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

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420 Principles of Radiation Interaction in Matter and Detection

There are several parameters characterizing scintillators. The scintillation ef-

ﬁciency, R

, is the ratio of the average number of emitted photons hN

i to the

energy E

of the incident radiation absorbed by the scintillator:

. (5.1)

The scintillation yield, R

, is the ratio of the total energy of the emitted light to

. It is obtained by multiplying the right-hand side of Eq. (5.1) by the energy, hν,

of the emitted photons:

= R

hν. (5.2)

The photoelectric eﬃciency, R

, of the scintillating material is often quoted in

medical physics for absorption of X- and γ-rays. This quantity is the ratio, R

, of

the number of the incident X- and γ-rays that have deposited all their energy in

the material, N

ph,absorbed

, to the total number of photons that have been detected,

ph,detected

ph,absorbed

ph,detected

. (5.3)

From its deﬁnition, R

features the importance of the absorption power of radiation

by the scintillating material. It depends on the incident energy and geometrical size

of the scintillating material struck by the radiation.

The scintillation spectrum has to be matched to the spectral sensitivity of the

photosensitive device coupled to the scintillator. The wavelength corresponding to

the maximum emission of light has to fall within the range of the spectral sensitivity

of the photocathode of the photomultiplier (photosensitive device).

As will be seen below, the time response of the scintillator material is controlled

by decay time constants.

The growth in time of the scintillation pulse is characterized by a fast rise time,

followed by a decay which has two components: a fast exponential decay and a

slower decay. The decay time constant of the fast component determines the time

response of the scintillating material. This parameter guides the choice of the type

of scintillating material for speciﬁc applications.

The scintillator material must be transparent to its own scintillation light. It

turns out that the emission wavelength is, in general, longer than the absorption

wavelength (Stokes’s shift).

5.1.1 Organic Scintillators

Organic scintillators are aromatic hydrocarbon compounds containing a benzenic

cycle. In organic scintillators, the mechanism of light emission is a molecular ef-

fect. It proceeds through excitation of molecular levels in a primary ﬂuorescent

material, which emits bands of ultraviolet (UV) light during de-excitation. This

UV light is absorbed in most organic materials with an absorption length of a few

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Scintillating Media and Scintillator Detectors 421

mm. The extraction of a light signal becomes possible only by introducing a second

ﬂuorescent material in which the UV light is converted into visible light (wavelength

shifter). This second substance is chosen in such a way that its absorption spec-

trum is matched to the emission spectrum of the primary ﬂuor, and its emission

spectrum, adapted to the spectral dependence of the photocathode quantum eﬃ-

ciency. These two active components of a scintillator are either dissolved in suitable

organic liquids or mixed with the monomer of a material capable of polymerization.

Plastic scintillators can be produced in a variety of shapes adapted to the ap-

plication needs. As an indication, most frequently used are rectangular plates with

thicknesses from 0.1 up to 30.0 mm and area from a few mm

up to several m

. They

are of current use in a wide range of applications such as b eam counters and active

medium of sampling calorimeters. In sampling calorimeters (discussed in Sect. 9.2)

using scintillators as active medium, the incoming particle energy is measured in a

numb er of plastic scintillating layers interspersed with layers of absorbing material

(metal), the latter speeding up the cascade process. A schematic description of a

sampling calorimeter is shown in Fig. 9.1 in the chapter on Principles of Parti-

cle Energy Determination. The scintillation light is coupled from the scintillator

layers to the photosensitive device via light guides. However, in most cases, such

arrangement is not practical, since it does not favor good transverse and longi-

tudinal segmentations and create large gaps in which energy may be lost. In the

case of ﬁxed target experiments with large solid angle coverage or colliding beam

experiment, the scintillating light is transported to the photosensitive device via

wavelength shifter (WLS) material (see Sect. 5.3 on wavelength shifter).

