Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

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610 Principles of Radiation Interaction in Matter and Detection

emission, etc. So, there is propagation of an ionization avalanche through the whole

gas volume and along the central wire, with a rapid collection of the electrons.

The positive ions, much slower, escape collection and create a positive cloud

around the central wire. The existence of this cloud terminates the avalanche pro-

cess since the electrons in this region are captured by these positive ions, before

reaching the anode. When the cloud of positive ions is near the cathode wall, the

electrons extracted from the wall by UV photons are captured. Some of the electrons

enter high energy orbits of the ions and can make transitions into lower energy orbits

with UV emission, eventually extracting electrons from the cathode wall and trig-

gering another avalanche and, therefore, a secondary pulse. The solution adopted

to prevent this secondary pulse is to use a quenching gas. Usually an organic com-

pound, this gas releases electrons, easily. The molecules of this gas can neutralize

the positive ions by giving them electrons which allows the conversion of the positive

ion-cloud into ionized molecules of the quenching gas.

The Geiger-Mueller counter produces very large pulses since the ionization

avalanche releases huge amount of charges. However, as seen above, the number

of electrons produced is independent of the applied voltage and independent of the

numb er of electrons produced by the initial ionization. Discrimination between in-

coming particles is not possible with this type of detector since the signal pulse is

independent of the type of radiation.

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Chapter 9

Principles of Particle Energy

Determination

9.1 Experimental Physics and Calorimetry

Collisions between two particle beams (collider experiments) or by a beam inter-

acting with a ﬁxed-target (ﬁxed-target experiments) or the interaction of cosmic

rays with space matter or the Earth’s atmosphere (astrophysics, gamma-ray as-

tronomy, cosmic-ray studies) frequently produce a variety of particles through very

complicated conﬁgurations of events covering a large solid angle.

The geometry of the collisions imposes a deﬁned structure to detectors. For in-

stance, detectors operating in collider experiments have a barrel structure, with end-

caps to cover the forward region. The occurrence of a large number of events to inves-

tigate and the variety of physics goals pursued impose the construction of a detector

composed of many sub-detectors assigned to dedicated tasks. These sub-detectors

have complementary capabilities which can be combined in a optimized way to mea-

sure the energy, mass, momentum, charge and direction of the particles produced. In

particular, the measurement of particle energy is performed with calorimeters. A

review of the properties of electromagnetic and hadronic shower propagation in

matter and of calorimeters was provided by Leroy and Rancoita (2000).

Calorimeters are instrumented blocks of matter in which the particle to be mea-

sured interacts and deposits all its energy in the form of a cascade of particles, whose

energy decreases progressively down to the threshold of ionization and excitations

that are detectable by the readout media. The deposited energy is detectable in the

form of a signal which is proportional to the incoming energy. This proportionality

is the base of calorimetry measurement.

Calorimeters contribute also to the measurement of the position and angle of

the incident particle. Their diﬀerent response to electrons, muons, and hadrons can

be exploited for particle identiﬁcation. Neutrinos, which interact only weakly with

matter, are detected through the absence of any energy deposit (missing energy).

Electromagnetic calorimeters are used to measure the energy deposited by elec-

tromagnetic particles (electrons, photons), while the hadron (such as pions, protons)

energy measurement is achieved with hadronic calorimeters. Furthermore, calorime-

ters are classiﬁed into two types: homogeneous calorimeters, where the incoming

611

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612 Principles of Radiation Interaction in Matter and Detection

particle energy is measured in a homogeneous block of sensitive absorbing material

(lead-glass, sodium iodide (NaI) crystal, bismuth-germanium oxide (BGO) crystal,

etc.), and the sampling calorimeters, where the incoming particle energy is measured

in a number of sensitive layers interspersed with the layers of absorbing material,

the latter speeding up the cascade process. Various active medium (scintillator,

silicon

∗

, liquid argon, gas, . . .) and absorbers (Fe, Cu, Pb, U, . . .) are used.

