BehteBloch, Landau

1
Behte-Bloch, Landau Brehmstrahlung The
interaction of photons with matter Photo-effect
Compton scattering Pair production April 8, 2008
2
Bethe- Bloch
Z
C1/v2 . ln C2 v3?2
dE E-E
dX
3
dE/dx for pions as computed with Bethe-Bloch
equation
dE/dx divided by density r (approximately material
independent)
slope due to 1/v2
high bg dE/dx independent of bg due
to density effect, "Fermi plateau"
relativistic rise due to ln g

• about proportional to ne,
• as ne na Z NA r Z / A, -gt ne NA r / 2

From PDG, Summer 2002
4
Counts
Landau distribution fluctuation of disposed energy
Most probable
Average
Pulse heigth
From F.Sauli, CERN Yellow report 77-09
5
Not a simple example of a Landau curve ! Part of
electrons stop in detector, rest either
loses part of their energy when passing
through the detector or backscatter out of the
detector or create escaping bremsstrahlung
Number of events
Monte Carlo simulation
6
Photon (invisible)
Kink in trajectory
Curvature smaller after kink due to lower
momentum
e
Walter Heitler
Hans Albrecht Bethe
http//teachers.web.cern.ch/teachers/archiv/HST200
2/Bubblech/mbitu/electromag-events1.htm
7
Photons can not be radiated in vacuum
Ef,pf
Before Ei2 - pi2 me2 After
e
g
e
Ei,pi
not possible
Feynman diagram
Photons can be radiated in the field of an object
with charge
Ef,pf
e
Very heavy pointlike spinless object with charge
Z2 (atomic nucleus)
Classically electric field accelerates
electron. Quantum-mechanically virtual
photon exchange decreases pf, so that Ef2 - pf2
me2 is satisfied
g
e
Ei,pi
g
e
This diagram also contributes
e
Z2
8
ESRF European Synchrotron Radiation Facility,
Grenoble, France
300 m circumference booster synchrotron, 6 GeV
16 m linac, 200 MeV
9
Electrons with energies in the MeV range can also
produce photons up to the MeV range by
Bremsstrahlung. This is much more likely for a
high Z-material and should be taken into account
when shielding a beta source. A combination of
a light material (usually acryl or perspex) near
the source and a surrounding layer of lead for
absorbing photons from the source and/or
produced in the light material should be used.
The thickness of the light material is typically
of the order of a few - 10 cm, see range curves
on next slide.
10
(main contributions)
dominates below Eg few 100 keV
dominates around Eg 1 MeV
dominates above Eg 2 MeV (minimum energy 2
me 1.02 MeV)
11
From PDG, Summer 2002
12
NB see discussion on slides 43-45
13
Kleinknecht, p.20
Photoelectric effect
A photon causes emission of a "photoelectron' from
an atom, the energy of this electron is equal to
the energy of the photon minus the binding energy
of the electron. -gt The electron has a
well-defined energy, directly related to the
energy of the photon, therefore energy
measurement of the electron (by determining the
energy deposition when stopping in matter)
provides the possibility to measure the energy of
the photon
Albert Einstein Nobel Prize 1921 "for his
services to Theoretical Physics, and especially
for his discovery of the law of the
photoelectric effect"
14
The cross-section for the photo-electric effect
has maxima at photon energies equal to binding
energies of electrons and decreases in between
for increasing photon energy
"K-edge" or "K-absorption edge"
with and for eKltelt1
Rayleigh scattering, atom neither ionized nor
excited
Pair production, nuc nuclear field, e electron
field
For e gtgt 1
Note the dependence of s on the 5th power of Z
re e2 / mec2 2.82 x10-13 cm
15
From PDG, Summer 2002
16

• The photo-electric effect is exploited in photo
  cathodes to convert visible light
• into electrons. Important applications are
• Photomultipliers
• Night vision goggles
• Electron injectors for accelerators (using a
  laser as light source)

