Chapter 2
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2.1 Introduction
2.2 Passage of Charged Particles Through Matter
§
§
2.2.1 Energy Loss Through Ionization and Excitation
2.2.2 “Classical” Calculation of Energy Loss Through Ionization
§
§
§
2.3.1 Photoelectric Effect
2.3.2 Compton Scattering
2.3.3 Pair Production
2.2.3 Bremsstrahlung
2.3 Photon Interactions
2.4 Electromagnetic Showers
2.5 Neutron Interactions
2.6 Qualitative Meaning of a Total Cross-Section Measurement
2.7 Techniques of Particle Detection
§
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2.7.1 General Characteristics
2.8 Ionization Detectors
2.9 Scintillation Counters
2.10 Semiconductor Detectors
2.11 Cherenkov Counters
2.12 The Bubble Chamber
2.13 Electromagnetic and Hadronic Calorimeters
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Only Briefly
- Read book for
further details
- More in followup course
FYS4550
2
¡
To see a particle?
§ To observe object is to detect light reflected by its surface
▪ Light is a component of EM radiation detectable by eye (400nm-700nm)
§ Particle detector is a translator that connects a sensory organ (or
computer) with the effect produced by the interaction of the particle
with matter
▪ through adequate amplifications and processing
¡
Objective: study
§ main processes of interaction of radiation with matter
§ and related experimental detection techniques
¡
Radiation (E> keV)
§ Charged – electron, proton, …
§ Neutral – photon, neutron, …
§ Radiation interacts with / “see” matter (electrons, atomic nuclei,
nucleons, quarks, …)
¡
Particle detectors based on Energy loss by particles in given medium
§ Excitation / ionisation, …
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3
¡
A fast charged particle moving in given medium
§ loses energy almost constantly
§ is slightly deflected from its initial direction.
¡
Effect of 2 types of collisions:
§ 1. Inelastic collisions with atomic electrons
▪ produce ionization and/or excitation of the atoms of the medium
▪ excited atom de-excites, emitting one or more photons
▪ main source of energy loss
§ 2. Elastic collisions with nuclei
▪ less frequent;
▪ do not cause a loss of energy,
▪ lead to variation in the direction of the incident particle
¡
Bremstrahlung
§ Emission of a high energy photon
§ important for light relativistic particles (electrons)
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4
¡
Energy loss for fast particles
§
¡
~2 MeV g-1 cm2 of crossed material à ∼ 2 MeV for every cm of crossed material with the
water density
“Classical” Calculation of Energy Loss Through Ionization
à read in book
§ Classical Bohr’s formula
§ Gives reasonable description of dE/dx for α particles and heavier nuclei
§ Not for light particles
2 4
§
Z,A = atomic number and atomic weight of the absorber medium
me = electron mass
ρ = material density
Ne = NA Z ρ/A
NA = Avogadro’s number = 6.022 x 1023 mol-1
ze = charge of the incident particle
Electrons are bound in atoms with angular frequency ν
β=v/c of incident particle
γ=1/sqrt(1-β2)
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⎧ ⎡ m γ 2 v 3 ⎤⎫
dE 4π z e
e
−
=
N
ln
⎨
⎢
⎥⎬
e
2
2
dx
me v
⎩ ⎣ ze ν ⎦⎭
5
¡
Classical Bohr’s formula
§
¡
dE 4π z 2 e 4 ⎧ ⎡ meγ 2 v 3 ⎤⎫
−
=
N e ⎨ ln ⎢ 2 ⎥⎬
2
dx
me v
⎩ ⎣ ze v ⎦⎭
Bethe-Bloch formula