Calorimeters

†

of all types were used and are currently in operation in many

particle physics experiments. They have played a key role in recent experiments

leading to fundamental results like the discovery of the vector bosons W and Z

(UA1, UA2) [Arnison et al. (1983)] and of the top quark (CDF, D0) [CDF Collab.

(1988)]. Major searches and studies, e.g., the search for the quark gluon-plasma

in heavy-ion collisions at very high energy (NA-34/HELIOS, NA-35, WA-80) [HE-

LIOS Collab. (1988)], the study of e

−

collisions at LEP (ALEPH, DELPHI, L3,

OPAL) [LEP (1982)], the study of e-p collisions at HERA (H1, ZEUS) [H1 Collab.

(1993b)], and the search for possible neutrino oscillations (CHORUS [Eskut et al.

(1997)], NOMAD [Altegoer et al. (1998)]), also make large use of calorimeters. This

type of detector is also used in cosmic ray (for instance AMS [AMS Collab. (2002)]

and PAMELA

‡

[Boezio et al. (2006)]) and gamma-ray experiments (for instance

EGRET [Kanbach et al. (1988)], GLAST [GLAST Collab. (1998)]) performed in

space and in balloon (such as HEAT [Barwick et al. (1997)], CAPRICE [Bocciolini

et al. (1996)]) and in air shower experiments with particle detectors (e.g., KAS-

CADE [Klages et al. (1997)]).

Large calorimeters will be also important elements of the central detection sys-

tems that are needed to perform the high-luminosity experiments (ATLAS [AT-

LAS Collab. (1994a)], CMS [CMS (1994)], ALICE [ALICE (1993)], LHC-B) at the

Large Hadron Collider (LHC) in the LEP tunnel at CERN. These experiments

provide the opportunity to search for new physics; for instance, the search for

heavy leptons, supersymmetric particles, the Higgs particle(s), and the additional

vector bosons predicted in many possible extensions of the Standard Model [LHC

(1990)]. The radiation environment of LHC-experiments is treated in Sects. 4.1.1–

4.1.1.2.

Large and compact calorimeters (like the one based on Si/W) are also needed

to be operated at the future International Linear Collider (ILC) (for instance,

see [Strom (2008)]).

Independently of its structure, a calorimeter must be of suﬃcient thickness to

allow the particle to deposit all its energy inside the detector volume during the

subsequent cascade of particles of lower and lower energy. The total depth of the

calorimeter must be large enough to allow a longitudinal containment of the cascade

∗

The usage of silicon detectors as active medium in calorimetry was ﬁrst proposed by Rancoita

and Seidman (1984); silicon electromagnetic and hadronic calorimeters were originally developed

by the SICAPO collaboration.

†

A recent review of calorimeter developments has been provided by Pretzel (2005).

‡

This pay-load employs a Si/W imaging calorimeter.

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Principles of Particle Energy Determination 613

in order to completely absorb the incoming energy. The necessary longitudinal depth

of a calorimeter varies with the incoming energy, E, as ln E and, therefore, the

calorimeter can remain a compact construction even at the highest energies [Fabjan

and Ludlam (1982)]. The incoming energy, being distributed among a large num-

ber of secondary particles, can be deposited at large angles with respect to the

longitudinal axis of the calorimeter. The result is that the transverse containment

of the cascade imposes a minimal radial extension of the calorimeter which must,

then, reach at least several times the average diameter of a cascade. Therefore,

the calorimeter dimensions must be large enough to avoid longitudinal and lateral

leakage of cascades.