For organic scintillators, the relation between the emitted light and the energy

deposited by an ionizing particle is not linear. The scintillator response dep ends also

on the type of particle and its speciﬁc ionization. The relation between emitted light

and energy deposited by ionizing particles is expressed by Birks’ Law [Birks (1951,

1964)]. This law assumes that the response of organic scintillator is linear. Possible

deviation from this linearity is explained by quenching interactions between excited

molecule created along the path of the ionizing particle, absorbing energy which

causes a reduction of the scintillation eﬃciency. Birks’ law correlates the amount of

emitted light per unit of length, the diﬀerential light output dL/dx, to the stopping

power of the ionizing particle dE/dx, namely

¶Áµ

1 + kB

, (5.4)

where R

is the scintillation eﬃciency [see Eq. (5.1)], B is the Birks constant of the

medium and k is the quenching parameter. Here kB acts as a saturation constant

achieving a value ∼ 0.01–0.02 g/cm

MeV for a scintillator. In practice, kB is handled

as an adjustable parameter to ﬁt experimental data for a speciﬁc scintillator with

giving the absolute normalization. The total amount of light, L, produced by a

particle of energy, E, in a scintillator is obtained by integration of Eq. (5.4).

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422 Principles of Radiation Interaction in Matter and Detection

For small dE/dx (e.g. for fast electrons), Eq. (5.4) reduces to

≈ R

, (5.5)

while for large dE/dx (e.g. for α-particles), Eq. (5.4) becomes:

≈

. (5.6)

The integration of Eq. (5.6) over x gives the amount of light as a function of the

range, R(E), of the particle with energy E

L(E) ∼

R(E). (5.7)

Practically, kB can be determined from the ratio between Eq. (5.5) and Eq. (5.6).

Organic scintillators can also be liquids. In a liquid scintillator, an organic crys-

tal (solute) is dissolved in a solvent with typical concentrations of ≈ 3 g of solute per

liter of solvent. The ionization energy absorbed by the solvent is transferred to the

solute which is responsible for ﬂuorescence. This transfer can be achieved as light

emission by the solvent, absorption by the solute and re-emission at larger wave-

length. The scintillation eﬃciency increases with the solute concentration [Schram

(1963)]. Liquid scintillators have fast response, corresponding to a decay time of a

few ns. For instance, the scintillator BIBUQ dissolved in toluene has the best time

resolution (≈ 85 ps) of any scintillator currently available [Bengston and Moszyn-

ski (1982)]. Liquid scintillators are very sensitive to impurities present in the sol-

vent. This can b e turned into an advantage by adding material to increase their

eﬃciency for a speciﬁc application. For instance, the eﬃciency of liquid scintillator

for neutron detection can be increased by adding boron, which has a large cross

section with neutrons.

Table 5.1 Prop erties of organic scintillators of current use (see for in-

stance [Anderson (1990); PDB (2002)]).

Properties naphtalene anthracene NE102A NE110

Density (g/cm

) 1.15 1.25 1.032 1.032

H/C ratio 0.800 0.714 1.105 1.105

Emission spectrum

λ(nm) 348 448 425 437

Decay time constant

τ(ns) 11 31 2.5 3.3

Scintillation amplitude

(vs anthracene) 11 100 65 60

All organic scintillators have low density and low atomic number and, therefore,

have relatively low absorption for charged particles and for γ- and X-rays. Being a

mixture of C and a high content of H, the organic scintillators have high absorption

for fast neutrons (Table 5.1). The absorption of γ- and X-rays in organic scintillators

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Scintillating Media and Scintillator Detectors 423

is dominated by the Compton eﬀect (low-Z material). It is possible to obtain emis-

sion spectrum with a maximum wavelength in the range 350–500 nm. For example,

anthracene has a maximum wavelength of about 450 nm (Table 5.1). Their scintil-

lation yield for γ and fast electrons is a few percents. The shape of the scintillation

pulse is characterized by a fast rise time of the order of 1 ns and a decay time of

a few ns (Table 5.1). The decay can be described, as a function of time, by an

exponential fast component characterized by a lifetime τ:

L(t) ∼ e

−t/τ

. (5.8)

This component is called the main component because it contains the largest part of

the emitted light. A delayed (non-exponential) component follows, whose intensity

depends on the ionization power of the radiation

L(t) ∼

(1 + Dt)

, (5.9)

where C and D are constants and n ≈ 1.

