1. Mauricio Barbi University of Regina TRIUMF Summer Institute July 2007
Calorimetry - 1
Mauricio Barbi
University of Regina
TRIUMF Summer Institute
July 2007

2. Some Literature
“Detector for Particle Radiation”, Konrad Kleinknecht, Cambridge University Press
“Introduction to Experimental Particle Physics”, Richard Fernow, Cambridge University Press
“Techniques in calorimetry”, Richard Wigmans, Cambridge University Press
Particle Data Group (PDG):
Thanks to Michele Livan (INFN and Pavia University) for letting me use some of his material and examples in these lectures

3. Principles of Calorimetry (Focus on Particle Physics)
Lecture 1:
Introduction
Interactions of particles with matter (electromagnetic)
Definition of radiation length and critical energy
Lecture 2:
Development of electromagnetic showers
Electromagnetic calorimeters: Homogeneous, sampling.
Energy resolution
Lecture 3:
Interactions of particle with matter (nuclear)
Development of hadronic showers
Hadronic calorimeters: compensation, resolution

4. Introduction  http://en.wikipedia.org/wiki/Calorimeter:
 A calorimeter is a device used for calorimetry
 Calorimetry is the science of measuring the heat generated or absorbed in a
chemical reaction or physical process.
 The word Calorimeter comes from the Latin
calor meaning heat, and from the Greek metry
meaning to measure.
 A primitive calorimeter was invented by Benjamin Thompson (17th century)
“When a hot object is set within the water, the system's temperature increases. By measuring the increase in the calorimeter's temperature, factors such as the specific heat (the amount of heat lost per gram) of a substance can be calculated.” (
Bomb calorimeter

5. Introduction
Specific heat is the amount of heat per unit mass required to raise the
temperature by one Kelvin:
Q = heat added (energy)
c = specific heat
m = mass
T = change in temperature
0.2
0.84
Glass
0.19
0.79
Granite
0.49
2.05
Ice (-10 C) 1
4.186
Water
0.58
2.4
Alcohol(ethyl)
0.033
0.14
Mercury
0.0925
0.387
Zinc
0.0321
0.134
Tungsten
0.0558
0.233
Silver
0.0305
0.128
Lead
0.0301
0.126
Gold
0.092
0.38
Brass
0.0923
0.386
Copper
0.0294
0.123
Bismuth
0.215
0.9
Aluminum
c in cal/gm K
c in J/gm K
Substance

6. Introduction How to measure the energy of a particle?
Let’s consider that we have a calorimeter with 1 liter of water as absorber. Using the
formula and table from previous slide, let’s solve the following problems?
What is the effect of a 1 GeV particle (e.g., at LHC) in the calorimeter?
This is a far too small temperature change to be detected in the calorimeter.
New techniques of detection are needed in particle physics.

7. Introduction Still at http://en.wikipedia.org/wiki/Calorimeter:
 In particle (and nuclear) physics, a calorimeter is a component of a
detector that measures the energy of entering particles

8. Introduction Main goals:
Provide information to fully reconstruct the 4-vector p= (E,p) of a particle
Complementary to tracking detectors at very high energies:
Provide particle ID based on different energy deposition pattern for different particles species (e/π, etc)
Though neutrinos are not directly detected, they can be identified from the missing energy needed for energy conservation to hold
Segmentation of the calorimeter can also provide space coordinates of particles. Time information also possible with high resolution achievable
Usually important in removing background (cosmic rays, beam spills, etc)

9. Introduction Basic principles: Sensitive to both charged
(e±, ±, π±, etc) and neutral
particles (, π0, etc)
Total energy absorption
Particle is “completely destroyed”
Destructive process
The mechanism evolves as:
Entering particle interact with matter
Energy deposition by development of showers of decreasingly lower-energy particles produced in the interactions of particle with matter
Electromagnetic showers  produced by electromagnetic processes
Hadronic showers  produced by hadronic processes (+ EM components)
The energy of the particles produced in the showers is converted into ionization or excitation of the matter which compounds the calorimeter  energy loss
The calorimeter response is proportional to the energy of the entering particle (note the statistical process in the previous item)  σ(E)/E=A/E-1/2

10. Introduction Calorimeter is a complicate device:
Particle has to be completely absorbed in order to have its energy fully detected
Depends on detector material, its size and geometry
Several things happen during this process
Showers are product of competing physics interactions between particle and matter
Again, this depends on detector material
Particle ID and energy measurement through development of showers (with exception of muons)
Statistical processes  fluctuations  detector resolution
Depends on the energy of the particle, calorimeter uniformity, etc
Detector material, its size and geometry to fully contain the showers
Different calorimeter types for different physics goals
Faster response? Better energy resolution? Spatial coordinates? Hadronic particles? EM particles? Etc…..

