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

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660 Principles of Radiation Interaction in Matter and Detection

Table 9.7 Energy resolution of homogeneous calorimeters (from [Leroy and Rancoita (2000)]).

Readout depth Energy resolution Reference Comments

σ(E)/E

Lead glass 20.5 5%/

√

E [Akrawy et al. (1990)] CEREN25 for lead glass

22.0 3.2% (at 6 GeV) [Akrawy et al. (1990)] 1.5X

of Pb in front

of the lead glass array

22.0 1.8% (at 50 GeV) [Akrawy et al. (1990)] 1.5X

of Pb in front

of the lead glass array

NaI(Tl) 8.8 3.9% E

−1/4

[Klopfenstein (1983)]

16.0 2.7% E

−1/4

[Oreglia et al. (1982)]

16.0 2.8% E

−1/4

[Partridge (1980)]

24.0 0.9% E

−1/4

[Hughes et al. (1972)]

CsI(Tl) 16.2 3.8% (at 0.18 GeV) [Blucher et al. (1986)]

16.2 1.6% (at 5 GeV) [Bebek (1988)]

21.6 ∼ 2% (4 to 20 GeV) [Grassman et al. (1985)] leakage ﬂuctuations:

1.3% and 0.7%

at 4 and 20 GeV

BaF

19.5 ≤ 1% (4 to 40 GeV) [Lorenz, E., Mageras, G. and Vogel, H. (1986)]

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Principles of Particle Energy Determination 661

Table 9.8 Energy resolution of other homogeneous calorimeters (from [Leroy and Rancoita (2000)]).

Readout Depth Energy resolution Reference Comments

σ(E)/E

BGO 21.5 0.5% (E ≥ 10 GeV) [Sumner (1988)]

21.5 2.0% (E ∼ 1 GeV) [Sumner (1988)]

21.5 5% (E ∼ 0.1 GeV) [Sumner (1988)]

22.3 ≤ 1% (E > 4 GeV) [Kampert et al. (1994)]

SCG1-C 20.5 1.46%/

√

E + 1.6% [Wagoner et al. (1985)]

20.5 3.43%/

√

E + 0.5% [Wagoner et al. (1985)] 3.5X

converter

0.2X

hodoscope in front

CeF

25.0 0.5% (E ≥ 50 GeV) [Auﬀray et al. (1996)]

PbWO

24.0 3.5%/

√

E + 0.35% (10 ≤ E ≤ 150 GeV) [Peigneux et al. (1996)] photomultiplier readout

24.0 6%/

√

E + 0.5% (10 ≤ E ≤ 150 GeV) [Peigneux et al. (1996)] avalanche photodio de readout

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662 Principles of Radiation Interaction in Matter and Detection

CsI(Tl) is obtained by doping CsI with thalium at a level varying from 150

to 2000 ppm. It has a rather short radiation length (1.85 cm) allowing compact

calorimeters and a peak emission of 550 nm (Table 5.2), which, in turn, permits

a readout by silicon photodiodes [Blucher et al. (1986); Bebek (1988); Fukushim

(1992)]. CsI(Tl) was used in homogeneous electromagnetic calorimeters. An exam-

ple is provided by CLEO [Blucher et al. (1986); Bebek (1988)] where the electro-

magnetic cascade detector consists of 8000 CsI(Tl) crystals readout with Si photo-

diodes. A prototype of this detector made of an array of 465 crystals providing a

depth of 16.2 X

was tested in a 180 MeV positron beam giving a measured energy

resolution of 3.8%. This array was later installed in CLEO and the energy spectrum

of electrons from Bhabha events at 5 GeV were measured with an energy resolu-

tion of 1.6%. Earlier data with 21.6 X

of CsI(Tl) [Grassman et al. (1985)] gave

an energy resolution of about 2% for incoming electron energy ranging between 4

and 20 GeV. Leakage ﬂuctuations contributed 1.3% and 0.7% at 4 GeV and 20 GeV,

respectively.