5.1.2 Inorganic Scintillators

Inorganic scintillators (e.g., see [Swank (1954)]) are ionic crystals doped or not

with color centers (activator). Examples of inorganic scintillators without activator

are BGO (Bi

), CeF

, BaF

or PbWO

. Production of luminescence in

inorganic scintillator such as NaI(Tl) or CsI(Tl) requires the presence of an activator

(Thalium), as explained below. Inorganic scintillators have high density and high

atomic number compared to organic scintillators. From these properties, one can

immediately expect the inorganic scintillators to have high absorption for γ- and

X-rays. They also have high absorption for electrons, alpha, protons and charged

heavy particles, in general. Crystals have rather short radiation lengths, between

0.9 and 2.6 cm, and densities from 3.7 up to 8.3 g/cm

(Tables 5.2 and 5.3).

Table 5.2 Properties of NaI(Tl), BGO and CeF

inorganic scintillators

(see, for instance, [Leroy and Rancoita (2000)]).

Properties NaI(Tl) BGO CeF

Density (g/cm

) 3.67 7.13 6.16

Radiation Length (cm) 2.59 1.12 1.68

Moliere radius (cm) 4.5 2.4 2.6

dE/dx(MeV/cm) [per mip] 4.8 9.2 7.9

short decay time (ns) 230 300 ∼ 5

long decay time (ns) 150[ms] 30

Peak emission(nm): short 415 480 310

Peak emission(nm): long 340

Refractive index at peak emission 1.85 2.20 1.68

light yield (vs NaI(Tl)) 1.00 0.15 0.10

light yield γ/MeV 4 × 10

8 × 10

2 × 10

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424 Principles of Radiation Interaction in Matter and Detection

The mechanism of scintillation for these crystals is a lattice eﬀect, rather than a

molecular eﬀect as it was the case for organic scintillators. The valence band contains

electrons that are bound at the lattice sites. Electrons in the conduction band are

free to move throughout the crystal. The passage of a charged particle through the

crystal may produce the ionization of the crystal, if the incoming particle transfers

suﬃcient energy to the electrons from the valence band for them to acquire suﬃcient

energy to move into the conduction band, leaving a hole in the valence band. If the

incoming energy is not high enough, the electron of the valence band will not reach

the conduction band and will form a bound state, called exciton, with the hole. The

excitons are located in an exciton band below the conduction band. Finally, there

exist activator centers in the scintillator which occupy energy levels in the gap,

between the conduction and the valence bands. So, the passage of charged particle

through the scintillator medium generates a large number of free electrons, free

holes and electron–hole pairs which move around in the crystal lattice until they

reach an activator center. They then transform the activation center into an excited

state. The subsequent decay of this excited state to the activator center ground

state produces emission of light. The decay time of this scintillation light is given

by the lifetime of the excited state. Therefore, to help the scintillation eﬃciency,

i.e., to increase the probability of visible light emission, one may introduce a small

amount of impurity called activator. Thalium (Tl) is often used as activator. For

instance, NaI(Tl) and CsI(Tl) usually contain about 0.1% of Thalium. The light

Table 5.3 Properties of BaF

, CsI(Tl) and PbWO

inorganic scintillators (see,

for instance, [Leroy and Rancoita (2000)]).

Properties BaF

CsI(Tl) PbWO

Density (g/cm

) 4.89 4.53 8.28

Radiation Length (cm) 2.05 1.85 0.89

Moliere radius (cm) 3.4 3.8 2.2

dE/dx(MeV/cm) [per mip] 6.6 5.6 13.0

short decay time (ns) 0.6 > 1000 5

long decay time (ns) 620 15

Peak emission(nm): short 220 550 440

Peak emission(nm): long 310 530

Refractive index at peak emission 1.56 1.80 2.16

light yield (vs NaI(Tl)) 0.05(fast) 0.40 0.01

0.20(slow)

light yield γ/MeV 10

5 × 10

1.5 × 10

emission is characteristic of the activator and it is possible to modify the emission

wavelength by varying the activator.