§ Better approximation including relativistic effects
§ Takes into account
▪ mean ionisation potential of the medium, I
▪ maximum energy transferred to the electron
Wmax
2me β 2γ 2 m 2
= 2
m + me2 + 2γ mme
≅ 2me β 2γ 2
E << m 2 / me
§ Considers 2 additional terms
I ≈ hυ
▪ density effects (screening), δ correction
▪ C shell correction (vi~v(atomic e-) -> stationary electron approximation not valid)
dE
Z z 2 ⎧ ⎡ 2meγ 2 v 2Wmax ⎤
C⎫
2 2
2
−
= 2π N a mere c ρ
⎨ ln ⎢
⎥ − 2β − δ − 2 ⎬
2
2
dx
Aβ ⎩ ⎣
I
Z⎭
⎦
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6
dE
Z z 2 ⎧ ⎡ 2meγ 2 v 2Wmax ⎤
C⎫
2 2
2
−
= 2π N a mere c ρ
⎨ ln ⎢
⎥ − 2β − δ − 2 ⎬
2
2
dx
Aβ ⎩ ⎣
I
Z⎭
⎦
¡
¡
¡
¡
¡
¡
¡
¡
¡
¡
¡
¡
¡
¡
re=e2/mec2 = 2.818 x 10-13 cm: classical electron
radius
Na = NA Z ρ/A
2πNare2mec2 = 0.1535MeV g-1 cm2
me = electron mass = 0.55110MeV/c2= 9.110 x 10-31
kg
NA = Avogadro’s number = 6.022 x 1023 mol-1
I ~10eV= mean ionization (excitation) potential
of the target (I/Z~12+7/Z ~ 10 eV)
Z,A = atomic number and atomic weight of the
absorber medium
ρ = material density
ze = charge of the incident particle
β=v/c of incident particle
γ=1/sqrt(1-β2)
δ = density effect correction (important at high
energy)
C = shell correction (already important at low
energy)
Wmax = maximum kinetic energy imparted to an
e- in a single collision ~2mec2 (βγ)2 for M>> me
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(a) Energy loss through ionization for π± mesons in copper. The general
behavior is shown together with some definitions and corrections due
to the density effect (responsible for the smaller relativistic rise) and
two different approximations at low energies.
7
Energy loss dependence on βγ
§ P=Mvγ=Mβγc à βγ=P/Mc
§ Dependence of dE/dx on material only
through ρ: dE/dx ~Z/A ~ constant
¡
Scaling law
dE2
z22 dE1 # m1 &
−
(E2 ) ≅ − 2
% E2
(
dx
z1 dx $ m2 '
¡
6
5
4
H e ga s
3
2
Liquid H2 (Z/A=1), Gaseous materials (He, Z/
A=0.5), Solid materials (Z/A~0.5)
1
0.1
Sn
Pb
1.0
Specific energy loss
At minimum ionisation: (dE/dx)min~1.5 MeV
g-1cm2
§ At high energy: (dE/dx)ctant~2 MeV g-1cm2
0.1
§
¡
H 2 liqu id
Difference in Energy loss
§
¡
8
− d E / d x (MeV g −1 cm 2 )
¡
10
0.1
Curves show min. for βγ=3 (MIPs – muons)
0.1
31/01/16
F. Ould-Saada
1.0
10
100
βγ = p/M c
Fe
Al
C
1000
10 000
1.0
10
100
Mu on m om en t u m (GeV/c)
1000
1.0
10
100
P ion m om en t u m (GeV/c)
10
100
1000
P r ot on m om en t u m (GeV/c)
1000
10 000
8
50000
20000
C
Fe
10000
Pb
¡
Integrate BB-formula in order to
determine the range
§
total path length of a particle that
looses energy only through ionization
R /M (g cm −2 GeV−1 )
5000
2000
H 2 liqu id
H e ga s
1000
500
200
100
50
20
10
¡
¡
¡
“Range” of charged particles,
normalized to the mass M of the
particle as a function of βγ
à
Proton of 200MeV energy (M~1GeV)
βγ ~ 0.2 à R/M x M ~ 1 g cm-2,
equivalent to ~1 cm of water.
1GeV proton: range is R ~ 100 g cm-2
5
2
1
0.1
2
1.0
5
2
10.0
5
2
5
2.0
5.0
100.0
βγ = p/M c
0.02
0.05
0.2
0.1
0.5
1.0
10.0
Mu on m om en t u m (GeV/c)
0.02
0.05
0.1
0.2
0.5
1.0
2.0
5.0
10.0
P ion m om en t u m (GeV/c)
0.1
0.2
0.5
1.0
2.0
5.0
10.0 20.0
50.0
P r ot on m om en t u m (GeV/c)
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9
¡
¡
Important application of the concept of range of a
particle in the medical field.