From the point of view of calorimetry applications, BaF

suﬀers from several

handicaps, namely a long radiation length (2.05 cm, Table 5.2), a large Moli`ere ra-

dius (3.4 cm, Table 5.2) and a relatively small ratio of hadronic interaction length

(see Sect. 3.3) to radiation length, hampering electron–hadron separation [Majew-

ski and Zorn (1992)]. However, BaF

has a high density (4.88 g/cm

), which fa-

vors detector compactness, a very short decay time of its fast scintillation com-

ponent τ

d,1

∼ 0.6 ns (Table 5.2), which favors applications where light collection

has to be achieved fast, and excellent radiation hardness. These features had moti-

vated the choice of this crystal for SSC-GEM (see references in [Majewski and Zorn

(1992)]). An energy resolution of ≤ 1% for incident electron energies between 4 and

40 GeV is obtained [Lorenz, E., Mageras, G. and Vogel, H. (1986)] (corrected for

beam momentum spread and leakage) by using a readout scheme involving ﬂuores-

cent ﬂux concentrators and silicon photodiodes.

BGO gives 7% of the light output of NaI(Tl) at room temperature. The light

output varies with temperature with a decrease of 1% per degree at 20

C [Suﬀert

(1988)] and therefore can be improved by cooling of the crystal. The relatively high

output and green spectral response allow the replacement of photomultipliers by

photodio des for the readout due to the availability of photodiodes of large area and

low noise, nowadays [Sumner (1988); Kampert et al. (1994)]. Energy resolution of

σ (E)

∼ 0.5%, ≤ 2.0% and ∼ 5% are obtained for incoming energy E ≥ 10 GeV,

∼ 1 GeV and at 0.1 GeV for the L3 electromagnetic calorimeter consisting of 10734

BGO crystals corresponding to a total depth of ∼ 21.5X

[Sumner (1988)]. These

results are compatible with the energy resolution

σ(E)

better than 1% measured for

incident energies above 4 GeV for a total length of 22.3 X

[Kampert et al. (1994)].

The scintillating glass (SCG1-C) is a crystal permitting the achievement of an

energy resolution comparable to that of NaI(Tl) and BGO and produced at much

lower costs. The SCG1-C is composed of BaO (43.4%), SiO

(42.5%) and other

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Principles of Particle Energy Determination 663

high-Z materials LiO

(4.0%), MgO (3.3%), K

O (3.3%), Al

(2.0%), Ce

(1.5%) with a density of 3.36 g/cm

and a radiation length of 4.35 cm. The Ce

acts as a scintillating component as well as wavelength shifter for short wavelengths,

i.e., shifting the UV photons into the sensitive blue region of the photocathode. The

light produced by SCG1-C has two components with a fast

Cerenkov component

which represents about 15% of the total light output.

The energy resolution (and the position resolution, as will be discussed in

Sect. 9.6) is often represented by an expression, where the account for diﬀerent

eﬀects (like the readout electronic noise, momentum spread, the amount of mate-

rial in front of the calorimeter being tested) modiﬁes Eq. (9.36) into (see also [Engler

(1985)])

σ(E)

√

+ c

√

, (9.41)

where a

is the intrinsic resolution term, b

the noise contribution and c

a constant

term (E is expressed in GeV).

For SCG1-C, the energy resolution is measured to be

σ(E)

(1.46 ± 0.1)%

√

+ (1.63 ± 0.05)%

for 20.5 X

of scintillating glass for positrons in the energy range between 1 and

25 GeV [Wagoner et al. (1985)]. When adding an active converter 3.5 X

deep, and

a 0.2 X

shower position hodoscope, the constant term in the energy resolution was

reduced and the resolution found to be [Wagoner et al. (1985)]:

σ(E)

(3.43 ± 0.18)%

√

+ (0.50 ± 0.08)%.

The energy resolution with the active converter was better since a better cascade

containment was then achieved and also allowed to correct for conversion point

ﬂuctuations within the glass. These ﬂuctuations were degrading the energy resolu-

tion because of the diﬀerential absorption of light by glass. The photon yield was

measured [Wagoner et al. (1985)] to be 1.6 × 10

γ/GeV.