17
Kleinknecht, p.21
Compton effect, scattering of photon from an
atomic electron, results in lower energy photon,
the energy lost is transferred to the electron
Incoming and outgoing photon not seen
Arthur Holly Compton
Nobel prize 1927
http//teachers.web.cern.ch/teachers/archiv/HST200
2/Bubblech/mbitu/electromag-events1.htm
18
k
k
k
T
k
k
cos
p
cos



q

f
0
k0
0
q
k
sin
p
sin
q

f
0
f
2
2
2
p
cos
k
k
cos
(
)
f

-
q
0
p, T
2
2
2
2
p
sin
k
sin
f

q
2
2
2
p
k
2
k
k
cos
k

-
q

0
0
2
2
k
k
T

-
p
T
2
mT


0
2
2
(
)
k
1
cos
1
cos
(
)
-
q
e
-
q
0
T
m


(
)
(
)
m
k
1
cos
1
1
cos

-
q

e
-
q
0
NB m me,
mk
k
0
0
k
k
T

-


0
m
k
1
cos
1
cos
q
1
q
(
)
(
)

-

e
-
0
Minimum value for k ? p,
19
The emission angle of the electron can be
expressed in terms of e and ?
k
k
cos
k
k
cos
-
q
-
q
0
0
cos
f


p
2
2
k
2
k
k
cos
k
-
q

0
0
k
cos
k
1
1
cos
q

e
(
)
-
q
(
)
0
0
k
k
cos
k
-
q

-

0
0
1
1
cos
(
)
1
1
cos
(
)

e
-
q

e
-
q
2
(1-cos ?)
k
2
2
(
)


e
e

2
2
0
k
2
k
k
cos
k
-
q


0
0
2
1
1
cos



e
-
q
(
)
1
cos
(
)
-
q
cos
1
(
)
f


e
2
2
(
)
1
cos
(
)

e
e

-
q
20
For high energies and scattering under 180
degrees
i.e. backscattered photons tend to have the same
energy, over a considerable angular range, which
can give rise to a "backscatter" peak at 256
keV in gamma spectra
21
Application Compton effect COMPTEL instrument in
CGRO satellite flown from 1991 - 2000
http//cossc.gsfc.nasa.gov/cgro/comptel.html
22
The Imaging Compton Telescope (COMPTEL) utilizes
the Compton Effect and two layers of gamma-ray
detectors to reconstruct an image of a gamma-ray
source in the energy range 1 to 30 million
electron volts (MeV). Gamma rays from active
galaxies, radioactive supernova remnants, and
diffuse gamma rays from giant molecular clouds
can be studied with this instrument. COMPTEL's
upper layer of detectors are filled with a liquid
scintillator which scatters an incoming gamma-ray
photon according to the Compton Effect. This
photon is then absorbed by NaI crystals in the
lower detectors. The instrument records the time,
location, and energy of the events in each layer
of detectors which makes it possible to determine
the direction and energy of the original
gamma-ray photon and reconstruct an image and
energy spectrum of the source.
Text from http//cossc.gsfc.nasa.gov/cgro/comptel
.html
23
Scintillator
Photomultiplier
NaI
Photopeak
ComptonRidge
24
Pair creation
Positron
Bremsstrahlung produces photon
Electron
25
Pair creation
http//teachers.web.cern.ch/teachers/archiv/HST200
2/Bubblech/omegaminus.html
26
Pairs can not be created in vacuum
E,p
E-,p-
Before Eg2 - pg2 0 After
-gt not possible
and
g
Pairs can be radiated in the field of an object
with charge
E,p
E-,p-
Very heavy pointlike spinless object with charge
Z2 (atomic nucleus)
Virtual photon exchange makes pair creation
possible, if Eg gt 2me (or gt 4me in the field of
an electron)
g
This diagram also contributes
Z2
27
Probability P that a photon interaction will
produce a ee- pair
From PDG, Summer 2002