geiger Muller” mode)

  • Compact

  • Low sensitivity to magnetic field

Hybrid Photodiode

  • Like photomultiplier tube, has a photocathode in an evacuated envelope

  • Photoelectrons accelerated towards a reverse-biased solid-state diode ( e.g Si)

Hybrid Photodiode

  • When accelerated photoelectron hits diode ( ~ kV ) it liberates several electron-hole pairs.

    • Energy for one electron-hole pair in Si ~ 3.6eV

    • Gain ~ 1000

  • Can also use avalanche photodiode to get extra gain

  • Less sensitive to magnetic field than PMT

  • Can have bigger light sensitive area than APD

  • Can divide diode in to “pixels” to get position of photons

Hybrid Photodiode

  • Used in e.g. readout of CMS HCAL

  • Wavelength shifting fibres used to couple light from scintillating sheets.

Scintillating Materials

Scintillating Materials

  • Emit light when excited by passage of charged particle

  • To be useful should be transparent to the light they produce.

  • Two types ( more or less ):

  • Organic (work at molecular level)

  • Inorganic (work at crystal level)

Organic Scintillators

  • Scintillation is a property of the individual organic molecules:

    • Cartoon of molecular energy levels

Organic Scintillators-Light Emission

  • Passage of charged particle excites molecule.

  • Can decay radiatively with photon energy , Eemission = EB1 – EB0

  • B0 rapidly decays to A0 by exchanging vibrational quanta with surroundings

Organic Scintillators-Light Absoption

  • Scintillator will absorb light – molecule state A0A1 ( atomic spacing doesn’t have time to change )

  • Photon energy Eabsorption = EA1 – EA0

  • Eabsorption> Eemission

  • Emission and absorption spectra not the same.

     Scintillator transparent to the light it produces (but usually put in a wavelength-shifter to move out of UV)

Bicron BCF-91A

Plastic wavelength shifter

Organic Scintillator

  • Plastic common. E.g. polystyrene doped with fluorescent molecules which shift the emission from UV to visible.

  • Can be in solid or liquid form.

  • Atomic number, Z, low. Density low.

    • Good or bad, depending on application

  • Fraction of energy converted to light is lower than for inorganic scintillators

    ~ 10 photons per keV deposited ( ~ 1% of energy deposited, or about 10,000 photons/cm for MIP)


Impurity levels


Inorganic Scintillators

  • Depend on properties of crystal.

  • Interaction of atoms in lattice broaden energy levels of individual atoms into bands.

  • In an insulator, valence band is full , conduction band is empty.

    • Electrons “locked into position”, (no available energy states)

    • If promoted to conduction band, electrons are free to move

Inorganic Scintillators

  • If promoted to conduction band electrons will move through lattice until trapped by an impurity/defect in the lattice or a deliberately introduced dopant

Inorganic Scintillators

  • For some traps, the electron decays by emitting a photon (scintillaton)

    • Electron decays from some traps without emitting light (quenching)

  • Efficiency ( ~ 10% ) higher than for organic scintillators.

  • Often high Z (low X0) – good for x-ray detection

  • More expensive than organic.

Position Detectors

Silicon diodes.

Gas ionization chambers.









Semiconductor Detectors

  • High ionisation density in solids – particularly semiconductors due to small band gap

    • Small excitation energy  large thermal background

  • p-n junction gives depletion region with few free charge carriers

Semiconductor detectors

  • Diffusion of holes from p-type into n-type

  • Diffusion of electrons from n-type into p-type

  • Results in charge separation.

Semiconductor detectors

  • Charge separation causes electric field which opposes further diffusion ( and sweeps free charge out of depletion layer)

Semiconductor Detectors

  • Depletion region widened by reverse bias voltage.

    • Thickness ~ 100’s mm

  • Ionisation in depletion layer collected on strips.

    • In a 300 mm depletion layer will give ~ 25000 electron-hole pairs for a MIP

    • Can “mass produce” pre-amplifiers with noise ~ 1000 electron-equivalent.

Semiconductor – Pulse Shape

  • View junction as a parallel plate capacitor.

  • As ionization charge moves within depletion region, charge flows into the “plates” of the capacitor to maintain constant voltage.