The “Crystal Clear” Collaboration [Lecoq et al. (2001)] has conducted studies in

order to produce CeF

crystal with optimal properties with respect to their p ossible

utilization in experiments at LHC. This collaboration has tested a CeF

matrix of 9

crystals readout via silicon photodiodes, 25 X

deep, with a lateral segmentation of

3×3 cm

and 2 ×2 cm

(at the 4 corners) exposed at CERN-SPS to electron, muon

and pion beams of momenta ranging from 10 to 150 GeV/c. An energy resolution

of 0.5% for energies above 50 GeV was achieved [Auﬀray et al. (1996)].

Lead tungstate PbWO

crystals were ﬁnally selected as active material of elec-

tromagnetic calorimeters for CMS [CMS (1994)] and ALICE [ALICE (1993)] at

LHC. PbWO

is grown from a 50%-50% mixture of lead oxide (PbO) and tungsten

oxide (WO

). Its high refractive index (Table 5.2) helps the light propagation along

the crystal but limits the eﬃciency of the light extraction. The decay time constant

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664 Principles of Radiation Interaction in Matter and Detection

has a mean value of 10 ns and about 85% of the light is collected in 25 ns. The

emission spectrum has two broad bands at 440 nm and 530 nm. The light yield

is about 150 γ/MeV for small samples and about between 50 and 80 γ/MeV for

20 cm long crystals. The light output varies with temperature with a decrease of

1.98% per degree at 20

C [CMS (1994)] and therefore can be improved by cool-

ing of the crystal. For instance, the light yield at −20

C is 2.3 times larger than

at +20

C. Beam tests of electromagnetic calorimeters made of PbWO

crystals

were performed at several energies and with various types of photosensitive de-

vices. Namely, a comparative study between photomultiplier and Si avalanche pho-

todio des was performed [Peigneux et al. (1996)]. The energy resolution measured

using photomultipliers (without unfolding the beam momentum spread) is

σ(E)

3.5%

E(GeV)

+ 0.35%

for a depth of 24 X

and for incoming electron energies ranging from 35 to

150 GeV. The energy resolution was found to be

σ(E)

6.0%

E(GeV)

+ 0.5%

(electrons of energy ranging from 20 up to 150 GeV) when the measurements were

carried out with avalanche photodiodes, showing the necessity of further devel-

opment for crystal and avalanche photodiodes. The eﬀect of putting a preshower

detector with 16 mm of lead (or 2.9 X

) in front of the crystals was tested. The

preshower detector increases the eﬀective length of the calorimeter, with the conse-

quence that the ﬂux of particle leaking out of the calorimeter is decreased and the

energy resolution is improved [Peigneux et al. (1996)].

9.6 Position Measurement

The impact point of a γ-ray or an electron can be measured by exploiting the

longitudinal segmentation and transverse granularity of the calorimeter, which de-

ﬁne cells. If the granularity of the crystals is chosen to be equal or smaller than

the Moli`ere radius, the lateral spread of the electromagnetic cascade over several

crystal modules allows the reconstruction of the impact point of the incident par-

ticle. Then, the particle impact coordinates are deﬁned by measuring the energy

deposit of the cascade in transverse directions. The position of the impact point is

usually measured by using the center of gravity of the energies, E

, deposited in the

modules:

¯x =

, (9.42)

where x

are the coordinates of each module hit with respect to the central one,

and E

is the energy deposited in the cell i. However, it is known that such methods

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Principles of Particle Energy Determination 665

calculates an impact point systematically shifted towards the center of the module

hit by the particle. There exists several ways to correct this eﬀect; see [Anzivino et

al. (1993)], for instance.

