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

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430 Principles of Radiation Interaction in Matter and Detection

with

p = mβγc. (5.32)

Therefore, using Eq. (5.30), Eq. (5.29) can be written as:

sin

= 1 −

− 1

−

. (5.33)

The particle momentum, p, and its velocity, β = v/c, are related through (at

threshold, β = 1/n )

p = mβγc =

mβc

1 − β

√

− 1

. (5.34)

So, being at the particle “2” threshold, one has

sin

= 0 =

− 1

−

, (5.35)

− 1 =

. (5.36)

Then with the use of Eq. (5.36), Eq. (5.33) becomes

sin

− m

) c

. (5.37)

So, the conditions of Eqs. (5.36, 5.37) have to be fulﬁlled to achieve separation of

particles “1” and “2”.

The length of the radiator needed to produce a given number of photoelectrons

increases with the square of the momentum. Then, the length L of the radiator can

be determined to secure a usable practical counting rate of photons. Taking into

account the quantum eﬃciency ², the number of photoelectrons [Eq. (5.18)] is:

= 491 cm

−1

× ²L

− m

) c

. (5.38)

To obtain N photoelectrons per cm, a radiator length of

L = N

491 × c

² (m

− m

)

(5.39)

is needed with the correct refractive index. If m

= m

= 139.6 MeV/c

and m

= 493.6 MeV/c

, with p = 5 GeV/c and a quantum eﬃciency of 20%, a radiator

length of 17 cm is needed to collect 15 photoelectrons. A radiator with a refractive

index n = 1.005 [Eq. (5.36)] has to be selected to prevent the radiation of the kaon

particles.

To separate particles “2”, one has to select a second radiator with refractive

index n

set at a value for which particle “3” is at threshold:

sin

= 0 =

− 1

−

. (5.40)

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Scintillating Media and Scintillator Detectors 431

Consider the case of secondary beams delivered by the CERN Proton-Synchroton

(PS) which contains pions, kaons and protons (m

< m

), one needs to use

three

Cerenkov detectors to achieve pion, kaon and proton separation. At ﬁrst, if

one uses two aerogel

Cerenkov radiators C1 with n = 1.1 and C2 with n

= 1.02,

one can separate pions and kaons [Eq. (5.34)]. Then the threshold momenta (p

thr

)

are:

for pions to emit light in C1:

p > p

thr

√

− 1

= 0.3 GeV/c (n = 1.1); (5.41)

for pions to emit light in C1 and C2

p > p

thr

√

− 1

= 0.7 GeV/c (n = 1.02); (5.42)

for kaons to emit light in C1

p > p

thr

√

− 1

= 1.1 GeV/c (n = 1.1); (5.43)

for kaons to emit light in C1 and C2

p > p

thr

√

− 1

= 2.5 GeV/c (n = 1.02). (5.44)

Therefore, pion/kaon separation can be achieved in the momentum range below

2.5 GeV/c with two

Cerenkov counters. If one adds a third

Cerenkov counter C3

with n = 1.005 (not aerogel), one ﬁnds threshold momenta to be added to the set

of Eqs. (5.41–5.44) such as:

for protons to emit light in C1

p > p

thr

√

− 1

= 2.1 GeV/c (n = 1.1); (5.45)

for protons to emit light in C1 and C2

p > p

thr

√

− 1

= 4.7 GeV/c (n = 1.02); (5.46)

for the three particles to give light in C1, C2 and C3

p > p

thr

√

− 1

= 9.4 GeV/c (n = 1.005), (5.47)

p > p

thr

√

− 1

= 1.4 GeV/c (n = 1.005), (5.48)

p > p

thr

√

− 1

= 4.9 GeV/c (n = 1.005). (5.49)

Thus, pion/kaon/proton separation can be achieved in the momentum range below

4.7 GeV/c. For a beam of 2 GeV/c particles, using this set of three

Cerenkov counters

with the same values of refractive indices, kaons, protons, and pions would emits

light in C1, C2 and C3; kaons and protons would give light only in C1.