The granularity is another important requirement for a calorimeter and charac-

terizes the spatial separation between two particles in an event. In electromagnetic

calorimeters, it can be increased by adding a so-called preshower detector. For

example, in the CMS apparatus at LHC a preshower detector

is located in front

of the Endcap Electromagnetic Calorimeter to increase the identiﬁcation of two

closely-spaced photons from π

decay. It has to be noted that the granularity is

imposed by physics and it is ﬁxed by the minimum angle to be detected between

particles, like the detection of a speciﬁc particle inside a jet, for instance. Cascades

must be separated at least by one cascade diameter in order to be individually rec-

ognized. This constraint deﬁnes the minimum distance between the detector and

the interaction point and requires the use of active layers organized in cells, whose

maximum dimensions can allow this cascade separation. In practice, this means that

the transverse cell size must be comparable to the lateral cascade dimension. In ad-

dition, the detailed measurement of the cascade position during its development

in the calorimeter volume also demands the best possible longitudinal granularity

and, therefore, requires a longitudinal segmentation of the calorimeter. For instance,

tower structures in sampling calorimeters using scintillator as active medium were

employed [HELIOS Collab. (1988)] to achieve the needed lateral and longitudinal

segmentations.

Calorimeters must have an energy resolution compatible with the experimental

goals. In the case of hadron calorimeters, this p ossibility is mostly dictated by their

relative response to the electromagnetic (e) and hadronic (π) cascade, measured

by the e/π signal ratio. The equalization between the electromagnetic and hadronic

signals (e/π = 1, i.e., the compensation condition) is the condition for obtaining the

linearity of the energy response of the calorimeter to incoming hadronic cascades,

and to achieve an energy resolution that improves as the incident energy increases.

However, in large experiments the best performing calorimetry may be in con-

ﬂict with sp eciﬁc requirements from other sub-detectors owing to the physics goals

of the experiments. Therefore, calorimeters in large experiments are not necessarily

the most eﬃcient from the point of view of calorimetry principles, but are certainly

It consists of two lead radiators each followed by a layer of silicon strip detectors with a strip

pitch of 1.9 mm [Topkar et al. (2006)].

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614 Principles of Radiation Interaction in Matter and Detection

optimized towards the achievement of the experiment goals and physics require-

ments.

Large calorimeters directly apply basic knowledge of the physics of cascade pro-

cesses in matter and the results of studies, that are often carried out on dedicated

test calorimeters. However, the conditions which prevail during the test measure-

ments have to be remembered, in order to assess the performance of these test

calorimeters with the view of extrapolation to larger calorimeters to be operated

in physics experiments. The physics conditions met in experimental zone by test

calorimeters is diﬀerent from those encountered in an operating experiment. For in-

stance, the energy resolution of a test calorimeter is assessed from the measurement

in its volume of the energy deposition of particles of a well known dedicated beam,

while a calorimeter operating in a physics experiment will face particles produced

in collisions (collisions between two beams or beam with a target). The energy of

these particles will cover a large range and many will be produced with relatively low

energy, leading to a degradation of the calorimeter energy resolution. The calorime-

ter performance is also aﬀected by the amount of material in front of the calorimeter

being tested and the eﬀect of the beam conditions, such as for example the momen-

tum spread in the test beam and the precision of beam counters, which vary from

one test to another. Again, the extrapolation of performance to larger calorimeters

in physics experiments has to take into account changing environment and beam

features. Usually, these test environment limitations are quoted in articles and re-

ports in order to separate circumstantial eﬀects from the fundamental properties of

shower propagation and the way the energy is degraded and deposited in matter.

The physics, which governs the electromagnetic (e) cascading and the propaga-

tion in complex absorbers, has been reviewed in Sect. 2.4, while the phenomenology

of the hadronic cascading in Sect. 3.3. In this chapter, the instrumental needs due

to shower generation and propagation in matter are pointed out. The chapter is

organized as follows. The electromagnetic calorimeter response, the e/mip ratio

and the local hardening eﬀect (exploited to reduce the e/mip ratio in high-Z ab-

sorbers) are discussed in Sect. 9.2. The ﬁltering eﬀect, which can be used to adjust

the e/mip ratio for complex absorbers, is dealt in Sect. 9.3. The energy resolution

of electromagnetic sampling calorimeters is presented in Sect. 9.4. The Sect. 9.5 is

devoted to a review of homogeneous on calorimeters. The use of calorimeters for

position measurement and electron–hadron separation is discussed in Sects. 9.6 and

