Детектори - II
4-ти курс УФЕЧ
1
2
3
Спирачно лъчение
(bremsstrahlung)
A charged particle of mass M and charge q=Z1e is deflected by a nucleus of charge Ze
which is partially ‘shielded’ by the electrons. During this deflection the charge is
‘accelerated’ and it therefore radiated  Bremsstrahlung.
Z2 electrons, q=-e0
M, q=Z1 e0
4
Спирачно лъчение
Bremsstrahlung is the emission of
photons by a charged particle
accelerated in the Coulomb field of
a nucleus.
The radiative process is characterised by:
Impact parameter :
b
(non-relativistic!)
Peak electric field prop. to e/b2
Characteristic frequency
c  1/t  v/2b
d B Z 2

  B  0.58  Z 2 (mb)
d

We now have an additional photon.
5
6
Critical Energy
For the muon, the second
lightest particle after the
electron, the critical
energy is at 400GeV.
The EM Bremsstrahlung is
therefore relevant mainly
for electrons at energies
provided by present
accelerators.
(Caveat: muons at LHC!)
Electron Momentum
5
50
500
MeV/c
Critical Energy: If dE/dx (Ionization) = dE/dx (Bremsstrahlung)
Muon in Copper:
Electron in Copper:
p  400GeV
p  20MeV
7
W. Riegler/CERN
7
8
Раждане на двойка е+е(Pair production)
Creation of an electron/positron
pair in the field of an atom.
As the two diagrams are more or
less identical, we would expect
the cross sections to be similar.
 pair
7
  B  0.45mb  Z 2
9
9
Раждане на двойка е+еFor E>>mec2=0.5MeV :  = 9/7X0
Average distance a high energy
photon has to travel before it
converts into an e+ e- pair is
equal to 9/7 of the distance that a
high energy electron has to
travel before reducing it’s energy
from E0 to E0*Exp(-1) by photon
radiation.
10
Electromagnetic Calorimeter
Rossi B. Approximation to
Shower Development.
1) Electrons loses a constant
amount of energy (e) for each
radiation length, X0
2) Radiation and Pair production
at all energies are described
by the asymptotic formulae.
e±

11
How a shower looks like
B
Electron shower in lead. 7500 gauss in cloud chamber. CALTECH
Electron shower in lead. Cloud chamber. W.B. Fretter, UCLA
12
F.E. Taylor et al., IEEE NS 27(1980)30
EM showers: longitudinal profile
tmax = 1.4 ln(E0/Ec)
Shower profile for
electrons of energy:
10, 100, 200, 300… GeV
Ntot  E0/Ec
Longitudinal containment:
t95% = tmax + 0.08Z + 9.6
X0
Ec  1/Z
•shower max
•shower tail
Shower parametrization
dE
 t  et
dt
13
From M. Diemoz, Torino 3-02-05
The shower maximum
Shower maximum
t=t(E,e)
and there must be a
difference between
e and 
E
t  X 0   ln    1.1
e 
E
t  X 0   ln    0.3
e 
for e
for 
14
U. Amaldi, Physica Scripta 23(1981)409
EM showers: transverse profile
Transverse shower profile
• Multiple scattering make electrons move away from shower axis
• Photons with energies in the region of minimal absorption can travel
far away from shower axis
Molière radius sets transverse shower size, it gives the
average lateral deflection of critical energy electrons
after traversing 1X0
21MeV
RM 
X0
EC
X0 A
RM 
 Z  1
EC
Z
75% E0 within 1RM, 95% within 2RM, 99% within 3.5RM
15
From M. Diemoz, Torino 3-02-05
Why is
Space Resolution
an issue in calorimeters ?
Consider a 0 - decay
 min
 
 
m0
2
E 0
For a calorimeter with
limited granularity,
this would give:
 min  2 RM
 
E
0
max
 
Rm  0

RM
Set R=2 m
16
20 GeV
 in copper
(simulation)
charged particles only
all particles
17
J.P. Wellisch
18
19
Nuclear Interaction Length i
is the average distance a high-energy hadron has to travel inside a medium
before a nuclear interaction occurs.
z
i
Probability not to have interacted after a path z
Pe
i  A
0.29
20
21
Hadronic Showers
20 GeV
 in copper (simulation)
J.P. Wellisch
Hadronic Showers (, n, p, ...)
Propagation :
inelastic hadron interactions
 multi particle production
Nuclear disintegration
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Монте Карло симулация на
адронен каскад
38
39