70
P. Lecoq
contained in the detector block. The total energy deposited in the detector block is
the same whether it results from a single or multiple interactions. The light response
may however differ due to the non-linear response of the scintillator. As a result,
the event-to-event statistical variation of the energy deposition mechanism induces
a broadening of the resolution.
As pointed out in ref. [22] one would expect an improvement of the resolution
by reducing the detector size, as the fraction of fully contained Compton events
decreases and consequently the proportion of true photoelectric events increases.
This is actually not the case, because photoelectric events may result at the atomic
scale from a complex cascade mechanism. Indeed, the photoelectric interaction of
an X- or γ-ray produces a mono-energetic electron from one of the inner shells
of the atoms of the absorber. However, this electron can be ejected not only from
the K shell but also from a L or even a M shell (although the cross-section rapidly
decreases for higher core levels) of the different atoms of the crystal. In the sequence
of photon detection, recoil electrons with different energies are produced, each
carrying the incident photon energy minus the binding energy of the shell, from
which it has been ejected. Moreover, the deep hole produced in the inner shell
will be filled by an electron from outer shells, which in turn will be replaced by
electrons rom even lower bound shells through a cascade of relaxation events, each
of them producing an X-Ray or an Auger electron converting in the crystal following
the same mechanisms. Figure 3.12 depicts a part of this cascade process for LSO
crystals, commonly used in medical imaging cameras.
Finally, the recoil electrons, as well as all charged particles detected in a
scintillator, slow down through a sequence of energy transfers to the absorber with
a progressively increasing ionization density.
The energy resolution of calorimeters used in high or medium energy physics is
generally parametrized as a function of energy according to the following formula:
σ (E)
E
=
a
√
E
⊕
b
E
⊕ c
(3.14)
where a is the statistical term, b the noise term and c a constant term, which takes
into account all the systematics (intercalibration error, temperature effects, light
yield non-uniformity in the crystal, shower leakage, etc.).
At high energy, the constant term is predominant and it requires a challenging
engineering effort to reach the sub-percent level for large detector systems with tens
of thousands of channels. This has been achieved for the LEP L3 BGO calorimeter
(with 12,000 crystals) with a high energy resolution of 1% and in the LHC CMS
PWO calorimeter (77,000 crystals) with a constant term of better than 0.5%.
At lower energy, the electronic noise plays an increasing role. The noise
contribution, which is energy independent, contributes therefore to the relative
energy resolution (3.14) as 1/E.
An interesting example is given in Fig. 3.13 for two heavy Lutetium based
crystals popular for medical imaging devices, LSO and LuYAP. In spite of a light
P. Lecoq
contained in the detector block. The total energy deposited in the detector block is
the same whether it results from a single or multiple interactions. The light response
may however differ due to the non-linear response of the scintillator. As a result,
the event-to-event statistical variation of the energy deposition mechanism induces
a broadening of the resolution.
As pointed out in ref. [22] one would expect an improvement of the resolution
by reducing the detector size, as the fraction of fully contained Compton events
decreases and consequently the proportion of true photoelectric events increases.
This is actually not the case, because photoelectric events may result at the atomic
scale from a complex cascade mechanism. Indeed, the photoelectric interaction of
an X- or γ-ray produces a mono-energetic electron from one of the inner shells
of the atoms of the absorber. However, this electron can be ejected not only from
the K shell but also from a L or even a M shell (although the cross-section rapidly
decreases for higher core levels) of the different atoms of the crystal. In the sequence
of photon detection, recoil electrons with different energies are produced, each
carrying the incident photon energy minus the binding energy of the shell, from
which it has been ejected. Moreover, the deep hole produced in the inner shell
will be filled by an electron from outer shells, which in turn will be replaced by
electrons rom even lower bound shells through a cascade of relaxation events, each
of them producing an X-Ray or an Auger electron converting in the crystal following
the same mechanisms. Figure 3.12 depicts a part of this cascade process for LSO
crystals, commonly used in medical imaging cameras.
Finally, the recoil electrons, as well as all charged particles detected in a
scintillator, slow down through a sequence of energy transfers to the absorber with
a progressively increasing ionization density.
The energy resolution of calorimeters used in high or medium energy physics is
generally parametrized as a function of energy according to the following formula:
σ (E)
E
=
a
√
E
⊕
b
E
⊕ c
(3.14)
where a is the statistical term, b the noise term and c a constant term, which takes
into account all the systematics (intercalibration error, temperature effects, light
yield non-uniformity in the crystal, shower leakage, etc.).
At high energy, the constant term is predominant and it requires a challenging
engineering effort to reach the sub-percent level for large detector systems with tens
of thousands of channels. This has been achieved for the LEP L3 BGO calorimeter
(with 12,000 crystals) with a high energy resolution of 1% and in the LHC CMS
PWO calorimeter (77,000 crystals) with a constant term of better than 0.5%.
At lower energy, the electronic noise plays an increasing role. The noise
contribution, which is energy independent, contributes therefore to the relative
energy resolution (3.14) as 1/E.
An interesting example is given in Fig. 3.13 for two heavy Lutetium based
crystals popular for medical imaging devices, LSO and LuYAP. In spite of a light