Hadron therapy
§
§
¡
Protons accelerated to 200MeV or carbon
ions accelerated to 4.7 GeV may be used to
irradiate deep tumors by following the tumor
contour with millimetric precision, allowing
one to preserve the surrounding healthy
tissue.
§
¡
is the most recent relative of conventional
radiotherapy, which uses X-rays.
uses beams of protons, carbon ions or neutrons.
The accelerated hadrons are able to destroy sick tissue
mostly at the end of their range in the body of the
patient, where the tumor is situated
A beam of charged hadrons releases the greatest
part of its destructive energy on the target tumor.
§
The dose received at the tumor can therefore be very
high while the healthy tissue is saved.
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¡
Unlike electrons or X-rays, the dose from protons to
tissue is maximum just over the last few millimeters of
the particle’s range.
10
¡
¡
¡
¡
In a typical treatment plan for proton
therapy, the spread out Bragg peak (SOBP,
dashed blue line), is the therapeutic radiation
distribution.
The SOBP is the sum of several individual
Bragg peaks (thin blue lines) at staggered
depths.
The depth-dose plot of an x-ray beam (red
line) is provided for comparison.
The pink area represents additional doses of
x-ray radiotherapy—which can damage to
normal tissues …
§
http://en.wikipedia.org/wiki/Proton_therapy
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11
¡
Bremsstrahlung
§
§
§
¡
¡
¡
Given small electron mass,
§
§
already happens for a few tens of MeV for electrons in lead
and hundreds of MeV for lighter materials
§
important for E> 500 GeV (muons much heavier than electrons, 210 x)
For muons,
Process – more in chapter 4
§
§
§
¡
emission of a photon from an electron deflected by a nucleus
process due to the EM interaction producing large energy loss
dominates the energy loss with respect to ionization and excitation for high βγ
slowing down of the incident electron caused by the nuclear Coulomb field
The amplitude of the emitted radiation ~1/me – probability ~1/me2
Cross section ~Z2 α3
Energy loss per path length unit:
2
3
em
2 4
e
2
⎛ dE ⎞
⎛ 183 ⎞
4N a Z α (!c)
−⎜
E ln ⎜ 1/3 ⎟
⎟ ≈
⎝Z ⎠
mc
⎝ dx ⎠rad
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§
§
Na = NA Z ρ/A: number of atoms cm-3
Logarithm due to screening of nucleus
from atomic electrons à limitation
12
200
§
¡
¡
Ionisation nearly constant
20
For E >20MeV, energy loss through
radiation is higher than that through
ionization.
Critical energy, Ec,
un
hl
ra
s≈
ac
E
tb
re
m
ss
t
30
al
em
Rossi:
Ion iza t ion per X 0
= elect r on en er gy
50
40
t
To
Ex
Energy loss through radiation linearly
increases with the electron energy.
70
Br
¡
d E /d x × X 0 (MeV)
100
g
Copper
X 0 = 12.86 g cm −2
E c = 19.63 MeV
I on i z a t i on
Br em s = ion iza t ion
10
2
5
10
20
50
E lect r on en er gy (MeV)
100
200
energy loss through radiation = ionization:
§ Z-material dependent
§
mec 2
Ec ≅ 1600
Z
¡
E>>Ec, radiation dominant è
E = E0 e
E0 initial energy; E after thickness x of
material;
§ Radiation length X0=Lrad : after X0 , E0
reduced to E0/e
−
x
X0
§
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F. Ould-Saada
X 0 = Lrad
716.4[g.cm −2 ]A
≅
# 287 &
Z(Z +1)ln %
(
$ Z'
13
¡
¡
¡
The main photon interactions are the photoelectric effect, Compton Scattering
and pair production.