  • If charge, e, moves by distance dx then the charge dQ flows into the diode:

  • Pulse shape determined by drift of charges in junction.

High Precision Silicon Vertex Detectors

This matrix of silicon microstrip detectors was at the heart of the ALEPH detector at LEP

Tracking With Precision Vertex Detectors

1 cm

event observed in the Delphi Vertex detector

Tracking With Precision Vertex Detectors

1 cm

event observed in the SLD detector

Movement of charges in gases

  • At modest E fields, electrons and positive ions drift at constant velocity

    • Careful choice of gas to avoid absorbing electrons.

    • If B field is present, drift is at an angle to the lines of E (Lorentz angle)

    • Can use time for electrons to arrive at anode to get distance of track from wire.

  • If electrons gain enough energy between collisions (ie. In one mean free path) multiplication of electron/ion pairs results ( needs large E )

Movement of charges in gases

  • Behaviour of electrons and ions in gas depends on details of gas mixture and electric (and magnetic) field

    • Drift velocity, Lorentz velocity, gain

  • Ions, being much heavier than electrons, have slower drift velocity and do not give amplification.

  • Like, Si detectors, velocity of charges determines pulse shape.

    • Fast part from electrons, slow “tail” from ions

Gas ionisation detectors

  • Thin (20–30m diameter) anode wires provide gain, due to electron avalanche in high field region near the wire ( E  1/r )

  • Many variants

    • Geiger counter

    • Multi-wire proportional chamber MWPC

    • Drift chamber

    • Time Projection Chamber TPC

    • MicroStrip Gas Chamber MSGC

Liquid Ionization Detectors

  • Usually liquid noble gas – eg. Argon.

  • No gain ( mean free path short, so electrons don’t get enough energy to cause further ionization)

  • Use in calorimeters ( e.g. H1 , Atlas )

    • Don’t care about multiple scattering

    • High density  many electron/ion pairs

    • No gain  less danger of signal saturation

Cerenkov counters for particle identification

  • Reminder: Cerenkov angle and intensity depend on particle velocity and refractive index of the medium

  • If momentum is known, measurements of  give b and hence particle mass and type

  • Cerenkov detectors used for p/K separation at medium or high energies

Cerenkov detectors

  • Cerenkov counters consist of radiator medium plus a photon detector

  • Use of liquid, gas or aerogel radiators gives a range of refractive index

  • Photon detectors usually either PM tubes or doped gas ionisation detector

  • Different detector layouts:

    • Threshold Cerenkov

    • Differential Cerenkov

    • Ring-imaging Cerenkov (RICH)

  • Very large liquid filled detectors used for neutrino detection


  • Silica based “foam”.

  • Tune refractive index by fraction of air ( ~ 99.8% air)

Super-K: Large Water Cerenkov detector for neutrinos

Threshold Cerenkov

  • All charged particle above b threshold will give a signal.

  • Adjust threshold by adjusting refractive index

    • Gas for high threshold (has low , adjust with pressure)

    • Liquid for low threshold (high )

Differential Cerenkov

  • Use circular annular collimator slit – only accepts light at a range of angles

    • Only get signal if particle in right b range.

  • Only works if particles on-axis

    • Useful for “tagging” particles in a low intensity beam,

Ring-imaging Cerenkov

The DELPHI Detector

DELPHI at LEP features extensive particle identification capability from its TPC and RICH counters

Conclusion: Aims

  • To introduce the interactions of fast particles and high-energy photons in materials, particularly those types of interaction which are important for particle detection and measurement.

Conclusion:“Learning outcomes”

  • Understand those properties of stable and long-lived particles important for their detection. Able to perform calculations of scattering kinematics and mean decay paths for relativistic particles.

Conclusion:“Learning outcomes”

  • Understand the variation of ionisation energy loss for charged particles as a function of velocity, as given by the Bethe-Bloch formula. Appreciate the physical origin of the various terms in this formula. Able to describe the underlying physics of other important energy-loss processes.

Conclusion:“Learning outcomes”

  • Understand the operation of certain types of detector. Able to analyse the effect of counting fluctuations on the performance of detectors. Understand the response of detectors to different particle types. Know the design elements of a "general purpose" particle detector.

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