Laboratory of nuclear and subnuclear physics slides 1 2018:2019

What!is!a!particle!detector?
!
General#Principle:#All#the#particles,#crossing#a#slab#of#
matter,#lose#a#fraction#of#their#energy#in#the#material#
with#some#probability#by#some#physical#process.#
– Charged!Particles:!inelastic!collisions!on!atomic!
electrons!hit!along!the!trajectory;!
– All!the!hadrons!(charged!and!neutral)!by!nuclear!reactions!
on!the!nuclei!hit!along!the!trajectory;!
– Electrons!emit!braking!radiation!(bremsstrahlung)!
– Photons!may!be!scattered!anelastically!or!not!(ie!Thomson/
Compton!scattering),!absorbed!(photoelectric!eff.),!
generate!pairs!e+!e<,!depending!on!the!photon!energy!
10
What!is!a!particle!detector?
!
• The! basic! operation! principle! of! ALL! the! detectors! is!
to! convert! the! energy! lost! in! the! active! part! in! a!
“concrete! signal”! that! can! be! “measured”! (current,!
voltage,!light,!heat,...).!!
• Different! tecniques,! materials! and! arrangements!
depending!on!the!particle!type!to!detect,!on!the!energy!
range,!speed,!on!the!particle!rate,…!
• For! example,! a! photon! detector! must! be! inevitably!
different!from!a!muon!detector.!!
• The! “signal”! depends! on! some! cinematic! or! dynamic!
“property”!of!the!particle!(eg!energy,!velocity,!linear!
momentum!p,!charge,!mass...)!which!is!being!detected. !
• “Universal”! detectors,! sensitive! to! all! the! particles!
over!all!the!range!of!their!“properties”!DO!NOT!exist!
11
What!is!a!particle!detector?!
General!operation!principle!of!a!detector:!
Particle!with!energy!E!→!!transfer!of!energy!fE!(f!≤!1)!to!
the!detector!!→!!conversion!in!a!accessible,!measurable!
form!of!energy!(light,!current,!voltage,!heat,...)!
!Modern!detectors!are!essentially!electrical:!fE!converted!in!
electrical!pulses!→!needed!electronic!circuitry!to!form!the!
signal!
electronic#
E#
fE#
analogic#
signal#
digital#
output#
12!
Which!is!the!more!familiar!
detector?!
Human#eye#(as#any#other#eye)#is#a#particle#
detector:#photons#
"
"
"
"
Test#particle#source#
Light#beam#
target#
detector#
Data#processing#
Target#
Detector#
Data#processing#
13
The!oldest!detector!of!photons…!built!billions!
of!times!
• High#sensitivity#to#photon#in#a#
well#defined#frequency#range#
• Good#spatial#resolution##
• Adaptative#optics#for#photon#
focalization#
• Large#dynamic#range#(1:1014)#+#
threshold#automatic#matching##
• Energy#discrimination#(wave#
length)#
• Rather#slow#(acquisition#speed#
+#analysis#~10#Hz)#
14
Other!ways!to!“see”?!
Ex.:#by#subtraction#
Ex.:#infrared#
15
Electromagnetic!emission!
from!a!body!
At!a!temperature!of!37!C!
(~310!K),!the!emission!is!
peaked!in!infrared.!
Most!of!matter!is!
“transparent”!to!IR!
16
Other!ways!to!“see”?!
Ultrasuonds#
“energetic” light (X rays)
Why#X#rays#and#ultrasounds#
are#used,#instead#of#
“light”?#
17
Multiwavelength!
vision!must!be!used!
to!see!different!
components!of!our!
galaxy!
18
We# see the#subatomic#matter#because#we#hit#it#with#
particles#produced#by#sources#(as#the#accelerators#or#
radioactive#decays)#which#scatter#or#produce#new#
particles#that#reach#the#detectors###
19
For!instance,!the!way!that!incident!particles!
are!scattered!off!by!targets!can!reveal!details!
of!the!target!particles!
20
Ex:!Rutherford’s!atomic!model!
!
Ernest Rutherford
1909
21
Photographic#Plates#
Use#of#photographic#paper#as#detector##
➠#Detection#of#photons#/#x(rays#
W.#C.#Röntgen,#1895#
Discovery#of#the# X(Strahlen # Photographic#paper/film#
#
e.g.#AgBr#/#AgCl#
#
AgBr#+# energy ##
➠#metallic#Ag#(blackening)#
#
+#Very#good#spatial#resolution#
+#Good#dynamic#range#
(##No#online#recording#
(##No#time#resolution#
##
22
Cathodic!ray!tube!
J.!Plücker!1858!!➠!J.J.!Thomson!1897!
Phosphorence!light!reveals!
the!impact!point!
accelerator#
manipulation#
By#E#or#B#field#
detector#
From:&J.J.&Thomson:&Cathode&Rays.&&
Philosophical&Magazine,#44,#293#(1897).##
#
…#The#rays#from#the#cathode#C#pass#through#a#slit#in#the#
anode#A,#which#is#a#metal#plug#fitting#tightly#into#the#tube#
and#connected#with#the#earth;#after#passing#through#a#second#
slit#in#another#earth(connected#metal#plug#B,#they#travel#
between#two#parallel#aluminium#plates#about#5#cm.#long#by#2#
broad#and#at#a#distance#of#1.5#cm.#apart;#they#then#fall#on#
the#end#of#the#tube#and#produce#a#narrow#well(defined#
phosphorescent#patch.#A#scale#pasted#on#the#outside#of#the#
tube#serves#to#measure#the#deflexion#of#this#patch…. ##
#
23
C.!T.!R.!Wilson,!!
1912,!Cloud!chamber!!
First!tracking!detector!
The!general!procedure!was!to!allow!
water!to!evaporate!in!an!enclosed!
container!to!the!point!of!saturation!
and!then!lower!the!pressure,!producing!
a!super<saturated!volume!of!air.!Then!
the!passage!of!a!charged!particle!
would!condense!the!vapor!into!tiny!
droplets,!producing!a!visible!trail!
marking!the!particle's!path.!!
24
Bubble!chamber
!
•
•
The!Big#European#Bubble#Chamber!(BEBC)!is!a!piece!of!
equipment!formerly!used!to!study!weak!interactions!at!
CERN.!BEBC!was!installed!at!CERN!in!the!early!1970s.!It!
is!a!stainless<steel!vessel!which!was!filled!with!35!
cubic!metres!of!liquid!deuterium,!D2!or!a!H/Ne!mixture,!
whose!sensitivity!was!regulated!by!means!of!a!piston!
weighing!2!tonnes.!During!each!expansion,!charged!
particles!left!trails!of!bubbles!as!they!passed!through!
it.!It!has!since!been!decommissioned!and!is!now!on!
display!at!CERN's!Microcosm!museum.!
The!BEBC!project!was!launched!in!1966!by!France!and!
Germany.!It!was!surrounded!by!a!3.5!T!superconducting!
solenoid!magnet.!In!1973,!it!began!operation!at!the!
Proton!Synchrotron!(PS).!From!1977!to!1984,!it!was!
operated!in!the!West!Area!neutrino!beam!line!of!the!
Super!Proton!Synchrotron!(SPS),!where!it!was!exposed!to!
neutrino!and!hadron!beams!at!higher!energies!of!up!to!
450!GeV.!By!the!end!of!its!active!life!in!1984,!BEBC!had!
delivered!a!total!of!6.3!million!photographs!to!22!
experiments!devoted!to!neutrino!or!hadron!physics.!
Around!600!scientists!from!some!fifty!laboratories!
throughout!the!world!had!taken!part!in!analysing!the!
3000!km!of!film!it!had!produced.!!(from!wikipedia)!
http://cerncourier.com/cws/article/cern/28742
25
Geiger<Muller!
The#“first”#
electrical#
detector#ever#
built#
Electrical!signal!reveals!the!passage!of!a!charged!particle!
26
Particle detection Principle
Particle Interactions: Examples
Energy Lass by Ionisation : Bethe-Bloch Formula
Bathe-Block: - Classical derivation
Bethe-Bloch Formula
dE/dx Fluctuations
Bethe-Block describe the mean energy loss. ; measurement via
energy loss ΔE in a material with thickness ΔX with
ΔE =
𝑁
𝑛=1
𝛿𝐸 n N = no. of collisions, 𝛿𝐸 is the energy loss in a single collision
Ionisation loss 𝛿𝐸 is statistically
Distributed.
So called
Energy loss “straggling “
It is a complicated probleme.g. thin absorbers gives
Landau distribution.
dE/dX Fluctuations – Landau Distribution
Particle Energy Deposit:
Energy Loss of Pions in Cu
Energy loss of pions in Cu!
Minimum
ionizing particles (MIP): βγ = 3-4
dE/dx falls ~ β-2; kinematic factor
[precise dependence: ~ β-5/3]
dE/dx rises ~ ln (βγ)2; relativistic rise
[rel. extension of transversal E-field]
Saturation at large (βγ) due to
density effect (correction δ)
[polarization of medium]
Units: MeV g-1 cm2
: Energieverlust in Kupfer. Gezeigt wird der Einfluß der SchalenkorMIP looses ~ 13 MeV/cm
βγ
=
3
4
r Dichteeffektkorrektur. Das Minimum des Energieverlustes
liegt8.94bei
[density of copper:
g/cm3]
or dem Minimum verhält sich dE/dx ∝ β −2 , nach dem Minimum
ogarithmisch
an und kommt dann inExperimental
den Particle
Sättigungsbereich
(DichteMarco Delmastro!
Physics!
6!
Understanding Bethe-Bloch!
Bethe-Bloch
Understanding
1/β2-dependence:
Remember:
Slower particles
Z fell electric
Z force of
dx
atomic electrons
for dt
longer
time
…
p? = F
=
F
?
?
v
i.e. slower particles feel electric force of
atomic electron for longer time ...
Relativistic rise for βγ > 4:
High energy particle: transversal electric field increases
Abbildung
2.2:interaction
Energieverlust
in Kupfer.
wird...der Einfluß de
due to Lorentz transform; Ey ➙
γEy. Thus
cross
section Gezeigt
increases
particle
at rest
γ=1
Marco Delmastro!
rektur und der Dichteeffektkorrektur. Das Minimum des Energieverl
βγfast
≃moving
3...4. Vor dem Minimum verhält sich dE/dx ∝ β −2 , nach d
particle
steigt
dE/dx logarithmisch an und kommt dann in den Sättigungsber
effekt). Man beachte: Corrections:
Die auf der Ordinate angegebene Größe ist vi
(nicht − dE
). Quelle: Phys. Rev. D 54:S132, 1996.
dx
low energy : shell corrections
grows
γ gross
high energy : density corrections
• Der fehlende Faktor 2 in der trivialen“ Ableitung kann wie folgt ve
”
EinExperimental
kleinerer
Grenzwert
von
Emin vergrößert den Anteil des Ene
7!
Particle Physics!
Understanding Bethe-Bloch!