11. Introduction
More about EM interaction of particle with matter in this lecture
Development of showers and
energy resolution in the next lecture εK εL e  
atom
Atomic electron 
Free electron
Compton scattering
EM shower in a sampling calorimeter

12. Introduction Some applications of calorimetry in particle physics
Basic mechanism used in calorimetry in particle physics to measure energy
Cherenkov light
Scintillation light
Ionization charge

13. Introduction Neutrino physics Super-Kamiokande (SK) - Japan
Measurement of neutrino oscillations
Water as active material
Energy measurement through Cherenkov
radiation
~12K PMTs
50K metric ton of water

14. Introduction Ultra high energy cosmic ray
The Pierre Auger Observatory (world’s largest calorimeter)
Measure charged particles with E > 1019 eV
Atmosphere as the calorimeter
Surface detectors to
measure energy
and shower profile
3000 Km2
Air shower
16K water Cherenkov detectors

15. Introduction Collider experiments ZEUS at HERA e-p collider, Germany
Study the proton structure and confront QCD predictions
Uranium-scintillator sampling calorimeter
Energy measured using scintillating light
Rear calorimeter
Forward calorimeter
Central tracking
Barrel calorimeter

16. Electromagnetic Calorimeters
Introduction
Collider experiments
ATLAS at LHC p-p collider, Switzerland
Search for Higgs, SUSY particles, CP violation, QCD, etc
Liquid Argon/Pb (EM) and Cu (or W) (Hadron) sampling Calorimeter
Energy measured using ionization in the liquid argon
Solenoid
Forward Calorimeters
Muon Detectors
Electromagnetic Calorimeters
EndCap Toroid
Barrel Toroid
Inner Detector
Hadronic Calorimeters
Shielding

17. Interactions of Particles with Matter
We have seen that the calorimeter is based on absorption
It is important to understand how particles interact with matter
Several physics processes involved, mostly of electromagnetic nature
Energy deposition, or loss, mostly by ionization or excitation of matter
One can initially separate the interactions into two classes
Electromagnetic (EM) processes (this lecture):
Main photon interactions with matter:
Compton scattering
Pair Production
Photoelectric effect
Main electron interactions with matter:
Bremsstrahlung
Ionization
Cherenkov radiation (not covered in this lecture)
Hadronic processes: more complicate business than EM nuclear interactions between hadrons (charged or neutral) and matter

18. Interactions of Particles with Matter
Interactions of Photons
For a beam of photons traversing a layer
of material (Beer-Lambert’s law):
α = /ρ is called mass
absorption coefficient.
Also,
λ = α-1 [g/cm2] = photon mass attenuation length ρ x
Probability that the photon will interact in thickness X of material

19. Interactions of Particles with Matter
Interactions of Photons
Photon attenuation length for different elemental absorbers versus photon energy
Note the different patterns for different elements  different response to photons as a function of the photon energy
Why?  Next slide

20. Interactions of Particles with Matter
Interactions of Photons
Cross-section for photon absorption
Total cross-section σ for photon absorption is related
to the total mass attenuation length λ:
Several processes contribute to the total cross-section:
The “+…” in the above expression includes:
Rayleigh scattering, where the atom is neither ionized or excited
Photonuclear absorption
Therefore, different
processes contributes with
different attenuations:

21. Interactions of Particles with Matter
Interactions of Photons
Cross-section for photon absorption
Since a calorimeter has to fully absorb the energy of an interacting photon:
Important to understand the cross-sections as a function of the photon energy in different material
Will ultimately define the geometry and composition of a calorimeter
The cross-section calculations are difficult due to atomic effects, but there are fairly good approximations:
Depend on the absorber material
Depend on the photon energy
Let’s then visit some of the processes cited in the previous slide

22. Interactions of Particles with Matter
Interactions of Photons
Photoelectric effect
Can be considered as an interaction between a
photon and an atom as a whole
Can occur if a photon has energy E > Eb
(Eb = binding energy of an electron in the atom).
The photon energy is fully transferred to the electron
Electron is ejected with energy T = E - Eb
Discontinuities in the cross-section due to discrete
energies Eb of atomic electrons
(strong modulations at E=Eb; L-edges, K-edges, etc)
Dominating process at low ’s energies ( < MeV ).
 Gives low energy electrons
p.e. cross-section in Pb
Kleinknecht E

23. Interactions of Particles with Matter
Interactions of Photons
Photoelectric effect
 Cross-section:
Let (reduced photon energy)
For εK < ε < 1 ( εK is the K-absorption edge):
For ε >> 1 (“high energy” photons):
σp.e goes with Z5/ε εL εK
p.e. cross-section in Pb εK
ε = 1 E

