Braibant S., Giacomelli G., Spurio M. Particles and Fundamental Interactions: An Introduction to Particle Physics
Подождите немного. Документ загружается.
36 2 Particle Interactions with Matter and Detectors
Table 2.4 Characteristics of some commercial scintillators: Density, refraction index n, luminous
efficiency (mean energy to produce a light photon), decay constant, wavelength to which the
maximum emission is obtained, ratio atoms of H/atoms of C, characteristic uses
Luminous Decay
Density efficiency constant
max
Scintillator Type (g cm
3
) n (eV/) (ns) (nm) H/C Uses
NE 110 Plastic 1.032 1.580 36 3.3 434 1.104 ; ˛; ˇ; n
NE 220 Liquid 1.036 1.442 39 3.8 425 1.669 Dosimetry
NE 311 With 5%B, Liq. 0.91 1.411 39 3.8 425 1.701 n
Anthracene Crystal 1.25 1.620 60 30. 447 0.715 ; ˛; ˇ, n
NaI(Tl) Crystal 3.67 1.775 138 230. 413 ; X
LiI(En) Crystal 4.06 1.955 45 1200. 475 n
BGO Crystal 7.1 300 300. 480
CeF
3
Crystal 6.16 240 10. 320
Organic scintillators. They are formed from aromatic compounds containing
chemical ring structures, for example, benzene. These scintillators emit light with
decay times of a few nanoseconds. The light is produced in transitions that involve
valence electrons of molecules. Organic scintillators of various types exist: organic
crystals (for example, the anthracene), organic liquids in liquid solutions of one or
more scintillating materials and plastic ones formed as those from liquid solutions,
though now at the solid state. The greatest advantage of plastic scintillators is due
to their manufacturing flexibility.
Inorganic scintillators. Inorganic scintillators are crystals, often of alkaline type
with a small amount of activator impurities. The widely used type is the sodium
iodide doped with thallium, NaI (Tl). Others are Bi
4
Ge
3
O
12
(bismuth germanate,
BGO) and BaF
2
(barium fluoride). These scintillators have a high luminous
efficiency, though they are one or two orders of magnitude slower than the organic
scintillators (see Table 2.4).
Luminous efficiency " (“light output”). It is defined as the energy necessary to
produce a light photon. It is important because the scintillator energy resolution
depends on it. Within ample limits, the quantity of light emitted by a scintillator
is proportional to the energy lost by the particle that crosses it. Saturation effects
happen only for very high lost energies. At room or close to room temperatures
(i.e., from 10
ı
Cto80
ı
C), the quantity of emitted light barely depends on the
temperature; the dependence only becomes important for temperatures considerably
outside this interval.
Photomultipliers. Figure 2.13a shows the scheme of a photomultiplier. It is formed
with a photocathode where the light photons are converted into electrons (the so-
called photoelectrons), a focusing system of the electrons, the first dynode where
the first electron multiplication (by a factor 3–10) happens and finally the other
dynodes (from 8 to 12) at positive increasing voltages (up to about 2,000V), where
other multiplications occur up to a total factor of 10
5
–10
7
.
2.9 Scintillation Counters 37
10
300 400 500 600
0
0
20
40
60
80
100
120
5
Wave length (nm)
Emitted spectrum (rel. unit)
Photocathode response (rel. unit)
Bialkali PMT
CsΙ(Tl)
NaΙ(Tl)
CsΙ(Na)
BGO
S-ΙΙ Response
PMT
Photocathode
Electron optical
input system
Focusing
electrode
First dynode
Multiplier
Anode
ab
Fig. 2.13 (a) Scheme of a photomultiplier (from the Philips catalogue); (b) Luminous spectrum
emitted by some inorganic materials (full lines) and the response curve of some photomultiplier
photocathodes (dashed lines) (From the Harshaw Chemical Company catalogue)
In the nuclear and subnuclear physics experiments, the photomultipliers are used
in pulsed regime, which means that they respond to a fast luminous signal producing
a fast electronic output signal which sometimes must be subsequently amplified.
The photocathode quantum efficiency and its spectral response to luminous
radiation of different wavelengths are important parameters. The quantum efficiency
is the probability that a single incident photon on the photocathode produces an
electron that contributes to the detector electric current. If, as it happens, more than a
photon is present, the quantum efficiency is defined as the ratio between the number
of the produced electrons (photoelectrons) and the number of incident photons. The
most widely used cathodes are made of semiconductor material formed by antimony
and by one or two alkaline metals, with which quantum efficiencies up to 26% and
usable response curves for wavelengths from 320 to 580 nm may be reached (see
Fig. 2.13b). To obtain higher position resolutions, segmented scintillators with very
small pixels, namely, multianode photodetectors with very small anodes, can be
used.