Bethe-Bloch
Understanding
Density correction:
Polarization effect ...
[density dependent]
➙ Shielding of electrical field far from
particle path; effectively cuts of the
long range contribution ...
More relevant at high γ ...
[Increased range of electric field; larger bmax; ...]
For high energies:
Shell
⇤/2 ! ln(~⌅/I) + ln ⇥Abbildung
1/2 2.2: Energieverlust in Kupfer. Gezeigt wird der Einfluß de
rektur und der Dichteeffektkorrektur.
Minimum
Density Das
effect
leads todes Energieverl
βγ ≃ 3...4. Vor dem Minimum
verhält sich
dE/dx
∝ β −2
saturation
at high
energy
..., nach d
correction:
steigt dE/dx logarithmisch an und kommt dann in den Sättigungsber
Arises if particle velocity is close
to orbital
effekt).
Man beachte: Die auf der Ordinate angegebene Größe ist vi
Shell
correction
velocity of electrons, i.e. βc ~(nicht
ve. − dE
). Quelle: Phys. Rev.
D 54:S132,
1996.are
dx
Assumption that electron is at rest breaks down ...
Capture process is possible ...
Marco Delmastro!
in general small ...
• Der fehlende Faktor 2 in der trivialen“ Ableitung kann wie folgt ve
”
EinExperimental
kleinerer
Grenzwert
von Emin vergrößert den Anteil des Ene
8!
Particle
Physics!
Energy
charged
particles !
Energyloss
Lossofof(heavy)
Charged
Particles
6
27. Passage of particles through matter
10
Dependence on
Mass A
Charge Z
of target nucleus
Minimum ionization:
ca. 1 - 2 MeV/g
[H2: 4 MeV/g cm-2]
cm-2
− dE / dx (MeV g−1cm2)
8
6
5
H2 liquid
4
He gas
3
2
1
0.1
Sn
Pb
1.0
0.1
Marco Delmastro!
10
100
βγ = p/ Mc
Fe
Al
C
1000
10 000
1.0
10
100
Muon momentum (GeV/c)
1000
Experimental Particle Physics!
9!
TPC Signal [a.u.]
Identifying
by dE/dx!
dE/dx andparticles
Particle Identification
180
Measured
energy loss
140
[ALICE TPC, 2009]
100
60
Bethe-Bloch
Remember:
dE/dx depends on β!
20
0.1 0.2
1
2
Momentum [GeV]
Marco Delmastro!
Experimental Particle Physics!
10!
dE/dx for particle identification
dE/dx
The energy loss as a function of
momentum p=mcβγ is dependent
on the particle mass
By measuring the particle
momentum (deflection in a
magnetic field) and the energy
loss one gets the mass of the
particle, i.e. particle ID
(at least in a certain energy
region)
18
Dependence on absorber thickness
•
•
The Bethe-Bloch equation describes the mean energy loss
When a charged particle passes the layer of material with thickness x , the
energy distribution of the δ-electrons and the fluctuations of their number
(nδ) cause fluctuations of the energy losses ΔE
The energy loss ΔE in a layer
of material is distributed
according to the Landau
function:
energy
For a realistic thin silicon
detector nδ 1-10,
fluctuations do not follow
the Landau distribution
19
Energy loss at small momenta
•
•
energy loss increases at small βγ
particles deposit most of their
energy at the end of their track
# Bragg peak
# Important effect for tumor therapy
20
Energy loss at small momenta
Small energy loss
$ Fast Particle
Cosmis rays: dE/dx α Z2
Small energy loss
$ Fast particle
Pion
Large energy loss
$ Slow particle
Pion
Discovery of muon and pion
Pion
Kaon
21
Mean particle range
from the total energy T to zero
More often use empirical formula
(# see exercise)
22
Mean particle range!
Marco Delmastro!
Experimental Particle Physics!
13!
Energy
Energyloss
Lossofofelectrons!
Electrons
Bethe-Bloch formula needs modification
Incident and target electron have same mass me
Scattering of identical, undistinguishable particles
⌧
dE
dx
el.

Z 1
m e 2 c2 ⇥ 2 T
= K
ln
+ F (⇥)
2
2
A
2I
[T: kinetic energy of electron]
Wmax = ½T
Remark: different energy loss for electrons and positrons at low energy as
positrons are not identical with electrons; different treatment ...
Marco Delmastro!
Experimental Particle Physics!
14!
Bremsstrahlung
%3:8;7*6$8%;8'5*8#&<6*78%;8'5*8
Bremsstrahlung and Radiation
Length!
!
! Bremsstrahlung
$%# arises
%
" if particles
&'
"
are accelerated
in Coulomb field of nucleus
$
!
!
#
$
!$
"
*A
!
#
✓
JKL
◆2
z Z
1 e
183
dE
E
= 4 NA
E
ln
/
1
dx
A BC,---8D*EF
4⇤⇥0 mc2
m2
$8&6'2"A2*6"'7?74'7<8
Z3
2
(
2
i.e. energy loss proportional to 1/m2 ➙ main relevance for electrons ...
... or ultra-relativistic muons
#! !
$%#
('
+% " &' $
'
Consider
electrons:
# #
"
,"
(
2
dE
Z2 2
183
= 4 NA
re · E ln 1
dx
A
Z3
"
dE
E
=
'dx X0
with
$%#
! !
( ' # +% &' $
Marco Delmastro!
#
#
X0 =
"" %
A
4 NA Z 2 re2 ln
*) ,"
183
1
Z3
E = E0 e
After passage of one X0 electron has
lost all but (1/e)th of its energy
2"$7"'7%#86*#)'58H).<3/I
[Radiation length in g/cm2]
Experimental Particle Physics!
x/X0
[i.e. 63%]
15!
(
1 PeV
10 PeV
Critical
Energy ! – Critical Energy
Bremsstrahlung
0
0.25
EcSol/Liq
610 MeV
=
Z + 1.24
dx
dx
Ion
Brems
200
Copper
X0 = 12.86 g cm−2
Ec = 19.63 MeV
100
al
t
To
70
Rossi:
Ionization per X0
= electron energy
50
40
30
E
lu
ng
710 MeV
Z + 0.92
Tot
ss
tr
ah
Ion
Approximation:
EcGas =
y = k/E
1
Br
Brems
dE
(Ec )
dx
dE /dx × X0 (MeV)
=
0.75
Figure 27.11: The normalized bremsstrahlung cross section k dσLP M /
✓
◆
◆
✓
✓The ◆
lead versus the fractional
photon
energy
y
=
k/E.
dE
dE
dE vertical axis has
of photons per radiation length.=
+
dx
dE
(Ec )
dx
0.5
em
Ex
s≈
ac
tb
re
m
Critical energy:
0
Ionization
20
Brems = ionization
Example Copper:
Ec ≈ 610/30 MeV ≈ 20 MeV
10
2
5
10
20
50
Electron energy (MeV)
100
200
Figure 27.12: Two definitions of the critical energy Ec .
Marco Delmastro!
Experimental Particle Physics!
16!
Total
of Electrons
Electrons!
Total Energy Loss of
27. Passage of particles through matter
from
PDG 2010
e–
e–
e+
e–
e–
Bhabha
e–
Marco Delmastro!
0.15
0.10
Ionization
Møller (e −)
Bhabha (e +)
e+
e+
Electrons
Bremsstrahlung
0.5
e–
Lead (Z = 82)
γ
0.20
0
1
(cm2 g−1)
Møller
− 1 dE ( X 0−1)
E dx
1.0
Positrons
0.05
Positron
annihilation
10
E (MeV)
100
1000
Figure 27.10: Fractional energy loss per radiation length in lead as a
Fractional energy loss per radiation length in lead
functionγ of electron or as
positron
energy.
Electron
(positron)
scattering is
a
function
of
electron
or
positron
energy
Annihilation as ionization when the energy loss per collision is below 0.255
considered
Experimental Particle Physics!
17!
27. Passage of particles through matter
Energy
muons ! Plot for Muons
Energyloss
Lossfor
– Summary
µ+ on Cu
µ−
10
LindhardScharff
100
Bethe-Bloch
Radiative
AndersonZiegler
Eµc
Radiative
losses
Radiative
Minimum
effects
ionization reach 1%
Nuclear
losses
Without δ
1
0.001
0.01
0.1
1
10
0.1
1
10
100
1
[MeV/c]
Marco Delmastro!
PDG 2010
Stopping power [MeV cm2/g]
4
βγ
100
1000
10 4
10 5
10 6
10
100
1
10
100
[GeV/c]
Muon momentum
[TeV/c]
Fig. 27.1: Stopping power (= ⟨−dE/dx⟩)
for positive muons in copper as a
Experimental Particle Physics!
18!
Note!that!the!trajectory!is!not!a!straight!line!because!of!the!
collisions!against!nuclei,!i.e.!multiple!scattering!(later).!
5
6
R/M!g!cmX2!GeVX1!!
Range
7
Percorso'delle'par,celle'(Range)'
50000
20000
C
10000
Pb
5000
R / M (g cm#2 GeV#1)
The!rangeXenergy!relationships!!
are!often!expressed!as!R(E)=(E/Eo)n!!
e.g.!the!range!in!meters!of!low!!
energy!protons!can!be!!approximated!!
with!n=1.8!and!Eo=9.3!MeV.!
!
Fe
2000
H2 liquid
He gas
1000
500
200
# E &1.8
R(E) ≅ % (
$ 9.3'
100
50
20
10
5
E!in!MeV,!!R!in!meters!of!air!
2
1
0.1
2
0.02
1.0
5
0.05
2
!" = p/ Mc
0.2
0.1
5
0.5
10.0
1.0
2
5
2.0
5.0
100.0
€
10.0
Muon momentum (GeV/c)
0.02
0.05
0.1
0.2
0.5
1.0
2.0
Pion momentum (GeV/c)
0.1
0.2
0.5
1.0
2.0
5.0
10.0 20.0
Proton momentum (GeV/c)
5.0
10.0
50.0
Scaling!laws
!
• Sometimes!data!are!not!available!on!the!range!or!energy!loss!
characteristics!of!precisely!the!same!particleXabsorber!combination!
needed!in!a!given!experiment.!Recourse!must!then!be!made!to!various!
approximations,!most!of!which!are!derived!based!on!the!Bethe!
formula!and!on!the!assumption!that!the!dE/dX!per!atom!of!compounds!
or!mixtures!is!additive.!This!latter!assumption,!known!as!the!
BraggXKleeman!rule,!may!be!written!!
• In!this!expression,!N!is!the!atomic!density,!and!Wi)represents!the!
atom!fraction!of!the!ith!component!in!the!compound!C.!!
• As!an!example!of!the!application!of!BB,!the!linear!stopping!power!
of!alpha!particles!in!a!metallic!oxide!could!be!obtained!from!
separate!data!on!dE/dX!in!both!the!pure!metal!and!in!oxygen.!!