In general, photons are more penetrating (in matter) than charged particles;
A beam of photons is not degraded in energy, but is attenuated in intensity
according to
100
I(x)=I(0)e-µx
Photon attenuation
coefficient:
µ=Na σ= σ NA ρ/A
¡
Mean free path /
radiation length
λ=1/µ
Absor pt ion len gt h λ (g/ cm 2 )
¡
10
as function of photon
energy
è
Si
Fe
Pb
0.1
H
C
0.01
0.001
10
10
10
–4
–5
–6
10 eV
31/01/16
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1
F. Ould-Saada
100 eV
1 keV
10 keV
100 keV
1 MeV
10 MeV
P h ot on en er gy
100 MeV
1 GeV
10 GeV
100 GeV
14
(a) Carbon ( Z = 6)
- experimental σtot
A photon is absorbed by an atomic electron with the
consequent emission of an electron
§
§
¡
¡
γ e-àeonly happens with bound electrons (energy-momentum
conservation); where the rest of the atom recoils
Emitted electron energy
σp.e.
1 kb
σRayleigh
κ nuc
σCompton
E=hν-hν0 (binding energy: hν0)
§
Strongly decreases with increasing energy
Cross section σp.e
(b) Lead (Z = 82)
1 Mb
very small for energies larger than 100 keV.
Series of peaks correspond to the ionization energy of the Kshell electrons and higher order shells (L, M, …)
§ Cross section approximation (K-edge<Energies<mec2)
§
7/2
2
σ pe ≅ 4α em
κe
10 mb
§
▪
- σp. e. for the
photoelectric effect on
atomic electrons
- σcoherent for elastic
collisions on atoms
(Rayleigh scattering)
- σincoh for Compton
scattering on electrons
1b
" mec 2 %
5
2Z σ 0 $
' ,
# hυ &
8
σ 0 ≅ π re2
3
Cross section (barns/atom)
¡
Cross section (barns/atom)
1 Mb
- experimental σtot
σp.e.
-
σRayleigh
1 kb
κN for pair production
in a nuclear field;
- κe for pair production
in the field of an
electron;
- σnuc for photon
absorption in nuclei
κ nuc
σg.d.r.
1b
κe
σCompton
§
σ0 : Thomson cross-section (E-> 0) for elastic process γ e- à γ e-
10 mb
10 eV
1 keV
1 MeV
Photon Energy
1 GeV
100 G
15
Compton scattering = elastic collision of a
photon with an electron,
¡
γ e-à γ eFor high energy incident photons, “bound
electrons” considered free
§
Kinematics of Compton scattering:
¡
è show
§
¡
hν ' =
hν
hν
; Γ=
1+ Γ(1− cosθ )
mec 2
To evaluate the energy response of some
detectors (scintillation counters),
important to know energy distribution recoiling
electrons in CS
à
§ Compton edge: Intensity maximum
corresponding to maximum energy allowed by
kinematics è show that
2Γ
Tmax = hν
1+ 2Γ
¡ Cross section à next slide
§
16
(a) Carbon ( Z = 6)
- experimental σtot
In pair production process a photon
converts into an e+e- pair in presence of an
atomic nucleus or e§ γ+ZàZ+ e+e§ Reaction threshold energy: 2mec2 = 1.022
MeV.
§ Cross section (κN, κe) à
σp.e.
1 kb
σRayleigh
κ nuc
σCompton
Mean free path
§ λpair~9 λrad / 7
κe
10 mb
(b) Lead (Z = 82)
1 Mb
§
- σp. e. for the
photoelectric effect on
atomic electrons
- σcoherent for elastic
collisions on atoms
(Rayleigh scattering)
- σincoh for Compton
scattering on electrons
1b
Cross section (barns/atom)
¡
Cross section (barns/atom)
1 Mb
- experimental σtot
σp.e.
-
σRayleigh
1 kb
κN for pair production
in a nuclear field;
- κe for pair production
in the field of an
electron;
- σnuc for photon
absorption in nuclei
κ nuc
σg.d.r.