9.7 respectively. Hadronic calorimetry is intro duced in Sect. 9.8, where the intrinsic

properties of hadronic calorimeter such as e/h, h/mip, π/mip and e/π ratios are

dealt. In particular, the relation of the e/π ratio to the compensation condition

is discussed in the same section. Section 9.9 is devoted to the study of the com-

pensation condition and the methods to achieve compensating calorimetry. The

compensation and the hadronic resolution are discussed in Sect. 9.10. In Sect. 9.11,

it is presented a brief review of the study of the cascade behavior in an energy

regime b eyond accelerator energies such as the energies characterizing the cosmic

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Principles of Particle Energy Determination 615

rays, the whole Earth atmosphere serving, then, as radiator volume.

9.1.1 Natural Units in Shower Propagation

The comprehensive treatment of the generation and propagation of electromagnetic

and hadronic showers is presented and the units employed for their parametrization

are discussed in Sects. 2.4-2.4.3 (for electromagnetic cascades) and Sects. 3.3-3.3.3

(for hadronic cascades).

For instance for electromagnetic showers, the radiation length

†

, X

, emerges as

a natural unit of length and expresses the mean-path length of an electron in a

material. Thus, the longitudinal propagation (referred to as the longitudinal direc-

tion) and the absorber depth are usually given in units of radiation length. For the

lateral development, the unit of the transverse depth of a cascade is the Moli`ere

radius (e.g., see Sect. 2.4.2.3).

The development of an hadronic cascade along the direction of motion of the

incoming particle is usually described in units of interaction length (or nuclear

interaction length) λ

(Sect. 3.3.2).

Furthermore, if not otherwise explicitly indicated, in this chapter A, Z and ρ

are the atomic weight (Sect. 1.4.1 and discussion at page 220), the atomic number

(Sect. 3.1) and the density of the material (in g cm

−3

), respectively.

9.2 Electromagnetic Sampling Calorimetry

9.2.1 Electromagnetic Calorimeter Response

Sampling calorimeters are made of layers of passive samplers interleaved with active

readout planes (Fig. 9.1). The energy of incoming particles is measured in active

layers, usually with a thickness (in units of radiation length) much smaller than

the thickness of the corresponding passive samplers, while the cascade process is

generated in the passive layers.

For calorimeters having homogeneous sampling the passive samplers have the

same thickness in units of radiation length along the longitudinal depth of the

calorimeter. For homogeneous sampling calorimeters, the sampling frequency, τ ,

is deﬁned as the passive sampler absorber thickness between two successive active

planes and is expressed in units of radiation length (X

). Therefore, the total number

of active readout planes is inversely proportional to τ . Only sampling calorimeters

of the homogeneous type will be considered in this chapter, unless explicitly stated

otherwise.

The calorimeter response to showering particles is the signal generated by the

active readout planes, which sample the incoming particle energy, i.e., it is the

measurement of the energy deposited by the electromagnetic cascade in the whole

†

It was discussed in Sect. 2.1.7.3 on Radiation Length and Complete Screening Approximation.

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616 Principles of Radiation Interaction in Matter and Detection

and

Incoming

particle

absorber

active medium data collection

signal handling

Fig. 9.1 Schematic description of a sampling calorimeter. The passive samplers (absorbers) are

interspaced by active readout detector planes (for instance scintillator layer or silicon mosaic)

from [Leroy and Rancoita (2000)].

set of the readout planes, after having performed the energy calibration of the

device.

This deposited energy is called visible energy and, usually, is a tiny fraction of the

incoming-particle energy. Therefore, the visible energy, ²

vis

, in sampling calorimeters

is the measurement, by the readout planes, of the energy deposited by incident

particles in the active layers of the calorimeter (e.g., see [SICAPO Collab. (1985a,

1987)] and references therein).