• Some!caution!should!be!used!in!applying!such!results,!however,!
since!some!measurements!for!compounds!have!indicated!a!stopping!
power!differing!by!as!much!as!10X20%!from!that!calculated!from!BB.!!
9
dE/dx!per!composti!e!miscugli.!
Una!buona!approssimazione!della!perdita!di!energia!per!composti!e!
miscugli!è!data!dalla!regola!di!Bragg:!una!media!pesata!delle!perdite!
di!energia!degli!elementi!i!del!composto!M,!pesate!con!la!frazione!di!
elettroni!dell’elemento!
!
1 dE w1 ' dE $ w2 ' dE $
= % " + % " + ⋅⋅⋅⋅
!
ρ dx ρ1 & dx #1 ρ2 & dx #2
!
wi = ai
Ai
AM
AM = ∑ ai Ai
i
Dove!a1,!a2,!…!e’!il!nr.!di!elettroni!nello!iXesimo!elemento!del!
composto!M!e!Ai!e’!il!nr!atomico!dell’elemento!
Possiamo!definire!dei!valori!efficaci!come!segue:!
!
!
!
!
Z eff = ∑ ai Zi
ln I eff = ∑
ai Zi ln I i
Z eff
Aeff = ∑ ai Ai
δeff = ∑
ai Ziδi
Z eff
E!riscrivere!la!dE/dx!in!termini!dei!valori!efficaci.!
!
#
10
dE/dX!vs.!depth!
!
A!plot!of!the!specific!energy!loss!along!the!track!of!a!charged!
particle!is!known!as!a!Bragg)curve.!!
Until!the!particle!is!a!MIP,!its!energy!loss!stays!constant!(more!
exactly!it!varies!slowly!–logarithmicallyXwith!βγ.!Remember:!dE/dX! !1/β2!
and!β!≈!1!for!MIPs)!
As!βγ!goes!down!below!MIP,!the!E!loss!increases!very!rapidly!because!of!
1/β2!dependence!or!as!1/T!(kinetic!E)!as!the!particle!becomes!non!
relativistic!and!there!is!a!peak!in!energy!deposit!:!Bragg!peak!
βγ!>!3.5:!<dE/dX>!≈!(dE/dX)min!
βγ <!3.5:!<dE/dX>!>>!(dE/dX)min!
Near!the!end!of!the!track,!the!charge!
is!reduced!through!electron!pickup!and!
the!curve!falls!off:!particle!becomes!
very!slow!and!easily!captures!
electrons!from!medium!and!becomes!
neutral!before!stopping.!
dE/dX!vs.!depth!
!
Particles!with!high!charge!
begin!to!pick!up!electrons!
early!in!their!slowingXdown!
process.!!
Note!that!in!an!Al!absorber,!
singly!charged!H!ions!(protons)!
show!strong!effects!of!charge!
pickup!below!about!100!keV,!but!
doubly!charged!3He!ions!show!
equivalent!effects!at!about!400!
keV.!!
!
17/03/11
dE/dx phenomena
2
2 2 2
'
.
dE
z
Z
2
m
c
β γ Tmax +
δ (βγ )$!
!1
2
2
2
e
= 4πN A re me c 2 & 2 ln ,
)−β −
#
2
dx
A
2
β
I
!% ,!"
)*
• Slow!particles!lose!most!of!their!energy!in!a!
short!distance,!since!kinetic!energy!T!~!β2
−
dE
dT
dE
=−
=
dx
dx
dx
T0
T0 T
ΔX = −
ΔX = − ∫
1
(dE / dx)o T0
∫
0
T0
dT
T0
dT / dx
0
T dT = −
ΔX = − ∫
TdT
T0
(dE / dx)o T0
0
T0
= ρΔy
2(dE / dx)o
• For!30!MeV!protons!in!water,!<dE/dx>!~!50!MeV!
cm2/gm,!so!Δy!~!0.3!cm!!
13
Application of Range
• The localized energy deposition of heavy charged particles
can be useful therapeutically = proton radiation therapy
14
Application of Range
• Monoenergetic!proton!beam!loses!energy!more!
rapidly!as!it!slows!down;!gives!sharp!Bragg!
peak!in!ionization!versus!depth!!
• Using!a!range!of!proton!
energies!allows!a!varied!
profile!versus!depth!
• Photon!beam!(xXrays)!
deposits!most!energy!!
near!entrance!into!tissue!
• Tumor!therapy!with!hadrons!
!!(adroXtherapy)!
15
Proton Therapy
• Energy range of interest from 50 (eye) – 250 (prostate)
MeV
16
Proton Therapy
17
18
Proton Therapy
• Schematic apparatus for hadron-therapy
19
Proton Therapy
• Modulator, aperture, and compensator
Modulator
20
Proton Therapy
21
Proton Therapy
22
Proton Therapy
• Lung cancer treatment
– Intensity modulated radiation therapy vs proton therapy
23
Pair!Production!
The!total!pair!production!cross!section!is!obtained!
integrating!over!the!the!energy!fraction!
! In!the!Born!approximation!(which!is!not!very!accurate!
for!low!energy!or!high!Z)!one!finds!
No screening (ξ >> 1) and mec 2 << hν << 137mec 2 Z −1/3
σ pair
( 7 " 2hν % 109 +
= 4Z α r * $ ln
−
2'
) 9 # mec & 54 ,
2
2
e
NB: ξ = screening parameter
Complete screening (ξ → 0 ) and hν >> 137mec 2 Z −1/3
σ pair
(7
1
−1/3 +
= 4Z α r * ( ln183Z )- −
)9
, 54
2
2
e
E. Fiandrini Rivelatori di particelle
1718
ie!high!energy!
2
Pair!Production!
! Notes!
%
%
%
%
σpair ~!Z2!
Above!some!photon!energy!(say!>!1!GeV),!
σpair becomes!a!constant!
In!order!to!account!for!pair!production!
from!the!Coulomb!field!of!atomic!
electrons,!Z2!is!replaced!by!Z(Z+1)!
approximately!since!the!cross!section!is!
smaller!by!a!factor!of!Z!
Usually!we!don t!distinguish!between!the!
source!of!the!field!
E. Fiandrini Rivelatori di particelle
1718
10
Pair!Production!
! 2me!(1.022!MeV)!of!the!photon s!energy!goes!into!creating!
the!electron!and!positron!
! The!electron!will!typically!be!absorbed!in!a!detector!
! The!positron!will!typically!annihilate!with!an!electron!
producing!two!annihilation!photons!of!energy!me!(0.511!
MeV)!each!
! If!these!photons!are!not!absorbed!in!the!detector!then!
the!pair!production!energy!spectrum!will!look!like!!
E. Fiandrini Rivelatori di particelle
1718
12
B)#CC&C(
B)#CC&C(
σG7+@(?*"
σG7+@(?*"
Interactionsofofphotons
Photons with
with Matter
Interaction
matter!
,&.
,&.
κ%HD
ge of particles through matter
B)#CC&C(D$?#%&&4.7)%C
E 7$#15
B)#CC&C(D$?#%&&4.7)%C
E 7$#15
,&-.
,&-.
σB#1>$#%
κ"
475&B7).#%&4!#9&F5
4.5&6(78&4!&9&:;5
Carbon
(Z =
6)
<&(=>()?1(%$7@&
<&(=>()?1(%$7@&σ
σ$#$
$#$
σ>A(A
4.5&6(78&4!&9&:;5
,&-.
Photo effect
σ>A(A
σG7+@(?*"
,&/.
,&/.
σG7+@(?*"
,&.
Rayleigh
,&.
scattering
,0&1.
,0&1.
,0&(2
1 MeV
σ*A8A)A
,&/(2
κ%HD
Lead
(Z = 82)
<&(=>()?1(%$7@&σ
$#$
σ>A(A
σG7+@(?*"
1 MeV
Pair
production
,&/.
σ*A8A)A
,&.
κ"
κ%HD
σB#1>$#%
σB#1>$#%
κ"
,0&1.
B)#CC&C(D$?#%&&4.7)%C E 7$#15
,0&1.
PhotonσB#1>$#%
Total Cross Sections
κ%HD
κ%HD
κ"
σB#1>$#%
κ"
,&-(2
!"#$#%&'%()*+
4.5&6(78&4!&9&:;5
,&3(2
,00&3(2
,0&1.
,0&(2
,&/(2
,&-(2
,&3(2
,00&3(2
!"#$#%&'%()*+
$#15
Pair
ProductionPhoton total cross sections as a function of ene
<&(=>()?1(%$7@&
σ$#$ 27.14:
Figure
: Photon
cross
sections
as
a
function
of energy
in carbon
,&-. total
Compton
scattering
σ
>A(A
t
and lead,
showing the contributions of different processes:
wing the contributions of different
processes:
Marco Delmastro!
30!
Particle Physics!
=ejection,
Atomic
photoelectric effect (electron ejection,
σp.e. Experimental
Atomic
photoelectric effect (electron
photon
Interactionsofofphotons
Photons with
with Matter
Interaction
matter!
I
Characteristic for interactions of
photons with matter:
I - dI
A single interaction
removes photon from beam !
Possible Interactions
dI =
Photoelectric Effect
Compton Scattering
Pair Production
[ µ : absorption coefficient ]
depends on
E, Z, ρ
Rayleigh Scattering (γA ➛ γA; A = atom; coherent)
Thomson Scattering (γe ➛ γe; elastic scattering)
Photo Nuclear Absorption (γΚ ➛ pK/nK)
Nuclear Resonance Scattering (γK ➛ K* ➛ γK)
Delbruck Scattering (γK ➛ γK)
Hadron Pair production (γK ➛ h+h– K)
Marco Delmastro!
µ I dx
Experimental Particle Physics!
➛
Beer-Lambert law:
I(x) = I0 e
with
µx
= 1/µ = 1/n⇥
[ mean free path ]
28!
Electromagnetic showers!
Showers
Electromagnetic
Reminder:
Dominant processes
at high energies ...
Photons : Pair production
Electrons : Bremsstrahlung
X0
Pair production:
◆
✓
7
183
⇥pair ⇡
4 re2 Z 2 ln 1
9
Z3
=
7 A
9 NA X0
Absorption
coefficient:
µ = n⇥ =
Marco Delmastro!
Bremsstrahlung:
[X0: radiation length]
[in cm or g/cm2]
dE
E
dE
Z2 2
183
= 4 NA
r · E ln 1 =
X0
dx
A e
3
Zdx
➛ E = E0 e
NA
7
· ⇥pair =
A
9 X0
Experimental Particle Physics!
x/X0
After passage of one X0 electron
has only (1/e)th of its primary energy ...
[i.e. 37%]
32!
Figure 27.11: The normalized bremsstrahlung cross section k dσLP M /dk
lead versus the fractional photon energy y = k/E. The vertical axis has un
of photons per radiation length.
Electromagnetic
Electromagnetic showers!
