||Dr C N Booth
Neutrons, protons, pions etc. interact with nuclei through the strong interaction.
In passing through matter, a hadron can therefore build up a shower
through multiple interactions, in a similar way to that discussed for electrons
in electromagnetic calorimetry. The shower
can be parametrised by a nuclear interaction
length, similar to the radiation length for electromagnetic showers.
However, unlike the case of bremsstrahlung by high energy electrons, it
should be noted that:
Fluctuations in the amount of energy deposited are largely due to the variable
fraction of the shower which is converted into an electromagnetic shower,
by the production of fast neutral pions and their subsequent rapid decay
into energetic photons.
Many different final states are possible in high energy hadronic interactions
Up to 30% of incident energy may be lost due to
nuclear excitation and break-up
spallation or "evaporation" of slow neutrons and protons
production of muons and neutrinos which escape from the calorimeter.
The inelastic cross section, and hence the nuclear interaction length,
is a function of both the energy and type of incoming particle.
The interaction length of dense materials is much greater than the radiation
length. E.g. for iron it is about 17 cm.
Practical Hadronic Calorimetry
The nuclear interaction length of "active" detector material is so large
(e.g. 68 cm for scintillator) that calorimeters have to be sampling devices.
A typical calorimeter
therefore contains alternate layers of "absorber" (e.g. iron or copper)
and detector (e.g. plastic scintillators,
proportional counters or liquid
The typical energy
is about 50%/√E
(with E measured in GeV), limited largely by fluctuations in the
size of the electromagnetic part of the shower. The resolution can
sometimes be improved by one of two methods:
weighting With a finely segmented calorimeter, it is possible
to identify localised electromagnetic sub-showers within the overall shower,
and weight their contribution to match the hadronic signal.
If the calorimeter plates are made of depleted uranium, slow neutrons from
the hadronic shower induce fission, and fission products give an increased
signal in the detector medium. Compensation can also be achieved
by making the absorber plates sufficiently thin that a substantial fraction
of the slow nuclear products reach the detector regions.
Most practical calorimeters are combined electromagnetic and hadronic
detectors. Because the nuclear interaction length is so much bigger
than the radiation length, most hadrons pass through the electromagnetic
front compartment and interact in the hadronic part behind. The illustration
below shows a module of a combined calorimeter with a lead/scintillator
front electromagnetic section followed by an iron/scintillator rear hadronic
section. BBQ sheets are used to read out the scintillator with photomultipliers
behind the module. In this way, modules can be stacked next to each
other with minimal dead space between.
Other Calorimeter Designs
Barium Fluoride crystals can be used in an electromagnetic calorimeter.
Rather than detecting the (ultraviolet) photons with photomultipliers,
a special wire chamber is used, with a gas mixture easily ionised by u.v.
Calorimeters can be made with a matrix of scintillating fibres (in
stainless steel tubes) surrounded by lead. Because of the flexibility
of the fibres, these can be cast in whatever shape is required, and so
can make very "hermetic"
For a calorimeter to provide accurate energy measurements, more is needed
than a good intrinsic energy resolution. It should be highly uniform
and stable, and there should be a means of detecting any changes and correcting
for them. These features are provided by a calibration system.
The most significant limitation to the long term stability of a calorimeter
depends on the type of readout.
A light flasher can distribute light to the various scintillators over
optical fibres. If ultraviolet light is used, scintillation can be
induced in the detector, so better reproducing the normal behaviour.
A radioactive source can provide signals in the calorimeter. (In
a uranium calorimeter, the plates themselves act as sources!) Since
the decays are random, it is necessary to integrate the signal over a longer
time than for normal readout.
Particles with known properties are the best means of calibrating the calorimeter.
These may be high energy muons, which pass through the whole calorimeter
giving a signal (though they do not cause showers). At an electron-positron
collider, elastic scattering (known as Bhabha
scattering) provides a source of electrons of known energy, which are
very useful for calibrating electromagnetic calorimeters.
Scintillators may suffer from ageing and radiation
The purity of liquid in ionisation chambers may be difficult to maintain.
Non-uniformities in multi-wire proportional chambers may affect their performance.
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