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432 Principles of Radiation Interaction in Matter and Detection

Gaseous threshold counters are often used. They oﬀer the possibility to vary

the refractive index by pressure adjustment. The refractive index of the radiative

medium is given by the Lorentz–Lorenz law [Litt and Meunier (1973)]:

− 1

+ 2

ρ, (5.50)

where R is the molecular refractivity, M is the molecular weight, and ρ is the gas

density. In the case of a gas with n ∼ 1, Eq. (5.50) becomes (see for instance [Fernow

(1986)]):

n − 1 =

ρ. (5.51)

From the ideal gas law

, (5.52)

where P and T are the pressure and temperature, respectively, Eq. (5.51) becomes:

n − 1 =

. (5.53)

If n

is the refractive index of the gas for a given wavelength of light, at temperature

T and pressure P = 1 atmosphere, one has

− 1 =

. (5.54)

Combining Eqs. (5.53, 5.54) leads to:

n − 1 = (n

− 1)P. (5.55)

From Eq. (5.13), one obtains (n ∼ 1)

thr

√

− 1

2(n − 1)

2(n

− 1)P

. (5.56)

Consequently, the momentum threshold is

thr

= mγ

thr

c =

2(n

− 1)P

. (5.57)

Therefore, changing pressure modiﬁes the momentum threshold. In particular, one

can decrease the momentum threshold by increasing the gas pressure.

Note that in the case of a gaseous detector, Eqs. (5.36, 5.37) become (n ∼ 1)

n − 1 =

(5.58)

and

− m

) c

. (5.59)

Using Eq. (5.26), one can express Eq. (5.59) as

. (5.60)

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Scintillating Media and Scintillator Detectors 433

beam axis

Diaphragm

Particle

Photomultiplier

Spherical

mirror

Fig. 5.3 Schematic description of a diﬀerential

Cerenkov detector close to the type used in the

CERN-SPS beams (adapted and reprinted, with permission, from the Annual Review of Nu-

clear 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 a

photomultiplier tube (PMT). The light is ﬁltered by collimators in front of the PMT.

One may also note that:

− m

−

[β

− β

] [β

+ β

] . (5.61)

The gaseous threshold detector is built with the constraint [S´eguinot (1988)]

hθi =

≤

− m

(β

− β

)(β

+ β

) (5.62)

and the radiator length

L ≥

− m

) c

, (5.63)

or in practice, using the number, n

(≥ 3), of standard deviations

− m

) c

≥ n

. (5.64)

5.2.2 Diﬀerential

Cerenkov Detectors

The diﬀerential

Cerenkov detectors allow the tagging of particles in a selected range

of velocities. The

Cerenkov radiation, produced in the forward cone of opening angle

θ in a radiator gas, is reﬂected by a spherical mirror (Fig. 5.3).

The light is focused to form, in the focal plane, a ring of radius

r = f tan θ, (5.65)

where f is the focal length of the mirror. The radius of curvature of the spherical

mirror is 2f. The selection of the particles velocities is achieved by the presence

of a circular diaphragm of radius r and aperture ∆r: the width of the diaphragm

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434 Principles of Radiation Interaction in Matter and Detection

slit located in front of the photomultiplier tubes. The aperture ﬁlters the light. It

selects only light produced in the angular range ∆θ:

∆r =

cos

∆θ. (5.66)

A quality factor of such detectors is the velocity resolution which can be calculated

∆β

∆[1/(n cos θ)]

= tan θ ∆θ. (5.67)

Several eﬀects limit the performance of the diﬀerential

Cerenkov detectors. Multi-

ple scattering in the radiator and beam divergence enlarge the width of the ring of

Cerenkov light. Inhomogeneities of the refractive index over the length of the radi-

ator also aﬀect the radius of the ring of light. This can be seen by diﬀerentiating

cos θ = 1/(βn) which gives:

∆θ =

tan θ

∆n

. (5.68)

Combined with Eq. (5.66), one ﬁnds:

∆r =

tan θ

∆n

cos

. (5.69)