The shape of the scintillation pulse emitted by an inorganic scintillator is char-

acterized by a fast rise time of a few tens of nanoseconds and a decay which has

two components: a short (fast or prompt) exponential decay, whose decay time

constant (τ

d,s

) lies between a few nanoseconds and a few hundred of nanoseconds

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Scintillating Media and Scintillator Detectors 425

(Tables 5.2 and 5.3), which governs the main part of the pulse, and a long (slow)

delayed component with a decay constant (τ

d,l

) of few hundred nanoseconds up to

microseconds or even milliseconds (Tables 5.2 and 5.3). Then, the number, N, of

photons emitted at time t is given by

N = A

−t/τ

d,s

+ A

−t/τ

d,l

, (5.10)

where τ

d,s

and τ

d,l

are the short and long decay constants, respectively. A

and

are the relative magnitude of the short and long components, respectively. The

ratio A

varies with the material (see Tables 5.2 and 5.3).

For NaI(Tl), the γ is emitted with τ

d,s

∼ 230 ns and 80% of the light intensity

is emitted in 1µs. Phosphorescence may persist up to τ

d,l

= 150 ms (Tables 5.2 and

5.3). In BGO, there is a fast component τ

d,s

∼ 60 ns, accounting for about 10%

of the light intensity, and a slow component τ

d,l

∼ 300 ns, representing 90% of the

light intensity (Tables 5.2 and 5.3). BaF

is characterized by a very fast component

d,s

∼ 0.6 ns, which represents 20% of the total light intensity and a slow component

d,l

∼ 620 ns.

The decay time of the scintillator should be as short as possible. This becomes

an important constraint in experiments at LHC, where the light has to be collected

in less than 10 ns since the expected LHC interbunch crossing is 25 ns, requiring the

use of new types of crystals such as PbWO

which has a time decay constant with an

average value of 10 ns allowing 85% of the light to be collected during the interbunch

crossing time. Radiation hardness of the crystal is also an important issue at LHC

where crystals will be exposed to irradiation ﬂuence of 10

–10

hadrons/cm

de-

pending on pseudorapidity (see Sect. 3.2.3.1). The choice of PbWO

crystal, for the

electromagnetic calorimeter of CMS exp eriment at LHC, is a compromise between

best possible scintillation performance and best radiation hardness.

In inorganic scintillators, dL/dx also varies with energy but deviations to lin-

earity are weaker in most of the applications and in practice Birk’s law is not

applied. Non-linearity of the order of 20% can be observed at low energy. This

non-linearity of the response to low-energy γ- and X-rays is the consequence of the

non-linearity of their response to electrons responsible for the transfer of γ- and

X-rays energy to the crystal.

The photoelectric eﬃciency is maximal for γ- and X-rays of low energy (<

100 keV), for which the interactions with the crystal (high-Z) are largely dominated

by the photoelectric eﬀect, R

≈ 1. For higher energies, the value of R

depends

on various factors such as the incident γ energy, the absorption coeﬃcients of the

various interaction processes in the crystal, the mechanisms of γ energy deposition

in the scintillator, the geometrical size of the detector and the geometry of the

experimental setup. Inorganic scintillators such as NaI(Tl) and BGO are standardly

used as active elements of medical imagers.

Inorganic scintillators generally have two emission bands: a) one is characteristic

of the activator; b) the second corresponds to shorter wavelengths and is characteri-

stic of the crystal lattice. Tables 5.2 and 5.3 show that the maximum of the spectral

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426 Principles of Radiation Interaction in Matter and Detection

emission takes place in most inorganic scintillators at 220 nm ≤ λ ≤ 550 nm i.e., in

overlap with the spectral sensitivity domain of standard photocathodes.

Tables 5.2 and 5.3 summarize the values of decay constants and light yields for

various inorganic crystals. The detected signal in these tables is quoted in terms

of γ per MeV. One often expresses the detected signal in photo electrons per MeV

). This conversion into n

depends on several factors such as the light collection

eﬃciency and the quantum eﬃciency of the photosensitive device. It has to be noted

that the light yields reported in Tables 5.2 and 5.3 have been measured with a

photomultiplier with a bialkali photocathode.