Showers
200
dE
(Ec )
dx
Brems
dE
=
(Ec )
dx
Ion
✓
dE
dx
Brems
30
E
✓
dE
dx
EcSol/Liq
◆
Ion
10
610 MeV
=
Z + 1.24
Z ·E
800 MeV
2
5
10
20
50
Electron energy (MeV)
Transverse size of EM shower given by
radiation length via Molière radius
100
200
Figure 27.12: Two definitions of the critical energy Ec .
with:
incomplete, dE
and near y =
divergence is removed
dE the infrared
E 0, where
Ec
=
⇡
=
const.
& amplitudes from nearby scattering cent
the interference
dx of bremsstrahlung
X
dx
X
Brems
0
Ion
February 2, 2010
RM
21 MeV
=
X0
Ec
[see also later]
Marco Delmastro!
lu
ng
Ionization
Brems = ionization
710 MeV
=
Z + 0.92
◆
Rossi:
Ionization per X0
= electron energy
50
40
20
Approximations:
EcGas
l
ta
o
T
70
ss
tr
ah
Critical Energy [see above]:
Br
dE /dx × X0 (MeV)
100
em
Ex
s≈
ac
tb
re
m
Further basics:
Copper
X0 = 12.86 g cm−2
Ec = 19.63 MeV
Experimental Particle Physics!
0
15:55
RM : Moliere radius
Ec : Critical Energy [Rossi]
X0 : Radiation length
33!
Electromagnetic
Electromagnetic showers!
Showers
Typical values for X0, Ec and RM of materials
used in calorimeter
X0 [cm]
Ec [MeV]
RM [cm]
Pb
0.56
7.2
1.6
Scintillator (Sz)
34.7
80
9.1
Fe
1.76
21
1.8
14
31
9.5
BGO
1.12
10.1
2.3
Sz/Pb
3.1
12.6
5.2
PB glass (SF5)
2.4
11.8
4.3
Ar (liquid)
Marco Delmastro!
Experimental Particle Physics!
34!
Sim
rlo
Ca
te
on
(M
rs
ue
ha
Sc
en
sch
−
eti
e
gn
+ +
ma
e
γ
tro
+
lek
K
e+
se
+
→
die
K
ine
ng
ge
K
→
hlu
lun
γ+
ra
K
ick
sst
e+
ntw
em
Br
).
E0
rn
e
rch
Ke
ess
2
du
−
P
=
oz
=
n
Pr
1
se
K
vo
E
(
a
ie
td
igt
erg
ht
ier
l
r
En
sic
e
E1
v
ck
ie
rü
,d
X0
= 2
be
X0
ke
en
E±
ch
rec
t
na
rd
we
f
Au
Analytic
Shower
Model
A simple shower model!
rS
de
Simple shower model:
[from Heitler]
Only two dominant interactions:
Pair production and Bremsstrahlung ...
γ + Nucleus ➛ Nucleus + e+ + e−
[Photons absorbed via pair production]
rt
sie
ali
e + Nucleus ➛ Nucleus + e + γ
[Monte Carlo Simulation]
[Energy loss of electrons via Bremsstrahlung]
Shower development governed by X0 ...
Use
Simplification:
After a distance X0 electrons remain with
only (1/e)th of their primary energy ...
[Ee looses half the energy]
Photon produces e+e−-pair after 9/7X0 ≈ X0 ...
Ee ≈ E0/2
Assume:
E > Ec : no energy loss by ionization/excitation
ur
ch
Io
Marco Delmastro!
Electromagnetic Shower
Eγ = Ee ≈ E0/2
[Energy shared by e+/e–]
... with initial particle energy E0
E < Ec : energy loss only via ionization/excitation
Experimental Particle Physics!
35!
AAnalytic
simple Shower
showerModel
model!
Sketch of simple
shower development
E0
Simple shower model:
[continued]
Shower characterized by:
0
Number of particles in shower
Location of shower maximum
Longitudinal shower distribution
Transverse shower distribution
Number of shower particles
after depth t:
/
/
/
1
2
3
4
➛ t = log2 (E0/E)
6
7
... use:
Number of shower particles
at shower maximum:
t
t [X0 ]
8
Fig. 8.1. Sketch of a simple model for shower parametrisation.
Longitudinal components;
measured in radiation length ...
t=
N (E0 , E1 ) = 2t1 = 2 log2 (
Energy per particle
after depth t:
E0
E=
= E0 · 2
N (t)
5
x
X0
Total number of shower particles
with energy E1:
N (t) = 2t
Marco Delmastro!
/
E 0 2 E 0 4 E 0 8 E 0 16
E0/E
1)
=
E0
E1
E0
Ec
N (E0 , E1 ) / E0
N (E0 , Ec ) = Nmax = 2tmax =
Shower maximum at:
tmax / ln(E0/Ec )
Experimental Particle Physics!
36!
Electromagnetic
Showerdevelopment!
Profile
EM
shower longitudinal
8.1 Electromagnetic calorimeters
Longitudinal profile
600
5000 MeV
Parametrization:
dE
= E0 t e
dt
d E / d t [MeV/X0]
[Longo 1975]
⇥t
α,β : free parameters
tα : at small depth number of
secondaries increases ...
–βt
e : at larger depth absorption
dominates ...
400
2000 MeV
200
1000 MeV
500 MeV
Numbers for E = 2 GeV (approximate):
α = 2, β = 0.5, tmax = α/β
0
5
0
More exact
[Longo 1985]
[Γ: Gamma function]
Marco Delmastro!
⇥t
➛ tmax =
1
⇥
= ln
100
◆
E0
+ Ce
Ec 10
/ d t [MeV/X0]
(⇥t) 1 e
dE
= E0 · ⇥ ·
dt
( )
✓
Experimental Particle Physics!
1
10
t [X0]
15
20
with:
Ce =
0.5
[γ-induced]
Ce =
1.0
[e-induced]
lead
iron
aluminium
38!
EM
shower transverse
Electromagnetic
Showerprofile!
Profile
Transverse profile
z/X0
Abbildung 8.4: Longitudinalverteilung der Energiedeposition in einem elekt
energy
deposit
Schauer für zwei Prim
ärenergien
der Elektronen
[arbitrary unites]
Parametrization:
dE
= e
dr
r/R
M
+ ⇥e
r/
min
α,β : free parameters
RM : Molière radius
λmin : range of low energetic
photons ...
Inner part: coulomb scattering ...
Electrons and positrons move away
from shower axis due to multiple scattering ...
Outer part: low energy photons ...
r/ R
r/RM
r/R
MM
Photons (and electrons) produced in isotropic
processes (Compton scattering,
photo-electric
move away from
Abbildung
8.5: effect)
Transversalverteilung
der Energie in einem elektromagnetisc
shower axis; predominant beyond shower maximum, particularly in high-Z absorber media...
unterschiedlichen Tiefen gemessen
Shower gets wider at larger depth ...
Marco Delmastro!
Experimental Particle Physics!
159
41!
Longitudinal
Showerprofiles
Shape
EM
shower shower
longitudinal
development!
ctromagnetic
(longitudinal)
Energy deposit per cm [%]
Depth [X0]
Energy deposit of electrons as a function of depth in a
block of copper; integrals normalized to same value
[EGS4* calculation]
Depth of shower maximum increases
logarithmically with energy
tmax / ln(E0/Ec )
Depth [cm]
*EGS = Electron Gamma Shower
Marco Delmastro!
Experimental Particle Physics!
39!
Longitudinal development of EM shower
Shower decay:
after the shower maximum the shower decays slowly through ionization
and Compton scattering " NOT proportional to X0
Z = 82
26
13
11
The longitudinal shower shape
EM
showers
a nutshell!
Some
Usefulin'Rules
of Thumbs'
Radiation length:
180A g
X0 =
Z 2 cm2
Critical energy:
550 MeV
Ec =
Z
[Attention: Definition of Rossi used]
Shower maximum:
Longitudinal
energy containment:
Transverse
Energy containment:
Marco Delmastro!
tmax
E
= ln
Ec
Problem:
Calculate how much Pb, Fe or Cu
is needed to stop a 10 GeV electron.
Pb : Z = 82 , A = 207, ρ = 11.34 g/cm3
Fe : Z = 26 , A = 56, ρ = 7.87 g/cm3
Cu : Z = 29 , A = 63, ρ = 8.92 g/cm3
1.0
1.0
0.5
{
e– induced shower
γ induced shower
L(95%) = tmax + 0.08Z + 9.6 [X0 ]
R(90%) = RM
R(95%) = 2RM
Experimental Particle Physics!
43!
Thermalization energy of the neutron:
1/40 eV
Radial Field
The single wire proportional counter
E/p=Reduced electric field
See next slides
see next slides
Resolve left/right ambiguities
L
S
S
L
L
S
S
L
Dopo un percorso x gli elettroni hanno subito
uno sparpaglimento
dN/dr= (N_{0}/(\sqrt{4\pi Dt}))e^{-x^2/4Dt}
\sigma=\sqrt{2Dt}=\sqrt{2Dx/v}=
=\sqrt{2Dx/\mu E}
D=coe!ciente di di"usione
p_{0}= pressione gas
\sigma_{0}=
sezione d'urto di
collisione delle particelle con
una molecola del gas
m= massa particella
D= (2/3\sqrt{\pi})(1/\mu \sqrt{\sigma_{0}})(\sqrt{(kT)^3/m})
Rivelatori di Particelle
17
Time Projection Chamber
Time Projection Chamber
•
The most sophisticated gas position detector is the Time Projection Chamber or TPC: a 3D
tracking detector capable of providing information on many points of a particle track along with
information on the specific energy loss, dE/dx, of the particle.
•
The TPC makes use of ideas from
both the MWPC and drift chamber.
The detector is a essentially a
large gas-filled cylinder with a thin
high voltage electrode at the
center. (At high energy colliders, the
•
diameter and length of the cylinder can be as
large as two meters).
•
•
When voltage is applied, a uniform
electric field directed along the
axis is created. A parallel magnetic
field is also applied.
The ends of the cylinder are
covered by sector arrays of
proportional anode wires arranged
as shown. Parallel to each wire is
a cathode strip cut up into
rectangular segments. These
segments are also known as
cathode pads.
From Leo
Drift to endplace where x,y are measured
Drift-time provides z
Analogue readout provide dE/dx
38
Magnetic field provide p (and reduce transverse diffusion
during drift)
TPC
TPC
Traiettoria della particella
Pad catodiche
Fili
anodici
B
gas
Elettrodo centrale (≈ -50kV)
Piano di lettura
& La camera è divisa in 2 metà tramite un elettrodo centrale
& Gli elettroni di ionizzazione primaria si muovono nel campo elettrico verso le placche
finali della camera (normalmente delle MWPC). Campo magnetico // al campo
elettrico. La diffusione ortogonale al campo è soppressa dal campo B.
& Il tempo di arrivo degli elettroni sulle placche finali fornisce la coordinata lungo l’asse
del cilindro (z). La moltiplicazione degli elettroni avviene vicino agli anodi. x e y si
ottengono dagli anodi e dal catodo della MWPC suddiviso normalmente in pad.