As seen in Sect. 2.4.2.1, the total track length [Eq. (2.228)] is proportional to the

incoming particle energy E. The energy deposited in the readout layers corresponds

to the measurement of a fraction of the total track length, i.e., the part related to

the overall thickness of the active readout planes, and consequently:

vis

∝ E. (9.1)

Equation (9.1) is the basic principle of calorimetry and has the consequence that

the calorimeter response is expected to have a linear dependence on the incident

particle energy. The linearity is a fundamental property that is independent of the

nature, the thickness of active and absorber media, and of the sampling frequency.

A non-linear calorimeter response might occur, if the readout devices are not

providing signals proportional to the deposited energy.

Equation (9.1) holds for electromagnetic cascades, in which almost all incoming

particle energy is ﬁnally dissipated by processes of atomic ionization and excitation.

In the case of hadronic calorimeters, as will be seen later, an energy-dependent

fraction of the incoming energy goes in breaking up nuclei, in low-energy neutrons

and in undetectable neutrinos [Gabriel (1978)], thus preventing the linear calorime-

ter response to the incoming hadron energy. The restoration of Eq. (9.1) for hadron

calorimeters is at the core of the problem of compensation, that will be discussed

later in this chapter while dealing on hadron calorimetry.

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Principles of Particle Energy Determination 617

Fig. 9.2 ²

vis

measured with the silicon calorimeter of SICAPO Collaboration shown in Fig. 2.78

for W absorbers as a function of the incoming electron energy (reprinted from Nucl. Instr.

and Meth. in Phys. Res. A 235, Barbiellini, G., Cecchet, G., Hemery, J.Y., Lemeilleur,

F., Leroy, C., Levman, G., Rancoita, P.G. and Seidman, A., Energy Resolution and Longitu-

dinal Shower Development in a Si/W Electromagnetic Calorimeter, 55–60, Copyright (1985),

with permission from Elsevier; see also [Leroy and Rancoita (2000)]). The line represents:

vis

= [(5.558 ± 0.004) E[GeV] + (−1.3 ± 1.5)] [MeV].

Equation (9.1) was found to agree remarkably well with experimental data (see,

for example [Bormann et al. (1985); Nakamoto et al. (1986)]). An example [SICAPO

Collab. (1985a)] is given in Fig. 9.2, where measured values of ²

vis

, obtained using a

Si/W sampling calorimeter, are shown for incoming electron energies between 4 and

49 GeV. The least square ﬁt to the data shown in Fig. 9.2 gives [SICAPO Collab.

(1985a)]:

vis

= [(5.558 ± 0.004) E[GeV] + (−1.3 ± 1.5)] [MeV]. (9.2)

The ﬁtted values and their errors indicate the high degree of linearity of the calorime-

ter response, in agreement with Eq. (9.1).

In sampling calorimeters in which passive samplers are dominant (in terms of

thickness expressed in units of radiation length), the total number of active readout

planes increases as the sampling frequency decreases and, consequently, the sampled

fraction of the track length [Eq. (2.228)] is expected to increase since the longitudinal

depth of the calorimeter is ﬁxed. Thus, to a ﬁrst approximation, Eq. (9.1) becomes:

vis

∝

. (9.3)

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618 Principles of Radiation Interaction in Matter and Detection

Experimental data [SICAPO Collab. (1989c, 1994a)] on ²

vis

for an incoming-

electron energy of 4 GeV are shown in Fig. 9.3 as a function of 1/τ . These data

were obtained using a Si/Pb sampling calorimeter. The values of τ range between

1.96 and 3.39. The data show a linear dependence of ²

vis

on 1/τ . This holds for τ

larger than ≈ 0.8, as will be discussed at page 626.