1b
κe
σCompton
10 mb
10 eV
1 keV
1 MeV
1 GeV
100 GeV
Photon Energy
17
¡
Low energy
§ Energy loss of electrons dominated by ionisation
§ Muons – minimum ionisation (MIP)
§ (Photoelectric effect for photons)
¡
E>critical energy Ec
§ Bremsstrahlung
§ Muons/electrons à suppression (me/mµ)2
§ Eµ>100GeV Bremsstrahlung adds to ionisation
§ Eγ~1MeV, Compton scattering: γeàγe
§ Eγ>10 MeV, dominated by e+e- pair production in field of nucleus
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18
¡
EM shower / cascade
with many e+, e-, γ
§ In matter, a high
energy photon
converts into an e+epair; each e+/e- able
to radiate energetic
photons through
bremsstrahlung,
followed by e+epairs, …
¡
Process stops when
Ee<Ecritical
§ Electrons lose
energy only through
ionization and
excitation
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19
¡
Cascade development as statistical
process
§ primary γ (E0) converts into e+e-
after Lrad à <Ee>=E0/2
§ e+,e- emit γ after 2nd Lrad
à<Ei>=E0/4 , 22 particles
§ After 3rd Lrad à <Ei>=E0/8, i=23
¡ After tth Lrad à <EN>=E0/2t, N=2t
§ t=x/Lrad
x: medium thickness
¡
Same result for a cascade initiated
by an electron
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20
Maximum penetration of cascade
#E &
ln % 0 (
E0
$ Ec '
Etmax ≅ tmax
= Ec ⇒ tmax ≅
2
ln 2
¡
Pb
gas
Maximum number of particles in
cascade at given instant:
¡
N max ≅
¡
E0
Ec
The number of
electrons and positrons
increases, reaches a
maximum at a mean
energy of Ec, then
decreases.
31/01/16
¡
F. Ould-Saada
Simulation
§
electromagnetic
cascade is fully
contained in
about 20–25
radiation
lengths.
21
¡
Neutron interaction with matter is dominated by the strong interaction
Some EM interaction through magnetic dipole moment
§ Cross section varies with energy
§
¡
High energy neutrons (Tn>100 MeV) behave as protons – strong interaction
§
¡
Part of particle physics
Lower energy neutrons – nuclear physics
elastic collision : n + A → n + A
Fast neutrons (200keV<Tn<40 MeV)
§ Epithermal neutrons (0.1keV<Tn<100 keV)
§ Thermal / slow neutrons (Tn~kT~1/40 eV)
§ Cold / ultra-cold neutrons (Tn~ meV / µeV)
inelastic collision : n + A → n + A *
radiative n − capture : n + (Z, A) → γ + (Z, A +1)
§
Nuclear capture : (n, p), (n, d), (n, α ),...
Nuclear Fission
¡
In nuclear physics and for engineering purposes, it is usually necessary to slow down the
fast neutrons
§
§
Deceleration through elastic scattering
12C widely used – 110 elastic coll. needed to slow down 1 MeV-n to thermal energies (1/40 eV)
▪
31/01/16
In H2, ~17 collisions are needed
22
¡
Atomic, nuclear and particle level
§ Elastic collisions
§ Inelastic collisions
▪ Internal system modified (atom excited)
§ High energy collisions (deep inelastic)
▪ Energy transformed into mass with new particle creation
¡
Probability of collision type
§ measured through important quantity, energy/size/interaction-
dependent: Cross section, σ
§ σtot=σelast+σinelastic +σdis
§ Unit (surface): cm2, Barn, 1b=10-24 cm2; ~10 mb for hadronic collisions
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23
Other
parameters
include
Energy
resolution
Efficiency,
Radiation
hardness,
…
¡
31/01/16
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Read 2.7 and following
sections in book
24
¡
¡
Charged particle through medium leaves trail of ionised atoms + e’s
2 main tracking detector technologies
§ Detect tracks in large gas
volume by drifting electrons in
strong E-field towards sense
wire where signal is recorded
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§ Semiconductors using silicon pixels (2D
space points) and strips (O(25µm)
▪ Charged particle traversing doped silicon wafer
à ionisation à e-hole pairs (O(10 000))
