Transcript Document

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Interaction of gammas
Interaction of Radiation with Matter
Gamma Rays
W. Udo Schröder, 2004
g-Induced Processes
2
g-rays (photons) come from electromagnetic transitions between
different energy states of a system  important structural information
Detection principles
are based on:
•Photo-electric absorption
•Compton scattering
•Pair production
• g-induced reactions
1. Photo-electric absorption
(Photo-effect)
Interaction of gammas
Ekin    En ; En  binding energy
En
Z  

 Rhc 
n
2
2
Moseley ' s Law
Rhc  13.6 eV Rydberg constant
screening constants
 K  3,  L  5, different subshells
W. Udo Schröder, 2004
ħw
photon is completely
absorbed by e-, which
is kicked out of atom
Electronic
vacancies are filled
by low-energy
“Auger” transitions
of electrons from
higher orbits
Absorption Coefficient m/r (cm2/g)
Interaction of gammas
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Photo-Absorption Coefficient
“Mass absorption” is
measured per density r
 m/r (cm2/g)
Pt
“Cross section” is
measured per atom
  (cm2/atom)
Wave Length l (Å)
Probabilities for independent
processes are additive:
mPE = mPE(K)+mPE(L)+…
W. Udo Schröder, 2004
Absorption coefficient
 m (1/cm)
Absorption of light is
quantal resonance
phenomenon: Strongest
when photon energy
coincides with transition
energy (at K,L,… “edges”)
 PE ( Eg , Z )  Z 5  Eg7 4 low Eg
 PE ( Eg , Z )  Z 5  Eg1 2 high Eg
Templates and Nomograms
Overlay
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Data Graph
Eg
Interaction of gammas
absorber
thickness
Line up left reference lines
W. Udo Schröder, 2004
Photon Scattering (Compton Effect)
Relativistic E 2  ( pc) 2  (m0c 2 ) 2 photons : m0  mg  0
 Eg   g  pg c
pe  pg  pg 
pe2 c 2  Eg2  Eg2  2 Eg Eg   cos 
f
Energy balance :
Eg  me c  Eg  
Interaction of gammas
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l   l  lC  1  cos 
" Compton wave length lC "
2
lC 
 2.426 pm
me c
W. Udo Schröder, 2004
pe c   pg  pg  c
2

5
l
Momentum balance :
Eg  
 pec 
Eg
2
  me c

2 2
1   Eg me c 2  1  cos  
me c 2  0.511MeV
2
Compton Angular Distributions
Intensity as function of 
Klein-Nishina-Formula ( =Eg/mec2)
Forward scattering for high-energy
photons, symmetric about 900 for
low-energy
d C r  Eg  
 

d
2  Eg 
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2
0
2
 Eg Eg 

2 

 sin  

 Eg  Eg

“Classical e- radius” r0 = 2.818 fm.
Alternative formulation:
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

d C r
1
 1  cos   
 
d
2
1   1  cos   
Interaction of gammas
2
0
2


 2 1  cos  
 1 

2
 1  cos   1   1  cos    
Total scattering probability: C  Z (number of e-)
W. Udo Schröder, 2004
Compton Electron Spectrum
Actually, not photons but
recoil-electrons are detected
Compton Energy Spectrum
Recoil-espectrum
0.6
Cross Section (b)
0.5
Nexp ( E)
true
0.4
ddE( E)
0.3
Ekin  Eg  Eg  
1   Eg mec 2  1  cos 
Eg  Eg mec 2  1  cos 
1   Eg me c 2  1  cos 
Minimum photon energy :   1800
Eg
Eg  
1  2 Eg mec 2
0.2
finite
resolution
0.1
Eg  
Eg
Scattered recoil  electron energy :
Compton Edge
0.644 0.7
Scattered  photon energy
Maximum electron energy (Compton Edge) :
0
0
0
0
0.2
0.4
0.6
E
Energy (MeV)
0.8
1
1
Ekin  ECE  Eg