Several inorganic scintillators will deteriorate due to water absorption, if ex-

posed to air. This sensitivity to moisture is called hygroscopicity. Scintillators such

as NaI(Tl), CsI(Na) are hygroscopic while BGO, CeF

, BaF

, PbWO

are not. Hy-

groscopic scintillators have to be placed in an air-tight container to protect them

from moisture. CsI(Tl) is only slightly hygroscopic and may be handled without

protection.

5.2 The

Cerenkov Detectors

As seen in Sect. 2.2.2, a charged particle traveling in a dielectric medium of refractive

index n > 1 with a speed v greater than the speed of light in the medium (v > c/n

or β > 1/n) emits radiation, the

Cerenkov light (Fig. 5.1). It has to be noted that, in

Sect. 2.2.2, the refractive index has been indicated by the symbol r and the number

of electron per cm

by the symbol n, while in the present section the refractive

index is indicated by the symbol n. The

Cerenkov light is emitted in a forward cone

of aperture cos θ = c/(vn) = 1/(βn). One has

sin

θ = 1 −

. (5.11)

trajectory

Wave front

Incoming particle

β c t

Fig. 5.1 The principle of

Cerenkov light emission. The light is emitted in a forward cone of

aperture cos θ = [(ct)/n]/(βct) = 1/(βn).

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Scintillating Media and Scintillator Detectors 427

The maximum emission angle, θ

max

, corresponds to β = 1 or v = c,

i.e., cos θ

max

= 1/n. One can express the threshold condition for

Cerenkov light

emission as

thr

= v

thr

/c ≥ 1/n (5.12)

and the threshold Lorentz factor is

thr

1 − β

thr

√

− 1

. (5.13)

Equations (1.10, 5.13) deﬁne a particle threshold-energy, E

thr

, given by

thr

= γ

thr

, (5.14)

where m

is the particle rest mass. The threshold Lorentz factor, γ

thr

, depends

on the particle mass for a ﬁxed energy and explains why the measurement of the

Cerenkov radiation allows particle identiﬁcation.

Using Eq. (5.11), the energy emitted by a particle of charge number z and mass

m per unit length and unit wavelength moving with a velocity β in a medium of

refractive index n is given by [Fernow (1986)]:

dx dλ

= 4π

1 −

(5.15)

where r

= e

(= 2.817938 fm) is the classical radius of the electron.

The number of photons, N

, emitted per unit length of the track of the incident

particle of charge number z through the medium, in a wavelength interval, is given

by Eq. (2.138), which can be re-expressed in terms of dλ (see page 128):

= 2παz

1 −

dλ

(5.16)

where α ∼ 1/137 and n is the refractive index.

In the wavelength interval dλ, the radiation intensity depends only on the charge

numb er z of the incident particle and on the emission angle, and therefore on the

particle velocity. The presence of λ

in the denominator of Eq. (5.16) indicates

an emission concentrated at shorter wavelength. The emission takes place in the

wavelength domains of visible and UV light. If the emission takes place in the range

min

(= λ

) − λ

max

(= λ

after integration, Eq. (5.16) becomes:

= 2παz

1 −

¶µ

− λ

. (5.17)

It was assumed that n was independent of λ, i.e., the dispersion of the radiator was

neglected. In the wavelength domain of the visible and UV light, 400 to 700 nm,

which corresponds to the domain of spectral sensitivity of the standard photocath-

odes (e.g., bialkali photocathodes are sensitive to wavelengths of 400 to 575 nm),

Eq. (5.17) becomes

= 491 cm

−1

1 −

. (5.18)

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428 Principles of Radiation Interaction in Matter and Detection

The light emitted by a

Cerenkov radiator is smaller than that emitted by scin-

tillators of the same dimensions. For a particle with β ∼ 1 in water (n = 1.33),

sin

θ ∼ 0.43 [see Eq. (5.11)] and about 210 photons/cm [see Eq. (5.18)] are emit-

ted. Equation (5.15) integrated over the wavelength domain of 400 to 700 nm gives

an emitted energy of ∼ 1200 × 0.43 = 516 eV/cm corresponding to ≈ 3 × 10

−4

the energy lost by a mip (∼ 2 MeV/cm) in scintillator.