Optical aberrations degrade the angular resolution. In particular, chromatic aber-

rations enlarge the radius of the

Cerenkov light ring [Litt and Meunier (1973)]:

∆r = fθ

2ν

1 +

, (5.70)

where ν features the gas dispersion. A gas with the highest possible ν should be

chosen to minimize ∆ r. At very high energy, the term θ

becomes negligible

and ∆r is proportional to θ. In summary, the application of diﬀerential

Cerenkov

detectors is based on selecting the particle type by both tuning the radiator index

and the diaphragm aperture. It requires the direction of incoming particles to be

parallel to the optical axis, which is the case for ﬁxed target experiments or test

setups in secondary hadronic beams. CERN users are well acquainted with this type

Cerenkov detector (CEDAR:

Cerenkov Diﬀerential counter with Achromatic Ring

focus), operated in CERN-SPS beams. In the case of colliding beam experiments

(head-on collisions), particles are produced over the full solid angle and ring imaging

Cerenkov detectors have to be used.

5.2.3 Ring Imaging

Cerenkov (RICH) Detectors

The RICH detectors [S´eguinot and Ypsilantis (1977)] allow the identiﬁcation of

particle by measuring the

Cerenkov angle, after a precise measurement of the mo-

mentum. A RICH detector consists of two spherical surfaces with a radiator in

between (Fig. 5.4).

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Scintillating Media and Scintillator Detectors 435

A spherical mirror (SM), with a radius R

, has its curvature center located at

the point of origin of the particle. The

Cerenkov photons emitted within a cone of

aperture angle θ are reﬂected by the SM and focused onto a spherical detecting

(SD) surface with radius R

. Usually, R

= R

/2. Therefore, the focal length of

SD is R

/2. The photons fall on a circle of radius

r =

tan θ ≈

θ. (5.71)

The radius can be measured, once the center is known, from an associated tracking

system. The measurement of r allows the measurement of the

Cerenkov angle

θ =

= cos

−1

βn

, (5.72)

which in turn allows the determination of the particle velocity:

β =

n cos θ

n cos(2r/R

)

. (5.73)

Once the velocity of the particle is known, the particle mass, m, can be deter-

mined via Eq. (5.32), provided the particle momentum, p, is known. This can be

seen by rewriting Eq. (5.72) as

θ = cos

−1

pcn

, (5.74)

where E is the particle energy, or

θ = cos

−1

+ m

pcn

. (5.75)

Then, it is possible to distinguish two particles at a number of standard deviation

level, n

, up to a momentum p whose value is given by [Virdee (1999)]:

p =

√

− m

)

2σ

tan θ

, (5.76)

where m

(> m

) and m

are the particles masses. For aerogel, the maximum

numb er of photons per cm is ranging from 20 to 80 (corresponding to the refractive

index range from 1.02 to 1.1). For N

= 50, σ

= 1 mrad and θ = 38 mrad,

pion/kaon separation is achieved up to a momentum of 85 GeV/c for n

= 3.

5.3 Wavelength Shifters

The light emitted from a plastic scintillator often has to be collected at a location

distant from that scintillator. A wavelength shifter (WLS) is used for that pur-

pose. A WLS absorbs the primary scintillation light and re-emits it at a diﬀerent

wavelength to ensure its transport over a relatively long distance towards its col-

lection. The increase of wavelength decreases the absorption of the re-emitted light

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436 Principles of Radiation Interaction in Matter and Detection

beam axis

Target

Particle

Fig. 5.4 Schematic description of a Ring Imaging

Cerenkov (RICH) detector (reprinted from

Nucl. Instr. and Meth. 142, S´eguinot, J. and Ypsilantis, T., Photo-Ionization and Cherenkov

Ring Imaging, 377–391, Copyright (1977), with permission from Elsevier). It consists of a spherical

mirror (SM) of radius R

and a spherical detecting (SD) surface of radius R

, R

= R

/2.

and favors its transportation over long distances. The WLS material must be in-

sensitive to ionizing particle and

Cerenkov light [PDB (2002)]. The choice of the

WLS is made with the purpose of matching the emission spectrum to the absorption

spectrum of the photocatho de of a photomultiplier tube readout. The presence of

ultra-violet absorbing additives in the WLS suppresses the response to

Cerenkov

light.