2 Eg me c 2

1  2  Eg me c 2 
Scanning Spectral Data
A spectrum (e.g., probability
vs. energy) is generated by
scanning physical data, sorting
events according to the values
of a variable of interest
(energy). The values are
determined by scanning an
actual (true) data set and
grouping events according to
their (energy) values.
Interaction of gammas
Cross Section (b)
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scanner
window
True and Apparent Compton Spectrum
counts
0.01
W. Udo Schröder, 2004
0.25
True
Spectrum
energy
def.
Constructed
Spectrum
0.49
0.72
Energy (MeV)
0.96
1.2
Finite resolution of variable
 apparent spectrum
deviates from true
spectrum.
High-Resolution Scan
Interaction of gammas
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The number of true events (top)
within a well-defined scanning
acceptance bin (or within view)
is plotted below at the nominal
bin position.
W. Udo Schröder, 2004
A detector with high resolution
provides an apparent spectrum
very similar to true spectrum,
with minimum distortions
Low-Resolution Scan
Interaction of gammas
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As in previous case, but now the
scan is “fuzzy”, the bin is not
well defined. True events far
away from the center of the
scanning bin are seen with some
finite probability. The total
number of true events (top)
within a large range the finite
scanning acceptance bin is
plotted below at the nominal bin
position.
The apparent spectrum has
events in unphysical regions,
e.g., above the maximum true
energy.
W. Udo Schröder, 2004
A detector with low resolution
provides an apparent spectrum
very different from true
spectrum, with maximum
distortions at sharp structures.
Pair Creation by High-Energy g-rays
g-rays
A
{e+, e-,e-} triplet and one doublet in
H bubble chamber
e-
Magnetic field provides
momentum/charge analysis
Event A) g-ray (photon) hits atomic
electron and produces {e-,e+} pair
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e+
Interaction of gammas
B
Event B) one photon converts into a
{e-,e+} pair
ee+
e
Magnetic field
W. Udo Schröder, 2004
In each case, the photon leaves no
trace in the bubble chamber, before
a first interaction with a charged
particle (electron or nucleus).
Dipping into the Fermi Sea: Pair Production
Dirac theory of electrons and holes:
World of normal particles has positive
energies, E ≥ +mc2 > 0
Energy
normally empty
e-particle
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+[mec2+Ekin
+mec2
]
Fermi Sea is normally filled with
particles of negative energy, E ≤-mc2 < 0
0
Eg
-mec2
Interaction of gammas
-[mec2+Ekin]
W. Udo Schröder, 2004
e-hole
normally filled
Fermi Sea
Electromagnetic interactions can lift a
particle from the Fermi Sea across the
energy gap DE=2 mc2 into the normal
world  particle-antiparticle pair
Holes in Fermi Sea: Antiparticles
Minimum energy needed for pair
production (for electron/positron)
Eg  EThreshold  2mec2  1.022MeV
recoil
nucleus
e-
g
The Nucleus as Collision Partner
Eg  EThreshold  2me c 2


Actually converted : Eg  2mec 2  Ekin
 Ekin
 ....
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e+
Pb
Excess momentum requires presence of
additional charged body, the nucleus
5.81028 cm2
Interaction of gammas
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 P ( Z , Eg )
d PP
2 1  e
Z