Rivelatori di Particelle
39
Time Projection Chamber
40
•
•
•
At a colliders, the detector is positioned so that
its center is at the interaction point. The TPC
thus subtends a solid angle close to 4π.
Particles from IP pass through the cylinder
volume producing free e- which drift to the
endcaps where they are detected by the
anode wires as in a MWPC.
This yields the position of a space point
projected onto the endcap plane. One
coordinate is given by the position of the firing
anode wire while the 2nd is obtained from the
signals induced on the row of cathode pads
along the anode wire. Using the center-ofgravity method, this locates the position of the
avalanche along the firing anode wire.
The third coordinate, along the cylinder axis, is
given by the drift time of the ionization e-.
Since all ionization electrons created in the
sensitive volume of the TPC will drift towards
the endcap, each anode wire over which the
particle trajectory crosses will sample that
portion of the track. This yields many space
points for each track allowing a full
reconstruction of the particle trajectory.
TPC
From Leo
41
TPC
•
•
•
Because of the relatively long drift
distance, diffusion, particularly in the
lateral direction, becomes a problem.
B field confines the e- to helical
trajectories about the drift direction.
This reduce diffusion by as much as a
factor of 10.
In order to avoid deviating the
trajectories of the drifting e-, the B and
E fields must be in perfect alignment
and uniform over the volume of the drift
zone down to about one part in 104.
Rivelatori di Particelle
42
TPC
La TPC permette di determinare un punto nello spazio ( x,y,z ovvero r,φ,z ).
Il segnale analogico sull’anodo fornisce dE/dx.
E//B " angolo di Lorentz = 0 e la velocità di deriva è quindi parallela sia al campo
elettrico che magnetico.
Il campo magnetico sopprime la diffusione ┴ al campo (Gli elettroni spiralizzano attorno a
B.) Per E~ 50KV/m e B ~1.5 T " raggi di Larmor ~1 µm
Richieste:
i. Per misurare bene la coordinata z bisogna conoscere perfettamente la vD "
calibrazione tramite laser e correzioni per la pressione e temperatura.
ii. La deriva avviene su lunghe distanze " gas molto puro e sempre monitorato.
iii. Poco materiale (solo gas) " minimizzo lo scattering multiplo e la conversione dei
fotoni.
Esempi:
PEP-4 TPC p=8.5 atmosfere, Ar=80%, CH4=20% Vcentr=-55kV B=1.325T lunga 2m e
con raggio 1m.
Aleph TPC lunga 4.4 m e diametro 3.6 m, risoluzione σrφ=173µm, σz=740 µm
per leptoni isolati.
Rivelatori di Particelle
43
TPC
Molti ioni positivi creati nella zona di moltiplicazione vicino agli anodi della
MWPC che possono andare fino all’elettrodo centrale " carica spaziale che
deteriora il campo " si introduce una griglia (gate)
Gate open
Gate closed
Il gate è normalmente chiuso, viene
aperto solo per un breve tempo quando
un trigger esterno segnala un evento
interessante ! passano gli elettroni.
Viene chiuso di nuovo per impedire agli
ioni di tornare verso l’elettrodo centrale.
ALEPH TPC ΔVg = 150 V
(ALEPH coll., NIM A 294 (1990) 121,
W. Atwood et. Al, NIM A 306 (1991) 446)
Rivelatori di Particelle
44
TPC
•
A problem which arises during operation is
the accumulation of a space charge in the
drift volume due to positive ions from
avalanches drifting back towards the central
cathode. These ions are sufficiently
numerous that a distortion of the electric
field in the drifting volume occurs.
•
This is prevented by placing a grid at
ground potential just before the anode
wires. Positive Ions are then captured at this
grid rather than drifting back into the
sensitive volume. The grid also serves to
separate the drift region from the avalanche
zone and allows an independent control of
each.
Rivelatori di Particelle
45
TPC
•
•
Since the Q collected at the endcaps is
the energy loss of the particle, the
signal amplitudes from the anode also provide information on the dE/dx of the
particle. If p is known from the curvature of its trajectory in the B field, for
example, then this information can be used to identify the particle In order for
this method to work, however, sufficient resolution in the dE/dx measurement
must be obtained. This is much more difficult to realize as many factors must
be considered, e.g., electron loss due to attachment, wire gain variations in
position and time, calibration of the wires, saturation effects, choice of gas and
operating pressure, etc.,. all of which require careful thought!
Because of the very large amount of data produced for each event, an
important consideration is the readout and data acquisition system for a TPC
An approach which has been used to use flash ADCs directly coupled to the
sense wires. These ADCs are sufficiently fast such that several wires can be
multiplexed into one ADC.
Rivelatori di Particelle
46
Time Projection Chamber
TPC measures all 3 space coordinates
σx=σy~0.1-0.2 mm (drift time), σz~0.2-1mm (readout pad size) Used at LEP, RHIC
Many hits per track (>100) ⇒ excellent dE/dx measurement
PEP4/9-TPC
Drawbacks:
Very complicated electric field shaping: E||B to reduce effects of diffusion
Long drift times ⇒ complicated gas system
Lots of electronic channels ⇒ complicated electronics
47
Time Projection Chambers
Note that the electric and magnetic fields are parallel and must be very
homogeneous to permit accurate reconstruction. Laser “tracks” are used for
calibration and alignment but extracting good calibration constants is tricky.
Diffusion of the drifting electrons would normally smear out the measured
track but the magnetic field limits this by causing the electrons to spiral in the
drift direction
ATLAS TPC
Rivelatori di particelle
ATLAS TPC
48
Scintillators – General Characteristics
Trasparency
Principle:
dE/dx converted into visible light
Detection via photosensor
[e.g. photomultiplier, human eye ...]
Main Features:
Sensitivity to energy
Fast time response
Pulse shape discrimination
Plastic Scintillator
BC412
Requirements
High efficiency for conversion of exciting energy to fluorescent radiation
Transparency to its fluorescent radiation to allow transmission of light
Emission of light in a spectral range detectable for photosensors
Short decay time to allow fast response
Scintillators – Basic Counter Setup
Thin window
Mu Metal Shield
Iron Protective Shield
48
Light
Photomultiplier
[or other photosensor]
Scintillator
A N D B. R 1 G H I N I
vertical memory of the scope and is of no interest,
because the setup samples the vertical amplifier output
voltage before it is moved after each trigger pulse. The
X component, on the other hand, is worth more
attention; in fact at very low trigger rates this displacement becomes non-negligible between two subsequent
triggers, resulting in a decrease or increase of the
number of points used by the scope to produce a
complete CRT sweep and, therefore, in a widening or
narrowing of the time axis. There are different ways
of taking this error into account in order to make the
the necessary correction, but the easiest and most
reliable one is to count the points of the sweep in the
two following cases: when the sampling rate is high
(e.g. 1000 Hz), and at the actual sampling rate during
the measurement. This can be done by counting the
input trigger pulses of the scope during the time interval
between two sweep-trigger output pulses.
PMT Base
the lamp and the PM, two neutral fil
Wratten Nos. 96ND60 and 96ND30) and
(Kodak Wratten No. 98) are inserted in
holder (13). A variable light attenuator (7
the middle of the tube, consisting of t
sheets, one of them fixed, the other rotata
exterior. A slot [(10) and detail view A-A]
the proximity of the filters' holder to cl
completely when necessary. For all the m
here reported, only the central part of
cathode was illuminated by using a mask w
hole of 0.8 cm diameter.
As a lamp, a Philips type DM 160 indica
been used. The light emitted by the tube is
to the grid bias voltage, which can be
potentiometer: pulse driving of the lam
possible by a suitable connection.
Before recording the SER pulse shape it
to put the photomultiplier in SER oper
independent measurement. The required
SER spectrum is then located by SCA th
window-width setting.
For a setting corresponding to the SE
[voltage divider network etc.]
4. "SER" pulse visualization: mechanical setup and
measurement
The PM under examination is contained within an
iron tube connected to the light source (fig. 2); between
Scintillator Types:
Photosensors
G. B I A N C H E T T I
PMT Pulse
?
Output
Signal
Organic Scintillators
Inorganic Crystals
Gases
Photomultipliers
Micro-Channel Plates
Hybrid Photo Diodes
Visible Light Photon Counter
Silicon Photo Multipliers
F-I
0
0
I
5
5
I
10
10
I
15
Time [ns]
Fig. 3. SER pulse shape. I-IT= 2450 V- 50 sweeps. Measuring time l h 5 min. Pulse amplitude is about 120mV. Fwhm
Rise-time 1.6 ns.
Organic Scintillators
Naphtalene
Aromatic hydrocarbon
compounds:
e.g.
Naphtalene [C10H8]
Antracene [C14H10]
Stilbene [C14H12]
...
Very fast!
[Decay times of O(ns)]
Antracene
Scintillation is based on electrons
of the C = C bond ...
Scintillation light arises from
delocalized electrons in π-orbitals ...
Transitions of 'free' electrons ...
Two
pz orbitals
π bond
Organic Scintillators
Molecular states:
Absorption
in 3-4 eV range
Singlet states
Triplet states
Fluorescence in
UV range
[~ 320 nm]
➥ usage of
wavelength shifters
Fluorescence
:
Phosphorescence :
S1 ➛ S0 [< 10-8 s]
T0 ➛ S0 [> 10-4 s]
Organic Scintillators
Shift of absorption
and emission spectra ...
Intensity
Transparency requires:
Stokes-Shift
Absorption
Emission
λ
Franck-Condon Principle
Excitation into higher vibrational states
De-excitation from lowest vibrational state
Excitation time scale : 10-14 s
Vibrational time scale : 10-12 s
S1 lifetime
: 10-8 s
Energy
Shift due to
S1
Excited State
S0
Ground State
Vibrational
States
Nuclear
distance
Organic Scintillators – Properties
Scintillator
material
Density
[g/cm3]
Refractive
Index
Wavelength [nm]
for max. emission
Decay time
constant [ns]
Naphtalene
1.15
1.58
348
11
4⋅103 xxx
Antracene
1.25
1.59
448
30
4⋅104 xxx
p-Terphenyl
1.23
1.65
391
6-12
1.2⋅104 xxx
NE102*
1.03
1.58
425
2.5
2.5⋅104 xxx
NE104*
1.03
1.58
405
1.8
2.4⋅104 xxx
NE110*
1.03
1.58
437
3.3
2.4⋅104 xxx
NE111*
1.03
1.58
370
1.7
2.3⋅104 xxx
BC400**
1.03
1.58
423
2.4
2.5⋅102 xxx
BC428**
1.03
1.58
480
12.5
2.2⋅104 xxx
BC443**
1.05
1.58
425
2.2
2.4⋅104 xxx
Photons/MeV
* Nuclear Enterprises, U.K.