24. Interactions of Particles with MatterεK εL e  
atom
Atomic electron 
Free electron
Interactions of Photons
Compton scattering
 A photon with energy E,in scatters off an
(quasi-free) atomic electron
 A fraction of E,in is transferred to the electron
 The resulting photon emerges with E,out < E,in
and at different direction
Using conservation of energy and momentum:
The energy of the outgoing photon is:
, where E

25. Interactions of Particles with Matter
Interactions of Photons
Compton scattering
 The energy transferred to the electron:
Two extreme cases of energy loss:
  0 : E,out  E,in ; Te  0
 No energy transferred to the electron
Backscattered at  = π :
Compton edge
Coherent scattering
(Rayleigh)
E,out / E,in
Incoherent scattering
(electron is removed from atom) εK
ε = 1
E,in [MeV] E

26. Interactions of Particles with Matter
Interactions of Photons
Compton scattering
Total Compton cross-section per electron given by Klein-Nishina (QED) (1929): .
Two extreme cases:
ε << 1 :
 Backward-forward symmetry in  distribution
ε >> 1 :
  distribution peaks in the forward direction
Cross-section per atom:
Incoherent scattering only
Includes coherent and incoherent scattering

27. Interactions of Particles with Matter
Interactions of Photons
Pair Production
 An electron-positron pair can be created when
(and only when) a photon passes by the Coulomb
field of a nucleus or atomic electron  this is
needed for conservation of momentum.
Threshold energy for pair production at
E = 2mc2 near a nucleus.
E = 4mc2 near an atomic electron
 Pair production is the dominant photon interaction process at high energies. Cross-
section from production in nuclear field is dominant.
First cross-section calculations made by Bethe and Heitler using Born approximation (1934).
 + e-  e+ + e- + e-
 + nucleus  e+ + e- + nucleus

28. Interactions of Particles with Matter
Interactions of Photons
Pair Production (Attenuation length)
The interesting energy domain is that of several hundred MeV or more,
The cross- section per nucleus is:
Does not depend on the energy of the photon, but
Mass attenuation length for pair creation (check few slides ago): or
Accurate to within a few percent down to energies as low as 1 GeV
X0 is called radiation length and corresponds to a layer thickness of material where
pair creation has a probability P = 1 – e-7/9  54%

29. Interactions of Particles with Matter
Interactions of Photons
Pair Production
Photon pair conversion
probability
P=54%

30. Interactions of Particles with Matter
Interactions of Photons
Pair Production (Attenuation Length)
Along with Bremsstrahlung (more later), pair production is a very important process
in the development of EM showers  X0 is a key parameter in the design of a
calorimeter
There are more complicate expressions for X0 in the literature:
(PDG,
Lrad is similar to the expression for X0 in the previous slide
L’rad replaces 183Z-1/3 by 1194Z-2/3
f(z) is an infinite sum which, for elements up to U, can be approximate to
Where a = αZ
PDG also gives a fitting function:

31. Interactions of Particles with Matter
Interactions of Photons
Pair Production
For compound
mixtures:
Where,
wj = weight
fraction of each
element in the
compound
j = “jth” element

32. Interactions of Particles with Matter
Interactions of Photons
Summary
Photoeletric effect
Energy range versus Z for more likely process:
Pair production
Rayleigh
scattering
Compton
Michele Livan

33. Calorimeters?
Curiosity  Primitive calorimeter invented by Benjamin Thompson (17th century):
“We owe the invention of this device to an observation made just before the turn of the nineteenth
century by the preeminent scientist Benjamin Thompson ( Count Rumford). While supervising the
construction of cannons, Rumford noticed that as the fire chamber was bored out, the metal cannons
would heat up. He observed that the more work the drill exerted in the boring process, the greater
the temperature increase. To measure the amount of heat generated by this process, Count Rumford
placed the warm cannon into a tub of water and measured the increase in the water's temperature. In
doing so, he simultaneously invented the science of calorimetry and the first primitive calorimeter.
In simplest terms, a modern calorimeter is a water-filled insulated chamber. When a hot object is set
within the water, the system's temperature increases. By measuring the increase in the calorimeter's
temperature, a scientist can calculate such factors as the specific heat (the amount of heat lost per
gram) of a substance. Another application of calorimetry is the determination of the calorific value of
certain fuels--that is, the amount of energy obtained when fuel is burned. Engineers burn the fuel
completely within a calorimeter system and then measure the temperature increase within the device.
The amount of heat generated by this burning is indicative of the fuel's calorific value. “ (