Bars or plates of wavelength shifters are used in calorimetry to read stacks of

scintillator layers for sampling calorimetry applications (Fig. 5.5). The scintillation

light, produced by a charged particle in each of the plastic scintillator layers of

the sampling calorimeter module, is propagating through each layer until it exits

the layer and gets absorbed in a wavelength shifter bar or plate located along the

scintillator layers as shown in Fig. 5.5. After absorption, the wavelength shifted

(toward a longer wavelength) light is transported via internal reﬂection to the pho-

tosensitive device. The use of WLS material allows the readout of a large amount of

scintillator layers over large volume and the transport of the scintillation light over

a large distance to a photosensitive device whose area can be kept small (standard

PM). It allows one to regroup the readout devices at the back side of the calorime-

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Scintillating Media and Scintillator Detectors 437

ter module or stack, making possible a compact arrangement of several calorimeter

modules or stacks, which can be grouped without dead volumes, and keeping the

readout elements such as photomultipliers outside the path of particle beams.

WLS ﬁbers are also used instead of WLS plates (Fig. 5.6). They are very ﬂexible

as can be bent to follow distorted paths through and around scintillator plates or

tiles and along absorber supports with small loss of signal transmission eﬃciency,

and with the advantage that non-instrumented areas can be reduced to a minimum.

5.4 Transition Radiation Detectors (TRD)

The physics of the phenomenon of transition-radiation (TR) emission has been

already treated from a more theoretical point of view in Sect. 2.2.3. TR is the

electromagnetic radiation emitted as X-rays, when a charged particle crosses the

boundary between two media with diﬀerent refractive indices. TR emission mostly

takes place inside a cone of half-aperture inversely proportional to the Lorentz factor

γ of the particle

θ = 1/γ. (5.77)

TR emission is strongly peaked in the forward direction, i.e., at small angle with

respect to the charged particle direction. TR propagation is symmetric, at least

regarding the crossing medium. In practice, a TR detector (TRD) consists of a

radiator where the X-rays are emitted followed by an X-ray detector.

The radiator is a multilayer stack of foils separated by air gaps. Since the yield

of TR photons at each boundary crossing is rather modest (≈ 1%), a large number

of radiator foils in the stack is needed to achieve particle detection. However, this

numb er is limited by the absorption of the X-rays by the radiator material. There-

fore, the choice of the radiator material has to balance high density to favor high

particles

incoming

to photon

detector

WLS plate

scintillator

absorber

Fig. 5.5 Schematic description of a scintillator stack readout using a wavelength shifter plate.

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438 Principles of Radiation Interaction in Matter and Detection

photon-yield and low X-ray absorption coeﬃcient. The intensity of X-ray emission

varies as ≈ Z

0.5

. The absorption of X-rays in the radiator material is dominated by

the photoelectric eﬀect and the absorption coeﬃcients, then, behave as Z

. There-

fore, the radiator material should have low-Z. The eﬀective number, N

eﬀ

, of foils

in a stack is given by [Fischer, J. et al. (1975)]:

eﬀ

1 − e

−Nσ

1 − e

−σ

, (5.78)

where σ = (µρt)

+ (µρt)

with µ, ρ and t being the X-ray absorption coeﬃcient,

density and thickness of the material (f stands for foil, and g, for gas in the gap),

respectively. N

eﬀ

varies with the photon energy. For instance, N

eﬀ

∼ 35 for an X-

ray energy of 5 keV and ∼ 300 for an X-ray energy of 10 keV in the case of a CH

radiator (foil thickness of 20 µm) [Dolgoshein (1993)].