▪ Potential across silicon à holes drift in direction
of E-field à collection by p-n junctions
25
¡
Organic scintillators (Sc)
§ Detect passage of charged
particles – no precise spatial
information required
▪ à excited molecules à
emission of light (photons)
▪ Light guided to
photomultiplier tube (PMT)
▪ PM photocathode converts
photons into electrons
▪ Dynodes multiply electrons to
produce electronic signal
▪ Signal amplified
¡
Inorganic Sc
§ Crystals NaI (Tl), BGO, …
¡
Plastic & liquid SC routinely
used in neutrino experiments
26
¡
Charged particle in dielectric medium with
refractive index n polarises molecules
Emission of photons
§ If v>c/n à constructive interference, Cerenkov
radiation emitted as coherent wave front at
fixed angle θ to the trajectory of the particle
§ (analogous to sonic boom by supersonic
aircraft)
§
¡
¡
In time t particle travels d=βct
In t wave front emitted at t=0 travelled d’=ct/n è
β=
¡
¡
Cerenkov radiation only when β>1/n
Threshold behaviour è identification of particles
of given p
31/01/16
F. Ould-Saada
cosθ =
⇒
pc
=
E
β >1/ n
1
nβ
⎫
⎪
p2 + m2c2 ⎬
⎪
⎭
p
⇒ mc < n 2 −1 p ⇒ C − radiation
27
¡
Read section 2.12
Photos of particle
interactions produced by
BC will be shown and
discussed/studied
§ BEBC, the Big European
Bubble Chamber, with a
cylindrical 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
§
§
31/01/16
You will see an example
of BC at CERN (outside
Microcosmos / Library)
F. Ould-Saada
28
¡
Charged hadrons (p,π±)
§ Energy loss by ionisation + strong
¡
¡
¡
¡
A calorimeter is a detector that absorbs all
the kinetic energy of a particle and provides
an electronic signal proportional to the
deposited energy.
Electrons and photons lead to EM showers
Hadrons to hadronic showers
Muons to minimum ionisation in both ECAL
and HCAL
interaction with nuclei (also neutral
hadrons)
§ Hadronic showers parametrised by
interaction length λI
▪ Mean distance between hadronic
interactions of relativistic hadrons
▪ Fe: λI ~17cm, X0~1.8cm
▪ π0)àγγ: EM component
¡
Detection of quarks
§
Jet energy
▪
▪
▪
31/01/16
F. Ould-Saada
60% (charged, mainly π±)
30% (γγ from π0)
10% (neutral hadrons, mainly Kl,Ks)
29
¡
Particles
§ Stable: e-, p, γ, ν
§ Unstable: travel d=γvτ
▪ >10-10s – quasi stable (several meters in detectors): µ±, n, π±, K±
▪ <10-10s – short-lived: decay in detectors
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30
¡
Detect SM particles by way of their characteristic interactions
Fundamental elementary particles in the Standard Model, their detection
in particular detector subsystems and a signature allowing for particle identification
in those subsystems.
Particle
Signature
Detector
u , c, t → W + b
d , s, b
Jet of hadrons
(λo )
Calorimeter
Electromagnetic Shower
(Xo )
“Missing” transverse
energy
Calorimeter (ECAL)
Only ionization interactions
dE / dx
Muon Absorber
Decay with cτ > 100µ m
Silicon Tracking
g
e, γ
ν e ,ν µ ,ντ
W → µ +ν µ
µ ,τ → µ + ν τ + ν µ
Z →µ+µ
c, b,τ
31/01/16
F. Ould-Saada
Calorimeter
31
¡
Jet of hadrons with b-quark
§ Hadronisation à B-meson, τ~1.5 ps
§ In HE, d~βcτ~few mm before decaying
▪ Secondary vertex resolved from primary by silicon vertex detectors
(single hit resolutions of O(10µm)
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32
Particle detection
the various
particles have
different signatures
in different parts of
the detector
by combining the
various signatures,
we can reconstruct
how the particle
moved through the
detector
how the various
particles are
identified is shown
here
31/01/16
F. Ould-Saada
34
http://atlas.physicsmasterclasses.org/en/zpath_playwithatlas.htm
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