** Bicron Corporation, USA
Organic Scintillators – Properties
Organic Scintillators – Properties
Light yield:
[without quenching]
dL
dE
= L0
dx
dx
Quenching:
non-linear response due to
saturation of available states
Birk's law:
dE
dL
dx
= L0
dx
1 + kB dE
dx
[kB needs to be determined experimentally]
Also other ...
parameterizations ...
Response different ...
for different particle types ...
Inorganic Crystals
conduction band
Materials:
exciton
band
Mechanism:
Energy deposition by ionization
Energy transfer to impurities
Radiation of scintillation photons
scintillation
[luminescence]
Time constants:
Fast: recombination from activation centers [ns ... μs]
Slow: recombination due to trapping [ms ... s]
traps
excitations
impurities
[activation centers]
quenching
Sodium iodide (NaI)
Cesium iodide (CsI)
Barium fluoride (BaF2)
...
electron
hole
valence band
Energy bands in
impurity activated crystal
showing excitation, luminescence,
quenching and trapping
Inorganic Crystals
Crystal growth
Example CMS
Electromagnetic Calorimeter
PbW04
ingots
One of the last
CMS end-cap crystals
Light Output
Inorganic Crystals – Time Constants
Exponential decay of scintillation
can be resolved into two components ...
N = Ae
t/
f
+ Be
t/
s
⌧f : decay constant of fast component
⌧s : decay constant of slow component
Time
Scintillation Spectrum
for NaI and CsI
Intensity [a.u.]
Inorganic Crystals – Light Output
NaI(Tl)
CsI(Na)
CsI(Tl)
Wavelength [nm]
Strong
Temperature Dependence
[in contrast to organic scintillators]
Inorganic Crystals – Light Output
Spectral sensitivity
Inorganic Scintillators – Properties
Scintillator
material
Density
[g/cm3]
Refractive
Index
Wavelength [nm]
for max. emission
Decay time
constant [μs]
NaI
3.7
1.78
303
0.06
8⋅104 xxx
NaI(Tl)
3.7
1.85
410
0.25
4⋅104 xxx
CsI(Tl)
4.5
1.80
565
1.0
1.1⋅104 xxx
Bi4Ge3O12
7.1
2.15
480
0.30
2.8⋅103 xxx
CsF
4.1
1.48
390
0.003
2⋅103 xxx
LSO
7.4
1.82
420
0.04
1.4⋅104 xxx
PbWO4
8.3
1.82
420
0.006
2⋅102 xxx
LHe
0.1
1.02
390
0.01/1.6
2⋅102 xxx
LAr
1.4
1.29 *
150
0.005/0.86
4⋅104 xxx
LXe
3.1
1.60 *
150
0.003/0.02
4⋅104 xxx
Photons/MeV
*
at 170 nm
Inorganic Scintillators – Properties
Numerical examples:
NaI(Tl)
λmax = 410 nm; hν = 3 eV
photons/MeV = 40000
τ = 250 ns
PBWO4
λmax = 420 nm; hν = 3 eV
photons/MeV = 200
τ = 6 ns
Scintillator quality:
Light yield – εsc ≡ fraction of energy loss going into photons
e.g.
NaI(Tl) : 40000 photons; 3 eV/photon ➛ εsc = 4⋅104⋅3 eV/106 eV = 11.3%
PBWO4 :
200 photons; 3 eV/photon ➛ εsc = 2⋅102⋅3 eV/106 eV = 0.06%
[for 1 MeV particle]
Scintillators – Comparison
Inorganic Scintillators
Advantages
high light yield [typical; εsc ≈ 0.13]
high density [e.g. PBWO4: 8.3 g/cm3]
good energy resolution
Disadvantages
complicated crystal growth
large temperature dependence
Expensive
Organic Scintillators
Advantages
very fast
easily shaped
small temperature dependence
pulse shape discrimination possible
Disadvantages
lower light yield [typical; εsc ≈ 0.03]
radiation damage
Cheap
Scintillation in Liquid Nobel Gases
Decay time constants:
Materials:
Helium : τ1 = .02 μs, τ2 = 3 μs
Argon : τ1 ≤ .02 μs
Helium (He)
Liquid Argon (LAr)
Liquid Xenon (LXe)
...
Excitation
Excited
molecules
A
A*2
A*
A
De-excitation and
dissociation
A
Collision
[with other gas atoms]
Ionization
A*
+
A2
A*2
Ionized
molecules
Recombination
e–
UV
LAr : 130 nm
LKr : 150 nm
LXe : 175 nm
Plastic and Liquid Scintillators
In practice use ...
solution of organic scintillators
[solved in plastic or liquid]
+ large concentration of primary fluor
+ smaller concentration of secondary fluor
+ ...
Scintillator array
with light guides
Scintillator requirements:
Solvable in base material
High fluorescence yield
Absorption spectrum must overlap
with emission spectrum of base material
LSND experiment
Plastic and Liquid Scintillators
A
Primary fluorescent
- Good light yield ...
- Absorption spectrum
matched to excited
states in base
material ...
B
Energy deposit in base
material ➛ excitation
Solvent
S1A
S0A
C
Wave length
shifter
Primary Fluor
S1B
γA
Excitations
Secondary
fluorescent
Secondary
Fluor
S1C
γB
S0B
S0C
γC
Plastic and Liquid Scintillators
Some widely used solvents and solutes
POPOP
Polystyrene
...
...
p-Terphenyl
Wavelength Shifting
Principle:
Absorption of
primary scintillation light
Re-emission at
longer wavelength
Adapts light to spectral
sensitivity of photosensor
Requirement:
Good transparency
for emitted light
Schematics of
wavelength shifting principle
Scintillation Counters – Setup
Scintillator light to be
guided to photosensor
➛ Light guide
[Plexiglas; optical fibers]
Light transfer by
total internal reflection
[maybe combined with wavelength shifting]
Liouville's Theorem:
Complete light transfer
impossible as Δx Δθ = const.
[limits acceptance angle]
Use adiabatic light guide
like 'fish tail';
➛ appreciable energy loss
'fish tail'
Scintillation Counters – Setup
WS
fibre
Wavelength-shifting
fibre
Scintillator
Steel
Steel
Scintillator
Source
Source
tubes
tubes
2008 JINST 3 S
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Photomultiplier
Photomultiplier
ATLAS Tile Calorimeter
ounted in an external steel box, which has the cross-section
tains the external connections for power and other services
Finally, the calorimeter is equipped with three calibration
137 Cs radioactive source. These systems test the optical
nd are used to set the PMT gains to a uniformity of ±3%
Photon Detection
Purpose : Convert light into a detectable electronic signal
Principle : Use photo-electric effect to convert photons to
photo-electrons (p.e.)
Requirement :
High Photon Detection Efficiency (PDE) or
Quantum Efficiency; Q.E. = Np.e./Nphotons
Available devices [Examples]:
Photomultipliers [PMT]
Micro Channel Plates [MCP]
Photo Diodes [PD]
HybridPhoto Diodes [HPD]
Visible Light Photon Counters [VLPC]
Silicon Photomultipliers [SiPM]
Initially we used conductors, because it's easier to extract electrons; but now we use Semiconductors, because in a conductor material, even if it's a very thin layer
of material, the electrons loses all it's small energy, on the contrary that doesn't happen in a semiconductor. Semiconductors has a better quantum e"ciency, the
energy of the electrons is bigger than the one of the conductors. A photon passing through the semiconductor-> and electron is extracted, so now we have a hole
and an electron, but the energy of the electron can only be lost by creating a new couple hole-electron, not by recombination.
Photomultipliers
Principle:
Electron emission
from photo cathode
Secondary emission
from dynodes; dynode gain: 3-50 [f(E)]
Typical PMT Gain: > 106
[PMT can see single photons ...]
PMT
Collection
Photomultipliers – Photocathode
Bialkali: SbRbCs; SbK2Cs
γ-conversion
via photo effect ...
Photon
entrance window
photo
cathode
Electron
4-step process:
Electron generation via ionization
Propagation through cathode
Escape of electron into vacuum
Q.E. ≈ 10-30%
[need specifically developed alloys]
Photomultipliers – Dynode Chain
Dynodes
Electron
Anode
Voltage divider
UB
Multiplication process:
Electrons accelerated toward dynode
Further electrons produced ➛ avalanche
Secondary emission coefficient:
δ = #(e– produced)/#(e– incoming)
n = number of dynodes
Typical: δ = 2 – 10
n = 8 – 15
➛ G = δn = 106 – 108
Ub = di!erential potential between
cathode and anode
Gain fluctuation: δ = kUD; G = a0 (kUD)n
dG/G = n dUD/UD = n dUB/UB
Ud = di!erential potential between
tosubsequent dynodes
Photomultipliers – Dynode Chain
Optimization of
PMT gain
Anode isolation
Linearity
Transit time
B-field dependence
Venetian
blind
Box and
grid
Linear
focused
PM’s are in general
very sensitive to B-fields !
Even to earth field (30-60 μT).
μ-metal shielding required.
Circular
focused
Photomultipliers – Energy Resolution
Energy resolution influenced by:
Linearity of PMT: at high dynode current possibly saturation
by space charge effects; IA ∝ nγ for 3 orders of magnitude possible ...
light collection
efficiency
Photoelectron statistics: given by poisson statistics.
nne
ne
e
Pn (ne ) =
n!
p
n /hni = 1/ ne
dE
Photons
ne =
⇥
⇥ ⇥ Q.E.
dx
MeV
with ne given
by dE/dx ...
For NaI(Tl) and 10 MeV photon;
photons/MeV = 40000;
ne
η = 0.2; Q.E. =0.25
= 20000
n /hni = 0.7%
Secondary electron fluctuations:
Pn ( ) =
n
⇥n /hni = 1/
e
n!
p
with dynode gain δ;
and with N dynodes ...
✓
⇥n
hni
◆2
=
1
+ ... +
σn/<n> dominated by
first dynode stage ...
1
N
⇡
1
1
... important for
single photon detection
A particle to become a photon must lost around 100MeV:
n_{\gamma}= {(dE/dx)\over(100MeV)}
k*n_{\gamma}<n_{\gamma}
k*k'<1
k'(k*n_{\gamma})<k*n_{\gamma}
Scintillator
Light
Guide
PMT
Anode Signal
Quantum E!ect = N_{Photons}/N_{gamma}
The energy to produce a gamma is 100Mev
In principle we can say the find signal is proportional to the energy released in
the scintillator.
PHOTOCATHODE
For the photocathodeCONDUCTORS are not the best choice because the electrons have a low energy and so the do not get out of the material.
Quantum e!ect of conductors≈10^{-3} ≈0.2%
So we choose the SEMICONDUCTORS: the electrons goes to the valence bond and leaves an hole, the energy of the electron make him leaves the
material.
Quantum e!ect of semiconductors≈0.3≈30%
CuBe dynode
Photomultipliers – Energy Resolution
δ
δ
Philips photonic
'standard'
dynodes
For
detection of
single photons
GaP(Cs)
Negative
electron affinity (NEA)
Philips photonic
1 p.e.
Large δ !