In order to locate the position of a shower within the calorimeter, it is necessary

for the energy to be shared between a number of calorimeter cells. The precision of

this measurement increases with the number of calorimeter cells hit by the cascade

particles and decreases with the crystal cell size. However, the intrinsic resolution of

such a measurement is small, since the spatial distribution of the incoming showers

is rather limited. This is a consequence of the dependence on the incoming energy of

the processes contributing to the cascade transverse development: bremsstrahlung

and pair creation create electrons and positrons at angle

b,pc

∼

¢¤

where E(GeV) is the particle energy (e or γ). Angular spread of the cascade is

also generated by multiple scattering which, for relativistic particles traversing a

thickness x, results in an angular divergence

∼ 0.02

x/X

As E increases, more higher energy electrons, positrons and photons are generated

in the cascade. As a consequence of their 1/E dependence, θ

b,pc

and θ

decrease

with the increase of the energy, and the particles in the cascade do not spread out

forming the central core of the cascade. The electrons and positrons, with energies

close to the critical energy, are responsible for the dominant part of the energy

loss and do not modify the pattern of energy loss, since the critical energy is a

characteristic of the material and not linked to the incoming energy [Kondo and

Niwa (1984)].

For homogeneous calorimeters, a tower structure with a lateral side comparable

to the width of incoming electromagnetic cascades can be used to measure the

position of a photon with a spatial resolution much smaller than the cell size. This

structure favors two-photon separation and a spatial resolution improving close to

the cell edges [Amendolia et al. (1980)]. In the end, the choice of the cell dimensions

is a compromise between good position resolution, cascade containment in a tower

consisting of a moderate number of lateral cells and the total number of readout

channels. Good position resolution as well as a good knowledge of the transverse

cascade shape, which is important (as it will be shown below) to achieve good

electron–hadron separation, favor a small cell size while cascade containment in a

few cells favors large cell size. A cell dimension in the neighborhood of about one

Moli`ere radius is usually taken, corresponding to about 75% of the cascade energy

deposited in the center cell.

In practice, the detector matrix is made of a large number of total absorp-

tion counters each with a lateral size comparable with the electromagnetic cascade

width. These absorption counters are made of scintillating crystal (Table 5.2) or

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666 Principles of Radiation Interaction in Matter and Detection

lead glass (Table 9.6). In the case of lead glass (SF-5) used in [Prokoshkin (1980)],

the dep endence of the coordinate accuracy σ

on the cell size d at the incoming

energy of 25 GeV is parametrized as

(d) = σ

(d = 0) e

d/d

. (9.43)

For d ≤ 3 cm, σ

is constant while for d > 3 cm, σ

(d = 0) = 0.8 mm and d

6.5 cm [Prokoshkin (1980)] (the size of a lead glass cell in [Prokoshkin (1980)] was

4.5 × 4.5 × 65 cm

As discussed above, when the incoming energy increases, the lateral size of the

electromagnetic cascade remains almost unchanged. Since the number of cascade

particles increases with the incoming energy, the coordinates accuracy will scale

with energy as

(E) =

constant

√

, (9.44)

if the lateral correlations of the number of particles in the cascade is negligible. The

scaling law, given by Eq. (9.44), was veriﬁed in the energy range between 2 and

40 GeV [Akapdjanov et al. (1977)]. The two-photon separation is ∼ 5 cm.

The position resolution as a function of the energy for a calorimeter organized

in pointing cascade can also b e parameterized as [Zhu (1993)]:

(E) =

3 e

0.4D

√

(9.45)

where D is the cell size in radiation lengths. Again, this illustrates the importance

of the cell dimension.

The improvement of the spatial resolution with increasing energy is also observed

in the EMEC-OPAL calorimeter large lead glass array (see above) [Akrawy et al.

(1990)]. For electrons ﬁred centrally into a lead glass block at normal incidence,

the position resolution is (in mm) 9.9, 6.3, 4.4, 3.1 and 2.5 mm at 5, 10, 20, 35,

and 50 GeV, respectively. The multiple scattering contributions which amount to

∼ 25 mm/E has not been unfolded from these numbers [Akrawy et al. (1990)].

BGO data on position measurement are also found to follow the scaling law as

given in Eq. (9.44). The measured position resolution can be parameterized as

(E) ∼

3.3

E(GeV)

for electron momenta ranging from between 0.5 and 6 GeV/c [Kampert et al.

(1994)]. This result is not in disagreement with the measured spatial resolution

found better than 2 mm above 2 GeV for the BGO L3 electromagnetic calorime-

ter [Sumner (1988)]. The position resolution achieved with the CsI(Tl) CLEO II

detector at CESR is ∼ 0.3 cm and 1.2 cm at 5 GeV and 180 MeV, respectively.