Using the standard relation

E = hν =

2π~c

, (5.19)

the number of photons emitted per energy interval, dE, is given by:

dx dE

dx dλ

dλ

2π~c

dx dλ

. (5.20)

Furthermore, using Eq. (5.16), one ﬁnds (Frank–Tamm equation)

dx dE

αz

1 −

, (5.21)

or, equivalently, since ~c = 197.32710

eV fm and α ∼ 1/137

dx dE

= 370 × z

1 −

[eV cm]

−1

. (5.22)

For a radiator of length L, the number of photoelectrons, N

, detected in the

photosensitive device is proportional to the energy acceptance window

∆E = E

− E

of the photosensitive device and is given by:

= 370 eV

−1

× Lz

1 −

col

(E) ²

det

(E) dE, (5.23)

where ²

col

is the eﬃciency for collecting the

Cerenkov light (transmission, reﬂec-

tions) and ²

det

is the quantum eﬃciency of photo-conversion of the photosensitive

device. One deﬁnes the factor of merit, N

, of the detector [S´eguinot (1988)] by

= 370 eV

−1

× z

col

(E) ²

det

(E) dE [cm]

−1

. (5.24)

Deﬁning

¯² =

∆E

col

(E) ²

det

(E) dE, (5.25)

one can write the total number of detected photons as:

= N

1 −

(5.26)

with

= 370 eV

−1

× z

¯² ∆E [cm]

−1

. (5.27)

With a quantum eﬃciency of photo-conversion of 40% and eﬃciency for collecting

the

Cerenkov light of 75%, assuming ²

col

and ²

det

independent of energy, for z = 1

one ﬁnds

∼ 110 eV

−1

× ∆E [cm]

−1

. (5.28)

Cerenkov detectors of various types (threshold, diﬀerential and ring-imaging)

are used for particle identiﬁcation.

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Scintillating Media and Scintillator Detectors 429

5.2.1 Threshold

Cerenkov Detectors

Threshold

Cerenkov detectors can be used to separate particles of same momentum

and diﬀerent masses in a beam. This situation is usually encountered in secondary

beams of hadronic accelerator facilities. These secondary beams may contain elec-

trons, pions, kaons and protons of same momentum. The

Cerenkov light emitted

in a forward cone is reﬂected back by a spherical mirror into photomultiplier tubes

(one or two). Depending on the relative position of the spherical mirror and photo-

multiplier tubes, a plane mirror can be put at angle with the photomultipier tubes

to help focalize the light on the photocathodes (Fig. 5.2).

beam axis

Spherical

Particle

mirror

Photomultiplier

Fig. 5.2 Schematic description of a threshold

Cerenkov detector of the type used in CERN-PS

secondary hadronic beams (adapted and reprinted, with permission, from the Annual Review of

Nuclear Science, Volume 23

° 1973 by Annual Reviews www.annualreviews.org; [Litt and Meunier

(1973)]). The

Cerenkov light is reﬂected back by a spherical mirror onto the photocathode of the

photomultiplier tube (PMT).

Let us assume that one wishes to separate particles “1” and “2” in a beam which

also contains particles “3”. These particles have the same momentum p and rest

masses m

, m

and m

< m

), respectively. Two

Cerenkov detectors

(C1 and C2) are needed to separate particles “1” and “2”. The refractive index of

the radiator of C1 has to be adjusted at a value for which particle “2” is just at

threshold, i.e., does not radiate: then, β

= 1/n

and sin

= 0. From Eq. (5.13),

one also has n

= γ

/(γ

− 1). Then, the production rate of photons from particle

“1” is given by Eq. (5.18) with

sin

= 1 −

. (5.29)

The particle energy, E, and its velocity, β = v/c, are related through

(5.30)

and

= m

+ p

(5.31)