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

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440 Principles of Radiation Interaction in Matter and Detection

nique via transition radiation and detector optimization can be found in [Dolgoshein

(1993); Egorytchev, Saveliev and Aplin (2000)].

5.5 Scintillating Fibers

Standard scintillating ﬁbers consist of a core having a high refractive index (n

core

)

cladded with a non-scintillating material of lower refractive index (n

clad

). A scintil-

lating ﬁber traversed by an ionizing particle or radiation is illustrated in Fig. 5.7. The

diameter of the core material depends on the application. For particle tracking, for

which the best spatial resolution is needed, the ﬁber diameter is smaller than 1 mm

down to a few tens of µm. For calorimetry applications, for which the measure-

ment of energy deposition is the goal, ﬁbers with diameter of 1 mm and above

are used. The thickness of the cladding material is a few microns, typically 2 to

5 µm. The cladding material is surrounded by a thin opaque absorber a few mm

thick, called the extra mural absorber (EMA), which captures the untrapped light.

The presence of EMA helps to prevent cross-talk between neighbouring ﬁbers, which

clad

core

Cladding

EMA

radiation

reflected photon

Scintillator/core

Fig. 5.7 Schematic description of a scintillating ﬁber. The core (refractive index n

core

) is cladded

with a non-scintillating material (refractive index n

clad

). The extra mural absorber (EMA) cap-

tures the untrapped light.

is essential for particle tracking.

The scintillation light produced in the ﬁber by the passage of a ionizing par-

ticle or radiation is trapped by internal reﬂections on the ﬁber core/cladding in-

terface. The phenomenon of internal reﬂection can be understood from Snell’s

law. Consider a ray of light which propagates from medium “a” of refractive in-

dex n

, into medium “b” of refractive index n

, with n

> n

. If θ

and θ

are the

angles made with the normal for the incident and refracted rays, Snell’s law says

sin θ

= n

sin θ

. (5.81)

From Eq. (5.81) where one has put sin θ

= 1, the critical angle is deﬁned:

= sin

−1

. (5.82)

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Scintillating Media and Scintillator Detectors 441

At the critical angle θ

, the refracted ray is tangent to the interface at the point of

incidence. Most importantly for our purpose, when the angle of incidence is larger

than the critical angle, θ

> θ

, no refracted ray appears and the incident ray

undergoes total internal reﬂection from the interface. The operation of scintillating

ﬁbers is based on the principle of total internal reﬂection. In the case of a ﬁber,

Eq. (5.82) becomes:

= sin

−1

clad

core

. (5.83)

The emitted scintillation light hitting the core/cladding interface at an angle larger

than the critical angle [Eq. (5.83)] will be reﬂected back into the core. The scin-

tillation light becomes trapped in the ﬁber and will propagate inside the ﬁber via

total internal reﬂections on the core/cladding interface until it reaches the ﬁber end

where it will be detected by a photosensitive device.

Typical core materials are polystyrene with n

core

= 1.59 or glasses such as GS1

(with a few % by weight of Ce

) with n

core

= 1.69. Cladding materials are acrylic

with n

clad

= 1.49.

For light emitted at the axis of the ﬁber or close to it (called meridional rays),

traveling along the ﬁber axis, the fraction of light trapped is:

f =

1 −

clad

core

. (5.84)

In the case of isotropic light propagation inside the ﬁber, equal amounts are trapped

in both directions and the total fraction of trapped light is f

tot

= 2f . For n

core

1.59 and n

clad

= 1.49, θ

= 1.21, and f

tot

= 0.06. Light rays, oﬀ the ﬁber axis and

close to the ﬁber edge (called skew rays), follow spiral paths along the length of the

ﬁber. Adding meridional and skew rays would modify Eq. (5.84) into [Leutz (1995);

White (1988)]:

f =

1 −

clad

core

, (5.85)

which brings f

tot

= 0.12. Skew rays have larger solid angle acceptance and undergo

more reﬂections at the core/cladding interface than meridional rays. Then, skew

rays are very sensible to defects in the core/cladding interface and suﬀer losses from

these defects which reduce their propagation length in the ﬁber.