2 
dEkin
137  me c  Eg  2me c 2
2
Eg  2 me c 2
P slowly varying
1barn = 10-24cm2
W. Udo Schröder, 2004
Increase with Eg because interaction
sufficient at larger distance from nucleus
Eventual saturation because of screening
of charge at larger distances
g-Induced Nuclear Reactions
Real photons or “virtual” elm field
quanta of high energies can induce
reactions in a nucleus:
secondary
radiation
n
14
g
p
incoming
Interaction of gammas
nucleus
Nucleus can emit directly a high energy secondary particle or, usually
sequentially, several low-energy
g
particles or g-rays.
g-induced nuclear reactions
are most important for high
energies, Eg  (5 - 8)MeV
W. Udo Schröder, 2004
(g, g’ ), (g, n), (g, p), (g, ), (g, f)
Can heat nucleus with (one) g-ray to
boiling point, nucleus thermalizes,
then “evaporates” particles and grays.
Efficiencies of g-Induced Processes
Different processes are dominant at
different g energies:
Photo absorption at low Eg
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Pair production at high Eg
Compton scattering at intermediate Eg.
Interaction of gammas
Z dependence important: Ge(Z=32) has
higher efficiency for all processes
than Si(Z=14). Take high-Z for large
photo-absorption coefficient
Response of detector depends on
•detector material
•detector shape
•Eg
W. Udo Schröder, 2004
Escape Geometries
High-energy g-ray leading to e+/epair production, with e- stopped in
the detector.
g
g e+ is also stopped in the detector
511 and annihilates with another ekeV producing 2 g-rays of Eg = 511 keV
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Ge
crystal
Interaction of gammas
e-
g
511
keV
e+
each. If both g-rays are absorbed
 full energy Eg is absorbed by
detector  event is in FE peak.
If one g-ray escapes detector 
event is in SE peak at FE-511 keV
If both of them escape  event is
in detector  DE peak at FE-1.022
MeV.
Relative probabilities depend on
detector size!
W. Udo Schröder, 2004
Shapes of Low-Energy g Spectra
The energy Eg of an incoming photon
can be completely converted into
charged particles which are all
absorbed by the detector, 
measured energy spectrum shows
only the full-energy peak (FE, red)
Example: photo effect with
absorption of struck e-
measured intensity
Interaction of gammas
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Photons/g-rays are measured only via their interactions with charged
particles, mainly with the electrons of the detector material. The
energies of these e- are measured by a detector.
measured energy
The incoming photon may only
scatter off an atomic e- and then
leave the detector  Compton-eenergy spectrum (CE, dark blue)
An incoming g-ray may come from back-scattering off materials
outside the detector  backscatter bump (BSc)
W. Udo Schröder, 2004
Shapes of High-Energy g Spectra
The energy spectra of high-energy g-rays have all of the features of
low-energy g-ray spectra
FE
High-Eg can lead to e+/epair production,
e-: stopped in the detector
measured intensity
Interaction of gammas
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e+: annihilates with another
e- producing 2 g-rays, each
with Eg = 511 keV.
One of them can escape
detector  single escape
peak (SE) at FE-511 keV
Both of them can escape
detector  double escape
peak (DE) at FE-1.022 MeV
measured energy (MeV)
e+/e- annihilation in detector or its vicinity produces 511keV g-rays
W. Udo Schröder, 2004
Interaction of gammas
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Quiz
• Try to identify the various features of the g
spectrum shown next (well, it is really the spectrum
of electrons hit or created by the incoming or
secondary photons), as measured with a highly
efficient detector and a radio-active AZ source in a
Pb housing.
• The g spectrum is the result of a decay in cascade of
the radio-active daughter isotope A(Z-1) with the
photons g1 and g2 emitted (practically) together
• Start looking for the full-energy peaks for g1, g2,…;
then identify Compton edges, single- and doubleescape peaks, followed by other spectral features to
be expected.
• The individual answers are given in sequence on the
following slides.
W. Udo Schröder, 2004
Interaction of gammas
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Spectrum of g Rays from Nuclear Decay
W. Udo Schröder, 2004
Spectrum of g Rays from Nuclear Decay
Interaction of gammas
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g1
W. Udo Schröder, 2004
Spectrum of g Rays from Nuclear Decay
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
Spectrum of g Rays from Nuclear Decay
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
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g1
g2
Interaction of gammas
511
keV
W. Udo Schröder, 2004
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
BSc
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
511
keV
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Pb X-rays
BSc
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
511
keV
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Pb X-rays
BSc
Interaction of gammas
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g1
W. Udo Schröder, 2004
g2
511
keV
DE
g2
SE
g2
CE
g2
g1+g
2
Photo
Multiplier
Reducing Background with Anti-Compton “Shields”
g
BGO
Scintillator
Interaction of gammas
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g
W. Udo Schröder, 2004
e-
e+
Ge
crystal
High-energy g-rays
produce e+/e- pairs in
the primary Ge detector.
All e+ and e- are stopped
in the Ge detector.
e+ finds an e- and
annihilates with it,
producing 2 back-to-back
511-keV photons.
Escaping 511-keV photons
are detected by
surrounding annular
scintillation detector.
Escape events are
“tagged” and can be
rejected.
Compton Suppression Technique
Interaction of gammas
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The figure
shows a
comparison
between the
“raw” 60Co gray spectrum
(in pink) and
one (blue)
where Compton
contributions
have been
removed.
The disturbing Compton background has been reduced by app. a factor
8 by eliminating all events, where a photon has been detected by the
BGO scintillation shield counter in coincidence with a g-ray in the
corresponding inner Ge detector.
W. Udo Schröder, 2004
Interaction of gammas
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g-Ray/Photon Detectors
There is a variety of detectors for nuclear radiation,
including g-rays. A special presentation is dedicated
to the main detector principles.
The next image shows a section of one of the currently
modern g detector arrays, the “Gamma-Sphere.”
The sphere surrounds the reaction chamber on all sides
and leaves only small holes for the beam and target
mechanisms.
Each element of the array consists of two different
detector types, a high-resolution Ge-solid-state
detector encapsulated in a low-resolution BGO
scintillation counter detecting Compton-scattered
photons escaping from the Ge detectors
W. Udo Schröder, 2004
Modern g Detectors: “Gammasphere”
Interaction of gammas
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Compton
Suppression
W. Udo Schröder, 2004
Interaction of gammas
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e
n
d
W. Udo Schröder, 2004