The statistical error on the energy loss measurement is connected to the number
of photoelectrons. For this reason, it is necessary to collect the largest possible
fraction of the emitted light on the photocathode, sometimes making use of good
light guides and covering the scintillator and the light guides with reflecting or
diffusing material; besides, it is necessary to use a photomultiplier with high
photocathodic efficiencies. In order to be able to observe a single photoelectron,
it is also required to have a high sensitivity.
It is important that the luminous spectrum emitted by the scintillator be contained
in a bandwidth of equal wavelengths to that of the photocathode response. This is the
case in Fig. 2.13b for NaI (Tl) and BGO, but not for CsI (Tl). In case of a mismatch
between the emitted spectrum and that of the photocathode response, a wavelength
38 2 Particle Interactions with Matter and Detectors
shifter may be used in the scintillator. This is practically possible for scintillators
made from different materials.
The electric output signal of a photomultiplier used with a plastic organic
scintillator is a pulse about 0.5 V high, with a rise time of 2–4 ns and a fall time
of 10–20ns.
To maintain the gain stability, it is necessary to have high voltage generators
that are well stabilized both for short and long time terms. A photomultiplier is
very sensitive to external magnetic fields: indeed, only a small field may cause
the electrons to deflect inside the photomultiplier, especially in the first stage. For
this reason, it is necessary to mask the photomultiplier with a magnetic screen of
mu-metal.
2.10 Semiconductor Detectors
The semiconductor detectors, also called solid state detectors, are built with
crystalline semiconductor material such as silicon and germanium. The basic
principle of these detectors is analogous to that of the ionization gas detectors, with
the difference that the medium is solid. The passage of an ionizing particle creates
electron-hole pairs (instead of electron-positive ion pairs) that can be collected and
multiplied through an appropriate electric field. The advantage of a semiconductor
is due to the small energy necessary to create an electron-hole pair, namely, 3.6 eV
in silicon and 3.0 eV in germanium, that is, about an order of magnitude smaller
than that necessary for the gases used in ionization detectors (see Table 2.3). The
ionization is therefore ten times larger and better resolutions in energy can be
obtained. Also, note that the number of photoelectrons in a scintillation counter
is about 100 times worse. The first applications of the semiconductor detectors have
been radioactivity measurements with high energy resolutions. The main use in the
high energy field regards the silicon microstrip detectors with the primary goal to
obtain vertex and track detectors with high position resolution (5–10m).
Most semiconductor detectors, with the exception of the silicon and the gallium
arsenide detectors, have to be operated at low temperatures in order to reduce
thermal effects. Another difficulty is due to the possible damage caused by high
radiation doses; therefore, material usable at room temperature and less sensitive to
radiation doses have been found (for example, Ga and As).
The semiconductor detectors used in high energy physics are thin (thicknesses
of 200–300 m) and are composed of high purity crystalline (silicon) materials;
however, material doped with impurities pentavalent or trivalent (with respect to the
tetravalence of Si) are also used. The obtained signals are linear in the sense that the
electric output signal is directly proportional to the deposited energy.
2.11 Cherenkov Counters 39
–HV
20 μm
280 μm
Readout
Electronics
1 μm Al
0.2 μm SiO
2
n
+
- Implantation (As)
1 μm Al
p
+
- Implantation (B)
Si-crystal (n-type)
Fig. 2.14 Silicon microstrip detector scheme
In conclusion, the main characteristics of a semiconductor detector are:
1. Low energy necessary to create an electron-hole pair;
2. Linear response;
3. Presence of a dark current due to minority carriers of thermal type and to
superficial contributions;
4. The signals must be preamplified with low noise charge amplifiers; the output
signals must undergo proper shaping.
Figure 2.14 shows the scheme of a microstrip detector. It is composed of readout
strips spaced by 20 m. The strips of p
C
type (i.e., constituted from a p type
material with a high doping) with contacts in aluminum are implanted on n type
silicon (with a 2;000 ˝ cm resistivity). An electrode of n
C
type (n type material
with high doping) is installed on the other side. The detector thickness is 300m
and is operated with voltages of the order of 40 V.