The trapped light is transp orted to the ﬁber end via a maximum of n

total

internal reﬂections at the core/cladding interface [Leutz (1995)]:

cot θ

, (5.86)

where l and d are the ﬁber length and diameter, respectively. The critical angle θ

is given by Eq. (5.83). For a polystyrene core of diameter 0.25 mm and 1 m length

and an acrylic cladding, one ﬁnds n

∼ 1500.

One also deﬁnes the numerical aperture NA as [Leutz (1995)]

NA =

core

− n

clad

. (5.87)

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442 Principles of Radiation Interaction in Matter and Detection

Taking a ﬁber with a polystyrene core and an acrylic cladding, the numerical aper-

ture is N A = 0.55.

For tracking purpose, one wishes to select ﬁbers with diameter as small as possi-

ble to achieve good spatial resolution. From Eq. (5.86), one can see that the decrease

of the ﬁber diameter increases the number of reﬂections and, therefore, additional

light losses due to defects in the core/cladding interface are expected. The light in-

tensity I after n

reﬂections is related to the initial light intensity I

through [Leutz

(1995)]:

I = I

, (5.88)

where q ≤ 1 is the reﬂection coeﬃcient whose value reﬂects light losses at the

core/cladding interface. The combination of Eqs. (5.86, 5.88) gives:

= −(1 − q)

cot θ

, (5.89)

where ln q has been replaced by (q − 1), since q is very close to unity. The expe-

rimental value [Leutz (1995)] of (1 − q) is typically (5 − 6) × 10

−5

, depending on

wavelength. The reﬂection length, Λ

, is the ﬁber length after which the initial light

intensity is reduced to 1/e of its value as the result of reﬂection losses. It is given

by [Leutz (1995)]:

1.5

1 − q

core

d. (5.90)

The total attenuation length, Λ, is the sum [Leutz (1995)] (see discussion in this

reference):

−1

= Λ

−1

+ Λ

−1

+ Λ

−1

, (5.91)

where Λ

is deﬁned as the value of the light path length D (in meters) at which

the light yield drops to 1/e of its initial value at zero D. The attenuation, Λ

quantiﬁes Rayleigh scattering on small density ﬂuctuations in the core material

that can deﬂect a light ray which is no longer totally internally reﬂected.

5.6 Detection of the Scintillation Light

The ionization energy deposited by a particle traversing a scintillator material is

converted into photons. If one considers a plastic scintillator such as NE102A (see

Table 5.1), a scintillation photon is produced for about 3 keV of deposited energy,

which corresponds to a yield of about 500 photons per centimeter of scintillator

material. This scintillation light is of low intensity and has to be optically coupled

to a photomultiplier for ampliﬁcation in order to provide an electrical signal. A

schematic view of a photomultiplier is given in Fig. 5.8. The scintillation light has

to be transported to the photocathode of the photomultiplier where the impinging

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Scintillating Media and Scintillator Detectors 443

photons will be converted into photoelectrons via the photoelectric eﬀect (Einstein

equation):

E = hν − φ, (5.92)

where E is the kinetic energy of the emitted electron, ν is the frequency of incident

scintillation light and φ is the work function. The surface of the photocathode is

coated with a photosensitive material that has a low work function to favor electron

emission. The probability of this photon to electron conversion is the quantum

eﬃciency QE of the photocathode, i.e., the probability of liberating an electron per

photon striking the photocathode:

QE(λ) =

number of photoelectrons emitted

number of photons incident on the photocathode

. (5.93)

Photoelectrons

Dynode

Anode

Shield

Focusing grid

Incident radiation

Photocathode

Fig. 5.8 Schematic view of a photomultiplier.

The quantum eﬃciency depends on the type of photocathode material. The type

of photocathode is chosen to have an overlap between its peak spectral response

and the characteristic wavelength at maximum emission of the incoming light. The

quantum eﬃciency is typically 20–25%.