Fig. 9.3 ²

vis

measured with Pb absorbers as a function of 1/τ , where τ is the sampling frequency

(reprinted from Nucl. Instr. and Meth. in Phys. Res. A 345, Bosetti, M. et al., Systematic in-

vestigation of the electromagnetic energy resolution on sampling frequency using silicon calorime-

ters, 244–249, Copyright (1994), with permission from Elsevier, e.g., for the list of the authors

see [SICAPO Collab. (1994a)]; see also [Leroy and Rancoita (2000)]).

9.2.2 The e/mip Ratio

In a sampling calorimeter, the visible energy is the result of collision losses in active

readout layers by electrons and positrons (generated during the electromagnetic

shower development), traversing or ranging out in these layers. It has to be noted

that in a homogeneous calorimeter, the full device can be considered as an extended

active layer. Because the dominant process of energy dissipation is the process of

energy loss by collisions, the calorimeter response to minimum-ionizing and non-

showering particles (mip), like muons, can be used as a scale or, equivalently, as a

unit of measurement for the response to electromagnetic showers (e) (for instance

see [Wigmans (1987, 1988); Gabriel (1989); SICAPO Collab. (1989b,c); Drews et

al. (1990); SICAPO Collab. (1990b); Wigmans (1991); SICAPO Collab. (1992a)]).

For a given sampling calorimeter, the ratio of the energy dep osited by ionization

in active readout planes and passive samplers can be evaluated using the mean

dE/dx values for mip’s in diﬀerent materials, as for instance given in [Janni (1982);

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Principles of Particle Energy Determination 619

PDB (2008)].

Following the energy partition by a minimum ionizing and non showering par-

ticle, the shared energy E

in active readout planes is given by:

= E F (S) = E G(S) X

, (9.4)

where E is the incoming particle energy in GeV, F (S) = G(S) X

, X

is the active

depth of the readout detectors, and

G(S) =

£¡

, (9.5)

where L

is the physical thickness of the active readout detectors, L

is the thickness

of the absorber i, (dE/dx)

is the mip average energy-loss per unit of length in active

readout planes, and (dE/dx)

is the mip average energy-loss per unit of length in

the absorber i (as given in [Janni (1982); PDB (2008)].

It has to be emphasized that mip’s are ideal particles. The average energy de-

posited per unit length by non-showering particles, like muons, in a calorimeter

will be always larger than the deposited energy corresponding to the minimum va-

lue of the collision energy-loss dE/dx owing to processes like δ-rays production or

bremsstrahlung, even if the restricted energy-loss and the density-eﬀect are limiting

the relativistic rise. In fact, in dense materials the Fermi Plateau (deﬁned on page

51) occurs for mean collision losses close but slightly larger than the dE/dx for

β ≈ 0.96, at which the collision energy-loss of a massive particle is minimum, (i.e.,

it is a mip). Nevertheless, the above introduced mip values have the advantage of

being energy- and thickness-independent and allows a comparison among diﬀerent

calorimeter structures.

In Eq. (9.4), F (S) represents the fraction of the energy lost by a mip particle

depositing its energy by collision losses in similar (with respect to the sampling

electromagnetic calorimeter structure) but indeﬁnitely extended calorimeter, so that

the mip particle is completely absorbed. The value of F (S) can be computed by

considering a single passive sampler, which in turn can be made of several absorbers,

and a single readout active plane. For instance for a 10 GeV incoming-electron

energy, the calculated values of E

for a calorimeter with one X

of Pb passive

samplers are ≈ 210 and 770 MeV for 400 µm thick silicon detectors and 3 mm thick

plastic scintillators, respectively. Thus only about 2.1 and 7.7%, respectively, of the

incoming electron energy is shared by active samplers in these two calorimeters.

The e/mip ratio is deﬁned as:

e/mip ≡

vis

, (9.6)

where ²

vis

is the energy dep osited in the sensitive part of the calorimeter by the elec-

tromagnetic cascade initiated by a particle of energy E; E

is deﬁned in Eq. (9.4). It

provides a way to determine how much the energy deposition processes for showering

particles and mip’s diﬀer each other.