For the detection of rays with energies of the order of the MeV, the most used
detector is that with Germanium .Z
Ge
D 32/ at the liquid nitrogen temperature. The
dimension of a typical counter are 5 cm 5cm5 cm. They provide high detection
efficiencies and excellent energy resolutions.
2.11 Cherenkov Counters
The electric field produced by an electric charge Ze moving with a speed v D ˇc in
a medium with refractive index n propagates with a speed v
E
D c=n. If the speed
of the particle is larger than that of the field, v D ˇc > v
E
D c=n, one has a
phenomenon similar to that of the generation of a shock wave.
40 2 Particle Interactions with Matter and Detectors
The angle
c
of the emitted radiation relative to the particle direction is cos
c
D
.1=nˇ/; the number of emitted photons per unit energy and per unit path length of
a particle is
d
2
N
dE
dx
D
˛Z
2
„c
sin
2
c
D
˛
2
Z
2
r
e
m
e
c
2
1
1
ˇ
2
n
2
ZD1
! 370 sin
2
c
eV
1
cm
1
(2.27)
where .˛
2
=r
e
m
e
c
2
/ D 370 eV
1
cm
1
;ZD 1, r
e
D classical electron radius
D e
2
=m
e
c
2
D 2:82 10
13
cm. The number of photons per unit wavelength is
d
2
N
d dx
D
2˛Z
2
2
1
1
ˇ
2
n
2
: (2.28)
Note that the index of refraction is a function of the emitted photon energy, n D
n.E
/. Remembering the relationship between energy and wavelength, E D hc=,
one knows that the emitted photons with a wavelength between 300 and 600nm are
no more than 1/100 of the photons produced in a process of energy loss through
ionization and excitation.
In a threshold Cherenkov counter, the total light emitted above threshold is
collected. It gives a yes/no decision based on whether the particle speed is above
or below threshold, ˇ
t
D 1=n.Instead,theimaging Cherenkov counters make use
of the dependence of the fast particle speed ˇ from the photon emission angle .
These detectors make use of focusing lenses and pinholes to select the photons
emitted at a certain angle. With such a detector, it is indeed possible to select,
in a monochromatic particle beam, the light emitted by a certain type of particle,
for example, mesons. It is also possible to select another type of particle, for
example, K mesons, by varying the counter gas pressure and therefore its index of
refraction. In Cherenkov counters with a 4 geometry used in apparatuses covering
the full solid angle, a gas with index of refraction n D 1:0017 (C
5
F
12
) has been
used. Photons are optically focused with mirrors onto particular phototransducers,
for example, wire chambers.
Some large underground water detectors are used as Cherenkov counters. In the
Superkamiokande detector (see Chap.12), about 20% of the external surface of the
cylindrical vessel containing 50,000 t of water is covered with a large photomul-
tiplier (PMT). This detector has obtained fundamental results on atmospheric and
solar neutrino oscillations.
2.12 The Bubble Chamber
The bubble chamber is a detector that is no longer used. However, it was very
important because it allowed one to visualize the interactions between particles
and the production of new ones through photos. The bubble chamber allowed
the visualization of trajectories of high energy particles exploiting the ionization
2.12 The Bubble Chamber 41
process; it therefore belonged to the ionization detector category. A bubble chamber
contained a liquid that, during the passage of particles, was in a metastable
condition. An example of this particular state could be water at a temperature of
110
ı
C and at atmospheric pressure: water should boil, though it actually does not
for a small fraction of a second.
3
The liquid begins to boil where impurities are
present, for example, at the edges of the vessel, and also around a group of negative
and positive electric charges.
A fast charged particle that crosses a bubble chamber ionizes many atoms and
molecules of the liquid. In each of these interactions, the fast charged particle loses
a small part of its energy and is not deflected in an appreciable way. Along the path
of the particle, free electrons (negative ions) and atoms without an electron (positive
ions) are created around which the liquid begins to boil. This means that around
groups of ions, little bubbles of vapor are formed that dimensionally increase until
eventually they fill the whole chamber. If one takes a photo at the moment in which
the little bubbles have a diameter of slightly less than a millimeter, the trajectory of
the particles is visualized through a series of little bubbles.
To be able to again use the bubble chamber, one needs to increase the pressure (in
the example of water at 110
ı
C, the pressure could be brought to four atmospheres)
to force the liquid to stop boiling. At the right moment, the pressure is again
lowered (to one atmosphere) and the chamber is again ready. This moment must
be synchronized because it must precede the arrival of fast charge particles by a few
milliseconds.