The total energy emitted in the forward direction by transition radiation at

a single boundary crossing between two media is given by Eq. (2.149) (see page

133, and also [Garibyan (1960)]). Equation (2.149) shows that the total energy is

proportional to the Lorentz factor γ and indicates the possibility to detect X-rays

produced by a particle for a large Lorentz factor and, therefore, to identify particles

at very high energy, where the operation of

Cerenkov detectors becomes very hard

and very ineﬃcient.

It has been shown [Artru, Yodh and Mennessier (1975); Fischer, J. et al. (1975)]

that large threshold eﬀects occur from constructive interference b etween radiation

emitted by the many boundaries in a periodical arrangements of radiator foils and

gaps. These eﬀects produce a threshold behavior of the detector which becomes a

particle detector for values of the Lorentz factor γ & 1000. One should note that a

saturation value of γ exists (γ

sat

), which depends on the length, L, of the radiator

stack and on the TR wavelength, λ

, above which destructive interferences occur:

sat

∼

πLλ

. (5.79)

detector

particles

incoming

WLS fibers

scintillator

absorber

to photon

Fig. 5.6 Schematic description of a scintillator calorimeter module readout using wavelength

shifter ﬁbers.

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Scintillating Media and Scintillator Detectors 439

Increasing L would enlarge the γ range over which TR can be exploited but, as ob-

served above, this would increase the self-absorption of the radiator medium. Again,

one is faced with a compromise, this time between optimization of the useful γ

range and the minimization of self-absorption. The threshold factor, γ ∼ 1000, cor-

responds to a pion energy of 140 GeV (E

= γm

). Therefore, no TR will occur

for pions with energy below 140 GeV. It is interesting to observe that γ ∼ 19, 500

for an electron of 10 GeV (for instance). In general, pions and electrons in a beam of

energy E (in GeV) can be separated on the basis of their Lorentz factor compared to

the value of the threshold Lorentz factor: γ

∼ 19, 500 E(GeV), γ

∼ 7.2 E(GeV). If

E < 140 GeV, electrons will produce TR but pions will not. Additional examples

can be found in [Grupen (1996)]. The capability to operate the separation between

electrons and pions (hadrons, in general) in a TRD is featured by the rejection

factor [Dolgoshein (1993)] deﬁned by:

R =

, (5.80)

where ²

and ²

are the electron and pion detection eﬃciencies, resp ectively. The

quantity ²

also represents the pion contamination. The overall length, L, of the

TRD heavily inﬂuences its rejection power. For instance, assuming ²

= 90%, ²

decreases from 10% for L = 20 cm down to 1% for L = 40 cm and ∼ 0.1% for

L = 70 cm [PDB (2002)].

Particles with an energy corresponding to a Lorentz factor above threshold will

produce TR which will be detected in the X-ray detector put behind the radia-

tor. This X-ray detector is built with characteristics which are determined by two

opposed constraints. On one hand, the X-ray absorption being dominated by the

photoelectric eﬀect (∼Z

), the X-ray detector has to be made of a high-Z material

thick enough to maximize the absorption. On the other hand, the X-ray detector

has to be thin enough to limit ionization and excitation losses by the charged par-

ticle traversing the detector. The X-ray detector is typically a thin wire chamber

(10 mm) ﬁlled with high-Z gas, such as xenon.

The X-ray detector will detect the sum of ionization loss (dE/dx) of the charged

particle traversing the gas chamber and the energy deposition of the X-rays in

that chamber. The ionization and excitation signal is created by a large number

of low energy transfers to electrons (δ-rays, e.g., see page 55), producing in turn

charge clusters proportional to their energy. The absorption of TR will produce

few local strong energy depositions. Therefore, energy loss by TR is very localized

in contrast to the delocalized ionization and excitation energy which is distributed

over the depth of the detector due to ﬂuctuations in the numb er and energy of the

δ-rays. Clearly, delocalization of the ionization energy-loss puts a limit on X-ray

detection.

This pattern of energy distribution provides a mean of particle separation which

will then require the measurement of the total deposited charge in the wire chamber

and its spatial distribution. A complete discussion of the particle identiﬁcation tech-