A plastic light guide couples the scintillator to the photomultiplier. A “ﬁsh tail”

shape for the light guide is standard (Fig. 5.9), but other shap es are also used

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444 Principles of Radiation Interaction in Matter and Detection

depending on the application. It allows the coupling of photocathode, which are

of small area, to a scintillator with a large cross section. The light emitted in the

Scintillator plate

Photomultiplier

base

Light guide (fish tail)

Fig. 5.9 Schematic view of a scintillator coupled to a photomultiplier via a ﬁsh tail light guide.

scintillator is transported to the photocatho de through the scintillator and light

guide via total internal reﬂections. When the emitted light strikes the scintillator

surface, total internal reﬂection occurs when the incident angle is larger than the

critical angle [Eq. (5.83)]. In the present situation, Eq. (5.83) becomes

= sin

−1

med

. (5.94)

The surrounding medium is often air, n

med

= n

air

= 1, and Eq. (5.94) becomes:

= sin

−1

. (5.95)

For the example of NE102A above, n = 1.58 and therefore Eq. (5.95) gives θ

39.2

◦

. The fraction f of light emitted and transported via total internal reﬂection

in one direction is (e.g., see Equation 7.4 of [Fernow (1986)]):

f =

4π

2π

sin θ dθ dφ

(1 − cos θ

)

1 −

√

− 1

w 0.11. (5.96)

The scintillator and light guide are wrapped with an aluminium foil to prevent the

leak, from plastic, of light escaping total internal reﬂection. The scintillator, light

guide and photomultiplier are also wrapped with a layer of black tape to prevent

outside light from leaking inside the detector.

In this case, the cladding is replaced by the surrounding medium of refractive index n

med

and

the core by scintillator of refractive index n.

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Scintillating Media and Scintillator Detectors 445

Geometrical constraints often forces the bending of the light guide (which could

be also a bundle of ﬁbers) to achieve the coupling to the photomultiplier. However,

there exists a limit for maximum bending beyond which important light losses

occur. The maximum bending is calculated from the condition (Liouville’s law):

− 1 ≥

+ 1

, (5.97)

where d is the light guide diameter, r is the bending radius and n is the refractive

index relative to air. If the bending radius satisﬁes condition Eq. (5.97), the light

will be transported along the light guide via total internal reﬂections.

The intensity of light transported in the scintillator and light guide is attenuated

by atomic absorption and scattering from imperfections of the reﬂecting surface

(which should be negligible if the surface has been cleanly polished). The reduction

of light intensity, I, is a function of distance, l, and light wavelength, λ, can be

expressed by:

I(l, λ) = I(0, λ) exp

−

(λ)

, (5.98)

where I(l, λ) is the light intensity at distance l and wavelength λ, I(0, λ) is the

initial light intensity and I

(λ) is the photon attenuation length at wavelength

λ. As seen in Sect. 5.3, the introduction of a wavelength shifter in the scintillator

increases the attenuation length. Taking into account Eqs. (5.93, 5.96, 5.98), the

numb er of photoelectrons produced by the photocathode can be expressed by:

= n

I(L, λ) QE(λ) f(λ) dλ, (5.99)

where f , in Eq. (5.96), now depends on λ, and n

is the number of photons

produced in the scintillator of length L. Let us consider the example of a NE102A

scintillator counter of 1 cm thickness. Its light output is about 25% of NaI(Tl) (see

Table 5.1), i.e., 10

γ/MeV or 1 γ/100 eV. A minimum ionizing particle traversing

the scintillator thickness loses about 2 MeV/cm. Therefore, about 2×10

γ should be

emitted in 1 cm of scintillator. NE102A has an attenuation length of 250 cm which

gives an intensity loss of 0.4% in 1 cm according to Eq. (5.98). The fraction of

light trapped in scintillator within the critical angle is directly given by Eq. (5.96),

since the refractive index of NE102A is 1.58. Assuming a quantum eﬃciency of

20% for the photocathode and an optical collection eﬃciency of about 50% (due

to imperfections of the reﬂecting surface and imperfect coupling of the light guide

to the photocathode), one ﬁnds the number of photoelectrons, n

, coming oﬀ the

photocatho de:

≈ 220. (5.100)

The number of photoelectrons produced at the photocathode follows a Poisson

distribution P (n

) and the probability of production of n

photoelectrons for a

mean number ¯n

is (Appendix B.1):

P (n

) =

¯n

−¯n

. (5.101)

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446 Principles of Radiation Interaction in Matter and Detection

The detector eﬃciency, ², is the detection probability which is the complement of

non-detection probability. Therefore, one has:

1 − ² = e

−¯n

, (5.102)

where e

−¯n

is the ineﬃciency or the probability of detecting no photoelectron. In

this example, Eq. (5.100) gives e

−¯n

' 0 and the eﬃciency, ², is ' 100%.

The photomultiplier is powered by a high voltage power supply. The photocath-

ode, made of alkali metals, is the most negative electrode and put at a large negative

voltage, e.g., −1400 V up to −2200 V. The anode is at 0 V.

A set of metallic electrodes, called dynodes, forms the electron multiplier sec-

tion. The dynodes, set at progressively higher voltage, e.g., steps of (100–120) V, are

located between the photocathode and the anode (see Fig. 5.8). A dynode re-emits

electrons when struck by an electron. This emission of secondary electrons by a dy-

node, via the photoelectric eﬀect [Eq. (5.92)], is similar to photoelectron emission

by the photocathode. However, there is a major diﬀerence: incoming electrons are

responsible for secondary electron emission in the case of the dynode, while incident

scintillation photon are responsible for this emission for the photocathode. Like the

photocatho de, dynodes are made of low work function material to maximize elec-

tron emission by photoelectric eﬀect. Voltage to each dynode is delivered through

a resistive potential divider consisting of a chain of resistors in series contained in

the photomultiplier base (Fig. 5.9). The electrons ejected from the photocathode

are accelerated towards the ﬁrst dynode due to the diﬀerence of potential of (100–

120) V between the photocathode and the ﬁrst dynode, from which they knock out

several electrons. These secondary electrons are accelerated, through the potential

gradient between the ﬁrst and second dynodes, towards the second dynode, where

each of them ejects more electrons, and so on. The inter-dynode voltage allows the

multiplication of secondary electrons via photoelectric eﬀect from dynode to dy-

node, until they reach the anode where the charge is collected. The multiplication

factor (called the gain), M , between the ﬁrst stage of the n-dynode chain and the

anode is

M = δ

. . . δ

, (5.103)

where δ

is the multiplication factor at the dynode i of the chain. From Eq. (5.103),

a standard multiplication factor of 10

with a chain of 12 dynodes can be achieved,

if each electron produces about 4 secondary electrons when it strikes a dynode. A

chain of 10 dynodes would reduce M to 10

. The charge collected at the anode for

M = 10

is then

Q = e 10

= 1.6 × 10

−19

C × 10

= 1.6 × 10

−12

C = 1.6 pC. (5.104)

Since the charge is collected typically within 5 ns, the current at the anode is:

i =

1.6 × 10

−12

5 × 10

−9

= 0.32 mA. (5.105)

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Scintillating Media and Scintillator Detectors 447

Usually, the signal drives a 50 Ω load, i.e., the photomultiplier is terminated with

a 50 Ω resistance. Then, a pulse of

δV = 0.32 mA × 50 Ω = 16 mV (5.106)

is produced. Photomultipliers are also characterized by a rise-time (about 2 ns,

typically). The rise-time is usually deﬁned as the time required for the output signal

to increase from 10% to 90% of the maximal value. The time elapsed between

the illumination of the photocathode and the signal at the anode is the transit

time (about 30 ns, typically), which can be understood as the time needed for the

electron to travel the length of the photomultiplier. Information about the rise-time

and transit time are given by technical speciﬁcations released by the manufacturer

of the photomultiplier. The output pulse at the anode is subsequently analyzed by

an electronics system. A example of such a system is shown in Fig. 5.10.

PHAAMP

S, T, etc

Fig. 5.10 Schematic description of an analyzing electronics system consisting of a preampliﬁer

(PA), a high voltage power source (HV), an ampliﬁer (AMP), a pulse height analyzer (PHA),

followed by a spectrometer analyzer (S), a timing unit (T), etc. . .