The position resolution achieved with the matrix of CeF

crystals of [Auﬀray

et al. (1996)] is σ

= 0.67 mm and σ

= 0.7 mm for 50 GeV electrons. Then, the

angular resolution is 15 mrad for the 50 GeV electrons corresponding to

∼

100

√

mrad

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Principles of Particle Energy Determination 667

(E in GeV) [Auﬀray et al. (1996)].

The small Moli`ere radius of PbWO

results in narrow cascades. However the

energy deposited in the cells around the impact point is large enough to enable

the measurement of impact coordinates. The combination of preshower and crystal

matrix may achieve relatively good position and angular resolutions [Peigneux et

al. (1996)]. The position resolution on the center of gravity x

as a function of the

incoming energy, is

σ(x

) =

(2.02 ± 0.48)

√

+ (0.29 ± 0.06)

mm,

E in GeV for the PbWO

calorimeter of [Peigneux et al. (1996)]. The transverse

spread of the cascade after ∼ 3 X

of lead is a few mm. This gives a spatial resolution

of the preshower detector

σ(x

) =

(1.58 ± 0.46)

√

+ (0.36 ± 0.06)

mm,

with a stochastic term smaller than the one found for the crystals but with a larger

constant term, possibly because of noise and cross talk. The angular resolution of

the preshower-crystal system is found to be

(36.5 ± 6.5)

√

+ (4.1 ± 0.8)

mrad.

The position resolution is degraded for sampling calorimeters. The shower

spreads transversely with an exponential fall-oﬀ that becomes ﬂatter for larger lon-

gitudinal depths. This lateral decrease projected onto a plane is given as [Engler

(1985)]

≈ exp

−

, (9.46)

where x is the coordinate orthogonal to the shower axis. R

is smaller for the

absorber compared to the active medium (see Table 2.3) and therefore the cascade

in the absorber is wider transversely than in the active medium. As a consequence,

interspersing active medium planes with absorber layers leads to a larger overlap of

contiguous showers. The position resolution, found for a fully projective lead and

scintillating ﬁber calorimeter, is [Anzivino et al. (1993)]

(6.21 ± 0.17)

√

+ (0.32 ± 0.03) [mm]. (9.47)

The space resolution of the large-scale prototype of the ATLAS Pb/LAr accor-

dion electromagnetic calorimeter was determined by comparing the shower center-

of-gravity, reconstructed in the calorimeter, with the extrap olated impact point

provided by a beam chamber system (three multiwire prop ortional chambers used

to extrapolate the particle trajectory to the calorimeter front face). By ﬁtting the

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668 Principles of Radiation Interaction in Matter and Detection

data to the expected 1/

√

E law, the space resolution was found to be (the incoming

energy E is in GeV) [Gingrich et al. (1995)]:

= (0.186 ± 0.021) +

3.87 ± 0.05

√

[mm] (9.48)

in the direction perpendicular to the accordion waves, and

= (0.210 ± 0.015) +

4.70 ± 0.05

√

[mm] (9.49)

in the other direction.

9.7 Electron Hadron Separation

In calorimetry, the electron hadron separation is based on the diﬀerence in the

cascade proﬁles (e.g., see [Baumgart et al. (1988b)]). This diﬀerence is enhanced in

materials with very diﬀerent radiation and interaction lengths. Their ratio, using the

approximated expressions given in Eqs. (2.226, 3.77), and for Z/A ≈ 0.5 becomes:

g A

(g/cm

)

g 0

(g/cm

)

∼ 0.12 × Z

4/3

. (9.50)

Therefore, an electromagnetic calorimeter which has a depth of about one inte-

raction length already provides by itself a discrimination between hadrons and

electrons or photons due to the low probability for hadronic interaction in this

calorimeter volume (e.g., see [Heijne et al. (1983)]).