A bubble chamber is usually surrounded by a big magnet that produces a strong
magnetic field in the whole space of the chamber (typically B D 2 Tesla). The
charged particles that cross the chamber are deflected by the magnetic field along a
circular trajectory whose radius depends on the particle momentum. Then, analyzing
the tracks, information can be obtained on the mass of the particles and on their
momentum. Large bubble chambers have been used in experiments studying muon
neutrinos; in this case, intense neutrino beams are needed in order to have a
reasonable number of interactions.
Bubble chambers were built with operational liquids, for example, hydrogen,
deuterium, neon plus hydrogen, helium and others. Hydrogen bubble chambers offer
the advantage of allowing the study of collisions on protons that can be considered
as free. The density of liquid hydrogen is low (% ' 0:06 gcm
3
); therefore, the
quantity of matter on the trajectory of every particle is small. The probability of
interaction is low: well defined tracks can be seen, but interactions of rays are
not observed. In a bubble chamber with heavy liquid, for example, a mixture of
hydrogen and neon, there are many interactions of beam particles; besides, the
probability of the interaction of rays is elevated (due to the neon high density
and high atomic number).
3
Water is actually not suited to be used as a liquid in a bubble chamber; it is only used here as an
illustrative example.
42 2 Particle Interactions with Matter and Detectors
Fig. 2.15 BEBC, the Big
European Bubble Chamber,
with a cylindric shape of
3.7 m diameter during its
installation (the chamber is
now in disuse). The main part
is the cylindrical vessel
visible at the top; the beam
line was perpendicular to the
cylinder axis (CERN archive
photo)
Figure 2.15 shows the Big European Bubble Chamber (BEBC) used at CERN in
the 1970s until the end of 1983. A similar chamber was used at Fermilab until 1986.
The bubble chamber, invented in 1952 by Glaser (Nobel laureate in 1960), played
a crucial role from the 1960s to the 1980s. One of the reasons for its decline is the
impossibility of building an “electronic” bubble chamber, that is, a chamber able to
directly send signals to a computer. In the following chapters, we shall often use, for
didactic purposes, photos produced by bubble chambers.
2.13 Electromagnetic and Hadronic Calorimeters
With an always increasing colliding energy of large accelerators (discussed in the
next chapter), larger and more complex detectors have become even more important.
In particular, the role of the electromagnetic calorimeters, ECAL and of the hadronic
calorimeters, HCAL is becoming decisive. A calorimeter is a detector that absorbs
all the kinetic energy of a particle and provides an electronic signal proportional to
the deposited energy.
In a given medium, a ray and an electron of high energy produce an
electromagnetic cascade through successive processes of e
C
e
pair production and
bremsstrahlung. In a medium with high Z, such a cascade has limited longitu-
dinal and transversal dimensions, as illustrated in Fig. 2.16a. An electromagnetic
calorimeter measures the total energy produced through ionization (and excitation)
due to e
C
;e
;; usually its longitudinal thickness is of 20–25 radiation lengths.
Typical values of radiation lengths X
0
for some materials are listed in Table 2.5.
2.13 Electromagnetic and Hadronic Calorimeters 43
Detector (scintillator,
chamber, Cherenkov)
Heavy material
(Fe, Cu, Pb, U, lead glass)
electron
abc
hadron muon
Fig. 2.16 Behavior (a) of an electromagnetic cascade, (b) of a hadronic and (c)ofamuonwhen
traversing a sampling calorimeter constituted of interleaved detector and absorber layers of heavy
material. An ECAL measures the total energy deposited by the electrons/positrons that cross it.
A HCAL measures the energy deposited by the charged hadrons. In both calorimeters, the muon
behaves as a minimum ionizing particle and can be easily identified. In a multipurpose detector, an
ECAL is usually installed first, followed by a HCAL, both with cylindrical symmetry with respect
to the vacuum pipe where beams circulate
Table 2.5 Main
characteristics of detectors
and absorber materials used
in ECAl and HCAL
X
0
0
Material (cm) (cm) (MeV)
Active NaI 2.6 41 12.5
detectors BGO 1.1 23 7
Lead glass 2.36 15.8
Passive Fe 1.7 17 28
absorbers Pb 0.56 17 9.5
U 0.32 10.5 9
X
0
radiation length,
0
interaction length, critical energy D
energy to which energy loss through radiation is equal to that
through ionization and excitation
The hadrons deposit energy in matter through a series of collisions due to the
strong interaction and therefore through ionization/excitation from the produced
charged hadrons (the primary strong interaction produces many mesons which
successively interact through the strong interaction). The hadronic cascade is wider
and longer than that electromagnetic (see Fig. 2.16b), and therefore a hadronic
calorimeter (HCAL) must have larger dimensions than the ECAL ones; typically,
it has a thickness of six nuclear interaction lengths
0
. Some typical values of
interaction lengths are given in Table 2.5.