The size of the pulse at the anode is proportional to the energy absorbed from

the incident radiation by the scintillating material. This is the consequence of the

proportionality between the amount of light that reaches the photocathode surface

and the amount of photoelectrons ejected. Therefore, the scintillation detector can

be used to distinguish between diﬀerent types of particles or incoming particles of

diﬀerent energy by the shape of the emitted light pulse. The pulse produced by a

scintillator detector is controlled by the dominant decay time of the scintillator and

the electron transit time through the PM chain. The number of photons emitted

after the passage of the ionization radiation follows the exp onential law described by

Eq. (5.8) with decay constants for various scintillators ranging from a few nanosec-

onds to a few microseconds (Tables 5.2 and 5.3). The electron transit time is a

Gaussian function of time with a standard deviation of about 1 ns. When the scin-

tillator decay constant is 10 ns or larger, the eﬀect of the spread in the electron

transit time is negligible.

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448 Principles of Radiation Interaction in Matter and Detection

5.7 Applications in Calorimetry

A variety of scintillating and

Cerenkov materials can be used as the active medium

of homogeneous calorimeters (see Sect. 9.5) or active samplers of sampling calorime-

ters. The choice of a particular active medium is made to achieve the b est possible

energy and position resolutions over an energy range as large as possible (from MeV

up to TeV energies), taking into account practical and physical requirements. The

energy resolution is determined by the ﬂuctuations in the number of photons or ion

pairs produced by the cascade. The light yield, i.e, the number of photons produced

per MeV of energy deposition, should be large enough to minimize the contribution

of the statistical ﬂuctuations to the energy resolution.

A comprehensive treatment of calorimeter performance can be found in the

chapter Principles of Particle Energy Determination.

5.8 Application in Time-of-Flight (ToF) Technique

The excellent timing capabilities of scintillator counters make them applicable in

time-of-ﬂight (ToF) techniques [Atwood (1981)]. Measurements of particles ToF,

combined with the knowledge of their momentum, give information on their

mass. Therefore, ToF measurement may allow discrimination between particle of

same momentum but diﬀerent masses.

The speed of a particle of mass m, momentum p, traveling a distance L in a

time t is given by

v =

, (5.107)

then,

β =

. (5.108)

Using Eq. (5.32) with γ = 1/

1 − β

, one ﬁnds:

m =

βγc

− 1. (5.109)

A ToF measurement system consists of two scintillator plastic counters as shown

in Fig. 5.11. Plastic scintillators are chosen for their fast response. One of the coun-

ters serves as start counter, the other as stop counter. The time information is given

by a time to digital-converter (TDC) while charge measurement is obtained from

analog to digital converter (ADC).

If two scintillator counters are separated by a distance L, two particles “1” and

“2” of momentum p, with masses m

and m

, velocities v

and v

and energies E

and E

will traverse this distance with times of ﬂight

+ p

(5.110)

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Scintillating Media and Scintillator Detectors 449

TDC(t )

ADC(A )

DISC

ADC(A )

DISC

TDC(t )

particle

1 2

Stop

counter

Start

counter

Fig. 5.11 Schematic description of a T oF measurement system. The start and stop counters, 1

and 2, respectively, are read each by a photomultiplier (PM). The chain of time measurement

for each counter consists of a discriminator (DISC) and a TDC(t

), while charge measurement is

obtained from an ADC(A

and

+ p

. (5.111)

There will be a ToF diﬀerence between these two particles of

∆t = t

− t

+ p

−

+ p

. (5.112)

For relativistic particles, pc >> mc

, Eq. (5.112) may be approximated by:

∆t =

·µ

1 +

−

1 +

¶¸

, (5.113)

∆t =

− m

). (5.114)

In practice, the distance L is one or several meters and times of reference such as

times of resolution are in picoseconds (ps). Therefore, it is standard to express the

ration ∆t/L in ps/m units:

∆t

1667

− m

) [ps/m]. (5.115)