A modular calorimeter can be used to detect electrons and photons against

strongly interacting particles. The discrimination capability between electrons, pho-

tons and hadrons of the calorimeter is accomplished through the analysis of the lat-

eral dispersion and the longitudinal distribution of the cascade. The hadronic casca-

des present larger lateral dispersions than electromagnetic cascades. The dispersion

depends on the point of incidence relative to the module boundaries. A cut on the

lateral dispersion allows the rejection of a large fraction of hadrons at the price of

a rather modest loss in electrons.

Obviously, the lateral dispersion analysis becomes ineﬃcient at low energy since

then a lower number of calorimeter modules is involved in the cascade. Therefore,

the cut on lateral dispersion has to be combined with a cut on energy deposition

in the calorimeter modules. In general, the energy deposited by hadronic cascades

will be larger in the rear part compared to the front part of the calorimeter. The

electromagnetic cascades show the opposite behavior. The measurement of the ratio

front

/E of the energy deposited in the front part deﬁned in the calorimeter E

front

the total energy E allows the analysis of the longitudinal dispersion of the cascade. A

rectangular cut is then performed in the scatter plot of the particle lateral dispersion

versus E

front

/E.

It turns out that the longitudinal dispersion analysis proves to be more eﬃcient

at low energy, where the lateral dispersion analysis is less eﬃcient [Kampert et al.

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Principles of Particle Energy Determination 669

(1994); Auﬀray et al. (1996)]. The procedure combining lateral and longitudinal in-

formation allows to achieve a good electron–pion separation with eﬃciency in pion

rejection between 90 and 99%, so giving a level of ≈ 10

−3

for the pion contami-

nation for BGO (22.3 X

and 0.5 ≤ p ≤ 6 GeV/c, where p is the particle momen-

tum) [Kampert et al. (1994)], CeF

(25 X

and 10 ≤ p ≤ 150 GeV/c) [Auﬀray et

al. (1996)], PbWO

(24 X

and 10 ≤ p ≤ 150 GeV/c) [Peigneux et al. (1996)]. The

dispersion analysis can be generalized by using a method using the momenta of the

cascade. This method can be applied, when the incident particles hit the module

with its momentum non-parallel to the longitudinal module axis, a case in which

the dispersion is not well deﬁned [Gomez, Velasco and Maestro (1987)].

The separation between electrons, photons and hadrons is achieved in sampling

calorimeters by installing an electromagnetic calorimeter in front followed by an

hadron calorimeter. This takes advantage of the diﬀerence in the lateral and longi-

tudinal shower proﬁle of hadrons and electrons, as discussed above. In practice, this

is accomplished by dividing the sampling calorimeter modules into an electromag-

netic section several radiation lengths deep and a hadronic section with a depth of

several interaction lengths.

The calorimeter modules can be read out via wavelength shifting (WLS) plates or

ﬁbers. The ﬁber of each module or tower is split into two parts: an electromagnetic

ﬁber read through the front of the calorimeter and an hadronic ﬁber read through

the back. Using this method, one may expect more than 99% of pions rejected for

more than 99% electron eﬃciency [Bagdasarovand and Goulianos (1993)]. However,

in many cases electrons and pions are eﬃciently separated when using the tagging

information provided by devices such as

Cerenkov diﬀerential counter put ahead of

the calorimeter modules [HELIOS Collab. (1987)]. In the case of calorimeters with

scintillating ﬁber layers as active medium, the calorimeter towers are made of two

longitudinal sections deﬁned by short and long scintillating ﬁbers in lead achieving

a separation between electrons and charged pions. Pion rejection factors of the order

of 100 were obtained by using this longitudinal segmentation within one lead block

with short and long ﬁbers [Dagoret-Campagne (1993)].

9.8 Hadronic Calorimetry

9.8.1 Intrinsic Properties of the Hadronic Calorimeter

Hadronic calorimeters are mostly employed in High Energy Physics experiments,

where hadrons can have energies above tens or hundreds GeV. We will limit our-

selves by considering only primary hadrons with energies above a few GeV’s. At

lower energies, the energy loss by ionization alone becomes increasingly important

and the calorimeter performance may change considerably. Furthermore to compare

experimental (intrinsic) properties of calorimeters, the hadron reference energy is

usually taken at 10 GeV.