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C. W. Fabjan and D. Fournier
be as low as 0.6 when the Z of the passive material (lead) is much larger than the Z
of the active one (plastic scintillator, liquid argon). This effect, well reproduced by
Monte-Carlo simulations, is to some extent due to the “transition effect” between
the passive and active material, but also due to the fact that a significant fraction
of electrons produced in the high Z passive material by pair production or Compton
scattering do not have enough energy to exit this layer and are thus not sampled. This
same effect induces a depth dependence of e/mip, which decreases by few percent
towards the end of the shower.
Taking into account an energy independent contribution from electronics noise b,
and a minimum asymptotic value of the relative energy resolution c (constant term,
due for example to inhomogeneities in materials, imperfection of calibrations, . . . )
the energy resolution of a sampling calorimeter is in general written as 1
ΔE/E = a/
√
E ⊕ b/E ⊕ c
(6.23)
Experimentally it has been observed that the same relation holds also for
homogeneous calorimeters, in general with smaller ‘sampling terms’ a, although
their origin is not coming from sampling fluctuations, but from other limitations
(see Sect. 6.2.3).
6.2.5 Physics of the Hadronic Cascade
By analogy with electromagnetic showers, the energy degradation of high-energy
hadrons proceeds through an increasing number of (mostly) strong interactions with
the calorimeter material. However, the complex hadronic and nuclear processes produce a multitude of effects that determine the performance of practical instruments,
making hadronic calorimeters more complicated instruments to optimize and resulting in a significantly worse intrinsic resolution compared to the electromagnetic one.
Experimental studies by many groups helped to unravel these effects and permitted
the design of high-performance hadron calorimeters.
The hadronic interaction produces two classes of secondary processes. First,
energetic secondary hadrons are produced with momenta typically a fair fraction
of the primary hadron momentum, i.e. at the GeV scale. Second, in hadronic
collisions with the material nuclei, a significant part of the primary energy is
consumed by nuclear processes such as excitation, nucleon evaporation, spallation,
etc., generating particles with energies characteristic of the nuclear MeV scale.
The complexity of the physics is illustrated in Fig. 6.17, which shows the energy
spectra of the major shower components (weighted by their track length in the
shower) averaged over many cascades, induced by 100 GeV protons in lead. These
spectra are dominated by electrons, positrons, photons, and neutrons at low energy.
1 In a formula like (6.23), a ⊕ b means
√
(a 2 + b 2 ).
C. W. Fabjan and D. Fournier
be as low as 0.6 when the Z of the passive material (lead) is much larger than the Z
of the active one (plastic scintillator, liquid argon). This effect, well reproduced by
Monte-Carlo simulations, is to some extent due to the “transition effect” between
the passive and active material, but also due to the fact that a significant fraction
of electrons produced in the high Z passive material by pair production or Compton
scattering do not have enough energy to exit this layer and are thus not sampled. This
same effect induces a depth dependence of e/mip, which decreases by few percent
towards the end of the shower.
Taking into account an energy independent contribution from electronics noise b,
and a minimum asymptotic value of the relative energy resolution c (constant term,
due for example to inhomogeneities in materials, imperfection of calibrations, . . . )
the energy resolution of a sampling calorimeter is in general written as 1
ΔE/E = a/
√
E ⊕ b/E ⊕ c
(6.23)
Experimentally it has been observed that the same relation holds also for
homogeneous calorimeters, in general with smaller ‘sampling terms’ a, although
their origin is not coming from sampling fluctuations, but from other limitations
(see Sect. 6.2.3).
6.2.5 Physics of the Hadronic Cascade
By analogy with electromagnetic showers, the energy degradation of high-energy
hadrons proceeds through an increasing number of (mostly) strong interactions with
the calorimeter material. However, the complex hadronic and nuclear processes produce a multitude of effects that determine the performance of practical instruments,
making hadronic calorimeters more complicated instruments to optimize and resulting in a significantly worse intrinsic resolution compared to the electromagnetic one.
Experimental studies by many groups helped to unravel these effects and permitted
the design of high-performance hadron calorimeters.
The hadronic interaction produces two classes of secondary processes. First,
energetic secondary hadrons are produced with momenta typically a fair fraction
of the primary hadron momentum, i.e. at the GeV scale. Second, in hadronic
collisions with the material nuclei, a significant part of the primary energy is
consumed by nuclear processes such as excitation, nucleon evaporation, spallation,
etc., generating particles with energies characteristic of the nuclear MeV scale.
The complexity of the physics is illustrated in Fig. 6.17, which shows the energy
spectra of the major shower components (weighted by their track length in the
shower) averaged over many cascades, induced by 100 GeV protons in lead. These
spectra are dominated by electrons, positrons, photons, and neutrons at low energy.
1 In a formula like (6.23), a ⊕ b means
√
(a 2 + b 2 ).