... yields better
energy resolution
E [keV]
counts
counts
E [eV]
1 p.e.
2p.e.
CuBe dynode
Houtermanns
NIM 112 (1973) 121
NAE dynode
Philips photonic
pulse height
pulse height
Micro Channel Plate
"2D Photomultiplier"
Gain: 5⋅104
Fast signal [time spread ~ 50 ps]
B-Field tolerant [up to 0.1T]
But: limited life time/rate capability
Chapter 2 Light Detectors
ICFA
the device is covered with an anti-reflecting SIO2 lay
Silicon
Photomultipliers
Layout
Silicon Photomultiplier:SiPM
Geiger
Mode
tracks on
the
surface connect all pixels to the commo
Principle:
+
n
Pixelized photo diodes
• Pixelsinoperated
in Geiger mode
operated
Geiger Mode
(non-linear response)
Single pixel works as a binary device
Si* Resistor
Vbias
Al - conductor
Si02
+
Guard
ring n-
Photocurrent (log scale)
Features:
Granularity
Gain
Bias Voltage
Efficiency
:
:
:
:
-
EE,, V/cm
V/cm
1E5
Energy = #photons seen by
summing
over all pixels
no amplification
linear
amplification
6
1E6
10
4
1E4
10
1E3
2
1E2
10
1E1
1
1E0
non-linear
Geiger mode
Doping Structure of SiPM [1]
*
Resistor
2 Al - conductor
103Sipixels/mm
Figure 2.13: Left: Schematic view of the SiPM topology
Avalanche
region
material on the low resistive
substrate
serves as a drift reg
< 100 V
electron generated in this region
will subsequently drift i
a
b
layer where the electrical field is high enough for avalanch
ca. 30 %
Breakdown Voltage
electrical field in order to avoid unwanted avalanche break
1: (a) Silicon photomultiplier
microphotograph,
(b)
impurity levels are higher.
Right: Diagram of
the topol
electric
Works atFigure
room temperature!
E, V/cm
106
Reverse Bias Voltage
Insensitive
to magnetic
fields
tion
in epitaxy
layer.
4
2.3.1 Gain and Single Pixel Response
Alexander Tadday
24.05.07
Photo-detectors
Light amplifier
From light to electric charge
★ Principle: photo-electric effect to convert photons to photo-electrons (pe)
★ Input: weak signal (few photons)
★ Output: sizeable current (100uA~100 mA)
★ High photon detection efficiency (or Quantum Efficiency = Npe/Nγ)
Available Devices
★ Photomultipliers (PMT)
★ Microchannelplates (MCP)
★ Photodiodes (PD)
★ Hybrid PhotoDiods (HPD)
★ Silicon photomultiplier
Photomultiplier (PMT)
4 ) P r i m a r y p h o t o - e l e c t ro n s
emitted with a given probability
(QE) fby the photocathode
5) First focusing electrode:
collects and accelerates pe
emitted by the pc
9) Ultra High Vacuum (UHV): pe moves
in the vacuum (~10-6mb) in a glass vessel
8) HV supply to dynodes
1) Incoming light
7) Anode: collects
the charge
2) Transparent window
(glass or quartz)
3) Photocathode: emits pe when hit by photons
14
6) Dynodes: multiplying electrodes. Primary pe
are accelerated and multiplied to secondary
electrons by an external HV
Scintillation detectors
M.Battaglieri - INFN GE
PMT components
★ The window defines the light
frequency cut (glass, borosilicate,
UV-transparent, quartz (fused silica)
★Matched to the scintillation light
spectral emission and the
photocathode
Bialkali
★ The photocathode is a thin layer deposited
on the entrance window
★ Quantum Efficiency = Npe/Nγ ~ 5% - 50%
★ Different types of photocathodes
★ Bialkali (SbKCs): low ionizing potential, high
QE to visible light (blue)
★ Radiant Sensitivity: RS=Ioutput/Pinput
★QE= 124/λ(nm) RS (mA/W)
★ The PC is highly oxidisable requiring O2
partial pressure <10-8 mbar
15
Te-Cs
(Quartz)
Bialkali
(Quartz)
Bialkali
low noise
Cs - I
Scintillation detectors
M.Battaglieri - INFN GE
★ Primary PE are collected by the first dynode
★ Dynodes are kept at DV and covered by a bialkali layer with a Secondary
Emission Coefficient d>1 (2-5, depending on the incident electron energy)
★ HV (400-3000V) is distributed between dynodes by a resistive or capacitive
voltage divider
★PMT gain is defined as the ratio of cathode and anode currents
G = dn =(K DV)n
DG/G = n DV/V
• K = a constant depending on geometry and
collection
• DV = ΔV between dynodes (100-300V)
• n = number of dynodes
•G ~ 104 - 107
• If d=10, 1% variation on DV reflects in 10%
gain variation
• Electron multiplication is a stochastic process
• Poisson distribution fluctuations
Q = G Npe
(σQ /Q)2= 1/Npe
(σQ /Q)2= 1/(d-1)
• Fluctuations of secondary electrons
• Resolution is dominated by the first dynode stage (secondary statistics relevant for single photon detection)
16
Scintillation detectors
M.Battaglieri - INFN GE
Time resolution
★ Transit Time refers to the time to cross the tube (1 -10 ns)
★ Transit Time Spread: jitter of a single pe transit time. For Npe scales as TTS/√(Npe)
★ related to PMT size, HV, collection …
Linearity
★Relationship between incoming photons and anode charge
★ affected by: - current in the voltage divider; - spread in HV; - G drift …
Stability
★ PMT G as a function of time
★ affected by: - T variations; - high rate; - long shutdown
Magnetic fields
★ External fields affect PMT operations (even Hearth field!): time jitter, gain,
★ passive shielding (layers of ferromagnetic materials) up to 200 Gauss
17
Scintillation detectors
M.Battaglieri - INFN GE
Silicon photomultipliers (silicon PM or MPPC)
Photon-counting
★ Principle: pixelized photo-diode working in Geiger mode
★ Each pixels is a binary (on/off) device
★ Counts incident photons by summing the pixel
★Reverse voltage applied to a APD > Vbk produces a
discharge (Geiger mode)
★ Large output (detectable) for each incoming photon
★ A quenching resistor quickly stops the avalanche
18
Scintillation detectors
M.Battaglieri - INFN GE
Silicon Photomultipliers
HAMAMATSU
MPPC 400Pixels
One of the first SiPM
Pulsar, Moscow
Silicon Photomultipliers
CALICE
HCAL Prototype
Scintillation Counters – Applications
Time of flight (ToF) counters
Energy measurement (calorimeters)
Hodoscopes; fibre trackers
Trigger systems
ATLAS
Minimum Bias Trigger Scintillators
Particle track in
scintillating fibre hodoscope
Attenuation length
★ Scintillation light is lost in the scintillator for two reasons: lateral surface leak and reabsorbing
★ Sizeable scintillators (>1m) suffer by ‘light attenuation’
★ Attenuation length depends on surface machining and geometry
★ Data sheets report the bulk attenuation length: the real case need to be measured or simulated
Attenuation length
L(x) = L0
e(-x/l)
• L0 = light intensity at the origin
• l = attenuation length
Light intensity at distance x
L(x) = L0 e(-x/l)
l = (232±39) cm
EJ200 Mylar wrapping
Attenuation length
5
Scintillation detectors
M.Battaglieri - INFN GE
Birk’s law
★ Scintillator response depends on the energy and the ionizing particle (ionisation density)
★ Increasing the locally deposited energy, the light emission, per energy unit, decreases
★ E.g. in plastic, a low energy proton (higher ionisation) produces 1/3 of light an isoenergetic electron
★ Deviation from linearity is due to a saturation effect in molecular de-excitation
Attenuation length
A dE/dx
dL/dx = L0
1+ kB dE/dx
Light produced per length unity
• dE/dx: ionization
•L0 = light intensity at
low ionisation intensity
(electron)
• kB = Birk’s parameter
(measured)
electrons
6
protons
Scintillation detectors
M.Battaglieri - INFN GE
PULSE
SHAPE
DISCRIMINATION
Saldana, Stemen
2
Motivation
• In PROSPECT, we look at:
•
• Gamma-like prompt (positron)
and neutron-like delay events
(neutron capture).
• Our main backgrounds are
high-energy gammas
(dominant) and fast neutrons.
• Pulse Shape Discrimination
(PSD) is used on both
prompt and delay signals to
discern the type of event.
• Need to investigate what
level of PSD we need for our
scintillator.
• In lab we use gamma and
neutron sources to study
scintillator’s response.
• Neutron-like prompt (proton
recoil) and neutron-like delay
(neutron capture)
3
Saldana, Stemen
Pulse Shape Discrimination (PSD)
• Technique used to
discriminate between signals
of different types of radiation.
• E.g. gamma and neutron events.
• Organic scintillator:
– Fast (prompt fluorescence)
and slow (delayed
fluorescence) characterize a
pulse.
– Fraction of light in slow
component depends on nature
of incoming particle.
– Slow component depends on
𝑑𝐸
rate of energy loss 𝑑𝑥 . Greater
for particles with large
Image from Knoll, G. Radiation and Detection
Measurement. p. 227.
𝑑𝐸
.
𝑑𝑥
Particles detection with scintillator
detectors
- electrons
- gamma rays
-neutrons
- heavy ions
DETECTION <--- depends on the quantity of emitted light
Particle + Material -> Interaction mechanism -> Energy lost -> Quantity of emitted light
DIFFERENT KIND OF PARTICLES (Di!erent interaction mechanism) can need
di!erent materials to be detected and also
SAME PARTICLE
Detection or Energy measurement
CAN NEED DIFFERENT KIND OF DETECTORS
ELECTRONS
DETECTION: almost all kinds of scintillators are fine
ENERGY MEASUREMENT: problem: BACKSCATTERING
(e backscat./ e all) prop to Z
Z organic Scint. << Z inorganic Scint --> ORGANIC SCINT. more suited to detect e
BUT
if e- has very high energy -> dE/dx due to Bremsstralung and shower development
--> High Z scint. More suited ---> so inorganic scintillators
GAMMA RAYS
Interaction with matter mechanism:
1. Photoelectric interaction
2. Pair production
3. Compton Scattering
--> to be preferred materials where sigma 1. and 2. then sigma 3.
1. and 2. -> gamma interaction produces charged particle
3. -> gamma does not disappear
Inorganic scintillators -->because we try to avoid Compton scattering
Z
Photo
electric
Pair
compton
Er
HEAVY IONS
Large dE/dx --> large quenching e!ect --> "low" light emission (low scintillation
e"ciency)
1/10 in organic scintillators
1/2 in Inorganic Scintillators
--> Inorganic scintillators are preferred (NaI, ZnS, ...) giving also a better
proportionality SIGNAL/ENERGY
NEUTRONS
To be detected they have to interact in such a way to produce a detectable CHARGED
particle.