However, there are strong fluctuations in the hadronic cascade because of various
effects. The
0
mesons immediately decay in 2, producing an electromagnetic
cascade in which the energy is deposited in a narrow space. The
˙
mesons
44 2 Particle Interactions with Matter and Detectors
decay instead in ; the neutrino interacts so little that they always leave without
interacting in the hadronic calorimeter. This causes missing energy (about 30%) and
momentum. For the most part, the muons also leave the hadronic calorimeter, as
illustrated in Fig. 2.16c; the muons produce a signal at the minimum of ionization
in both calorimeters and can be sometimes measured in specific muon chambers
installed in the most external layers of the detector.
The calorimeters are divided into homogeneous and sampling calorimeters.
The first ones are made of only one material, for example, lead glass in the
case of electromagnetic calorimeters. The second calorimeters are made of active
detectors (e.g., scintillation counters) interleaved with absorber layers (e.g., lead in
electromagnetic calorimeters and iron in hadronic calorimeters) (see Fig. 2.16 and
Table 2.5). The best segmentations are usually half a radiation length for ECAL
and 0.25–0.5 interaction lengths for HCAL. The homogeneous calorimeters usually
have better performances with respect to the sampling ones, though they are more
expensive. Practically, all hadronic calorimeters are sampling calorimeters.
The important quantity for the energy resolution is the number N of track
segments (N cm in a homogeneous calorimeter, N samplings in a sampling
calorimeter). The energy E to be measured is the energy of the primary particle that
induces the cascade and is indeed proportional to the number of secondary particles
produced (particularly at the maximum, see (2.26)). The number of measured
secondary particles is proportional to the number N of track segments and the
energy resolution therefore has a percentage error, that is,
E
E
'
E
E
N
N
'
p
N
N
1
p
E
: (2.29)
Typical energy resolutions for ECAL and sampling HCAL (with many individual
channels) are respectively about E=E ' 0:2=
p
E and 1:0=
p
E with E in GeV.
In experiments at large accelerators (as we shall see in Chap. 9), electrons/
positrons are identified (and energies measured) in ECAL and hadrons in HCAL.
Chapter 3
Particle Accelerators and Particle Detection
3.1 Why Do We Need Accelerators?
Our knowledge regarding the structure of matter has been reached using optical
microscopes, electronic microscopes, radioactive sources and, finally, particle accel-
erators. The possibility of continuously investigating the subatomic world is related
to the construction of consistently larger and more sophisticated accelerators.
One reason for which the use of particles accelerated to high energy is necessary
is connected to the wave-particle duality and to the uncertainty principle. In the
framework of wave-particle duality, a particle exhibits wave-like properties and a
wave exhibits particle-like properties. A wave is characterized by its wavelength;
a particle is characterized by its energy or its momentum. The larger the particle
energy, the smaller the associated wavelength. Quantitatively, the relation between
the wavelength associated to a particle and the momentum p of the particle is
given by the de Broglie relation D h=p D 2„c=pc,whereh is Planck’s
constant, „Dh=2. Numerically, one has (see Appendix 5)
.cm/ D
6:626 10
27
(erg s/
p
D
1:24 10
10
(MeV s)
p.MeV=c/
(3.1)
that is (fm) D 1:24=p .GeV=c/. Sometimes, ¯ D =2 D„=p is used.
Intuitively, the wave-particle can be seen as a probability “cloud” with dimension
comparable to the associated wavelength. In this representation, the particle is
not an object with the dimension of the cloud: the particle is intrinsically smaller
and it can be found in any point within the cloud. The cloud volume can be
reduced by decreasing the wavelength which is equivalent to increasing the particle
momentum (and therefore its energy). In conclusion, the larger the particle energy,
the smaller associated wavelength is. Consequently, it is possible to study smaller
objects possessing finer details. At high energies, the wave-like aspects can often be
ignored; the particle can be considered to be a little ball (or a “spinning top” if its
spin is considered). In this case, accelerators are comparable to large microscopes.
S. Braibant et al., Particles and Fundamental Interactions: An Introduction to Particle
Physics, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-94-007-2464-8
3,
© Springer Science+Business Media B.V. 2012
45