TYPICAL REACTIONS TO DETECT NEUTRONS
(n,p) for Fast neutrons
(n,gamma) and (n,alpha) for Termic neutrons
(n,p) reaction take advantage from material with high H%(percentage of Hydrogen)
-->ORGANIC SCINTILLATOR (if possible choose one with good PFD!)
(n, gamma) and (n, alpha) HIGH sigma with 6Li and 10B--> choose scintillators
containing 6Li and 10B
Organic Liquid scintillators can be loaded with those elements and they also have a
good PSD!
Very low Z material--> to absorb more photons as possible
We can require thata the value on the right is <= to 1
to have the beta threshold
Beta threshold is very important
if we consider p=m \beta \gamma c
so particles of di!erent masses
have di!erent threshold!
Another relation that gives us theta
cherenkov that is related to the number
of photons emitted
Beta threshold is the minumum beta of the
particle needed to have cherenkov light
Che
r
e
nkovRadi
at
i
on
Angle between Cherenkov photons and track of particle
→ velocity of particle
particle lpart = t β c
photons llight = t c/n
correct for recoil:
cos  c =
c
1
=
n c n 
cos  c =
1
ℏk
1

1− 2 
n  2p
n
p: momentum of particle, ℏk momentum of photon (k = 2 π/λ)
ℏk<<p → correction for recoil usually not needed
●
●
●
●
Threshold: Cherenkov emission only for β>1/n
βs=1/n emission forward direction θc = 0
maximum for β=1 , Cherenkov angle θc = arccos 1/n
→ Cherenkov radiation occurs only in media and for frequencies with n(β) >1
Threshold energy
 s=
Es
m0 c
=
2
1
=
2
1
 1− 1−1/ n
2
s
Measurement of γs allows mass determination if energy is known
Katharina Müller autumn 14
3
Cherenkov radiation is emitted since the particle polarizes atoms along its track.
If v>c/n this polarization is not symmetric and there is a non-vanishing dipole field ->
emission of radiation
Particle's Trajectory
Number of
photons very low
In the detector if the particle
continues its trajectory we see:
In the detector if the particle
stops its trajectory we see:
Phot
onyi
e
l
d
Di!erence between what is emitted and what can be detected
Intensity of the Cherenkov radiation:
# γ per unit length of particle path and per unit of wave length
depends on charge and velocity of particle
→ Photon yield Number of photons emitted
2
 2− 1
1
d
dN
2
2
2
=2   z ∫ 1− 2
 2 ≈ 2   z sin  c
= 490 sin 2  c [cm−1 ]
2
dx
21
n   

1
blue!
400 - 700 nm
2
−1
1150 sin  c [cm ] incl. UV 200-700nm
dN/dλ
Example: characteristic
glow from reactor
Katharina Müller autumn 14
6
First of the three categories of cherenkov detectors:
p=m \gamma\beta c
Type
sofChe
r
e
nkovde
t
e
kt
or
s
Cherenkov detectors are mainly used for particle ID
●
●
●
Threshold – Cherenkov detector
Only particles with β>βc emit Cherenkov light
simple construction: radiator and light detector (Photomultiplier)
DiPerential Cherenkov detector (DISC-Zähler)
Use Θ(β)
allows to determine Θ-interval
Ring-Imaging-Cherenkov-Detectors (RICH)
Measure Θ(β)
spherical mirror used to focus light onto photon detector
centre of ring: direction of particle
radius → Θc → velocity β
Katharina Müller autumn 14
8
Thr
e
s
hol
dChe
r
e
nkovCount
e
r
Allows separation of particles with same momenta but different masses
Assume separation of two particles p1=p2 m2>m1
Threshold: choose radiator such that β1>1/n and β2<1/n
1
 2 = , rsp.
n
require: particle 2 does not radiate:
2=

1
1−1/ n
2
2

2
n =
2
2
 2 −1
Diffraction index needs to be adjusted, stabilised with high accuracy!
Length of radiator: lighter particle emits 490 sin2Θc photons per cm
2
c
2
2
−1
particle 1: # photons:
N =490 2  m1 −m 2 [cm ]L q
p
L: length of radiator, q: quantum efficiency, depends on energy, thickness and type of material
Katharina Müller autumn 14
9
Thr
e
s
hol
dChe
r
e
nkovCount
e
r
Combination of several threshold Cherenkov counters
Best one for the pi
x
x
x
x
x
Aerogel
n=1.025
Neopentan
1.0017
x

K
p
Ar-Ne
1.000135
K-p-π Separation up to roughly 100 GeV in beam with xed momenta
Beta_pi > Beta_K > Beta_p
They have same momentum p
p=m\beta \gamma c
m_pi > m_K > m_p
n_pi > n_K > n_p
Katharina Müller autumn 14
10
Radi
at
or
s
transparent material: solids, liquids, gases
material
n-1
βc
θc
solid natrium
Lead sulte
Diamond
Zinc sulte
silver chloride
Flint glass
Lead crystal
Plexiglass
Water
Aerogel
Pentan
Air
He
3.22
2.91
1.42
1.37
1.07
0.92
0.67
0.48
0.33
0.025-0.075
1.7 10-3
2.9 10-4
3.3 10-5
0.24
0.26
0.41
0.42
0.48
0.52
0.60
0.66
0.75
0.93-0.98
0.9983
0.9997
0.999971
76.3
75.2
65.6
65.0
61.1
58.6
53.2
47.5
41.2
12.6-21.5
6.7
1.38
0.46
Photons/cm (max)
462
457
406
402
376
357
314
261
213
24-66
7
0.3
0.03
Si
l
i
c
aAe
r
oge
l
DiPraction index of gas radiators may be modied with pressure
(n-1) = (n0-1)p/p0
Katharina Müller autumn 14
11
Che
r
e
nkovCount
e
r
→ tune refraction index by setting pressure
Example: CO2- pressure for Cherenkov radiation vs p
radiation
Mazziotta, GLAST
(2005)
no radiation
Katharina Müller autumn 14
12
Di
#e
r
e
nt
i
alChe
r
e
nkovCount
e
r
s
Measure Cherenkov angle → direct measurement of β
→ select particles in velocity interval
Minimum: Cherenkov requirement
 min =
1
n
Maximum: total refraction
1
sin = ,
n
cos =
1
1
  max =
n
 n 2−1
quartz radiator
Example: diamond n=2.42 βmin= 0.413 βmax = 0.454
●
●
Used for particle id in beam with xed momentum
Particles need to be parallel to axis
velocity resolution up to Δβ/β= 10-5
Pion/K separation up to 100 GeV
very precise timing signal
Discovery of anti-proton in 1955 by Chamberlain, Segre et. al. at Berkeley.
Nobel Prize in 1959, Physical Review Letters , Nov. 1, 1955
Katharina Müller autumn 14
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Ri
ngI
magi
ngChe
r
e
nkovCount
e
r(
RI
CH)
project cone of Cherenkov light onto matrix of photon detectors
(Multiwire proportional chambers, photomultipliers, TPCs )
signals on matrix form a ring
centre: direction
radius: velocity
incoming particle
Matrix of photon detectors
measured photons
radiator with diffraction
index n
Geometrical focussing: radiator thickness small wrt. distance to photon detectors
Katharina Müller autumn 14
14
Ri
ngI
magi
ngChe
r
e
nkovCount
e
r(
RI
CH)
Spherical mirror (Radius Rs ) with centre at interaction vertex
Focal width Rs/2
● Cherenkov light is reYected onto photon detector
at radius RD
●
●
radiator between Rs and RD = Rs/2
●
measured radius rc depends on β
rc = f θc=
●
Rs
θ
2 c
cos θc =
1
→β=1/(n cos(2 r c / R s))
nβ
momentum known → particle ID
p=γ m0 β c →
●
p √ 1−β2
m=
cβ
Detector RD
Mirror Rs
r
c
Radiator
particle known → measure momentum
p=γ m0 β c →
Δp
Δγ
2 Δβ
=γ β ≃ γ
p
First used by DELPHI (LEP)
W. Adam et al Nucl. Instr. And Meth in Phys. Res A 343 (1994) 68
Katharina Müller autumn 14
15
De
t
e
c
t
i
onofChe
r
e
nkovl
i
ght
Energy of Cherenkov photons: eV → photoePect dominates,
→ strong Z and E dependence
PhotoePect: Photon is absorbed, transmits energy onto electron.
Photoemission threshold Wph of various materials
TMAE,CsI
Ultra
Violet
(UV)
Visible
Bialkali
Infra
Red
(IR)
GaAs
Multialkali
TEA
12.3
4.9
3.1
2.24
1.76
1.45 E [eV]
100
250
400
550
700
850 λ [nm]
Ideal photo cathode: absorbs all γ, emits all electrons
Katharina Müller autumn 14
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De
t
e
c
t
i
onofUVphot
ons
Admixture of organic vapour:
quantum efficiency vs wave length
TMAE high eZciency for small λ
BUT: radiation damage
Energy[eV]
9,0
8,5
0,6
8,0
7,5
7,0
6,5
6,0
0,6
transparency cutoff
of fused silica
Quantum efficiency
0,5
2
dN
1
d
2
=2


z
1−

Reminder: # Photons:
∫
dx
n 2   2 2

5,5
TMAE
TEA
0,4
0,4
0,3
0,3
0,2
0,2
0,1
0,1
0,0
0,0
140
150
160
170
180
190
200
210
220
Wavelength [nm]
important to detect photons at small λ
1
Katharina Müller autumn 14
0,5
20
230
De
t
e
c
t
i
onofChe
r
e
nkovl
i
ghtI
I
Photo cathodes: thin layer of metal or semi-conductor with low work function( Austrittsarbeit)
typical material, CSI: Threshold 6 eV =210 nm
●
high QE
●
stable in air
●
cathode should not charge up
eV photons
0.4
PC32 (@STAR)
PC33
PC34
PC35
PC37, PC39
PC38
CsI photocathode QE
0.35
0.3
0.25
Alice CSI cathode:
average quantum eZciency 15% (155-210 nm)
0.2
0.15
Production: stability, reproducibility diZcult
for a long time
today: reproducible quality
0.1
0.05
0
5.5
6
6.5
7
7.5
8
photon energy [eV]
Katharina Müller autumn 14
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De
t
e
c
t
i
onofChe
r
e
nkovl
i
ght
Position sensitive gas detectors (MWPC, TPC) or photomultiplier
De
l
phi
Admixture of TMAE
Sensitivity in UV region
Disadvantage: slow! long drift time μs
Ageing problems due to TMAE
Al
i
c
e
ALICE
MWPC: multiwire proportional chamber
with photocathode
fast signal < 100 ns
Katharina Müller autumn 14
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De
t
e
c
t
i
onofChe
r
e
nkovl
i
ght
:phot
omul
t
i
pl
i
e
r
For example: SuperKamiokande, Ice Cube
Medicine:
Silicon photomultipliers (SiPM): avalanche photodiode array on common Si 20-100 μm.
Katharina Müller autumn 14
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