Transcript Slide 1

Nuclear Interactions of Neutrons
No electric charge  no direct atomic ionization  only
collisions and reactions with nuclei  10-6 x weaker
absorption than charged particles
W. Udo Schröder, 2003
2
Processes depend on available n energy En:
En ~ 1/40 eV
(= kBT) Slow diffusion, capture by nuclei
En <
10 MeV
Elastic scattering, capture, nucl. excitation
En >
10 MeV
Elastic+inel. scattering, various nuclear
reactions, secondary charged reaction products
Characteristic secondary nuclear radiation/products:
1. g-rays (n, g)
2. charged particles (n,p), (n, a),…
3. neutrons (n,n’), (n,2n’),…
4. fission fragments (n,f)
Rad Inter Neutrons
Neutron Cross Sections
W. Udo Schröder, 2003
3
1b=10-24cm2=100fm2
Rad Inter Neutrons
Neutron Mean Free Path
35
Mean Free Path of
Neutrons in Water
Neutron Mean Free Path (cm)
4
30
W. Udo Schröder, 2003
N  x   N 0  e x

25
1


1

mfp
: atomic density
: cross section
20
 = average path
length in medium
between 2 collisions
15
10
5
0

0
Rad Inter Neutrons
2
4
6
8
10
Neutron Energy (MeV)
12
14
 FWHM  2.35  
5
Interaction of Gamma Rays
Interaction of Radiation with Matter
Gamma Rays
W. Udo Schröder, 2007
g-Induced Processes
6
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
Interaction of Gamma Rays
Ekin    En ; En  binding energy
En
Z  

 Rhc 
2
2
Moseley ' s Law
n
Rhc  13.6 eV Rydberg constant
screening constants
 K  3,  L  5, different subshells
W. Udo Schröder, 2007
1. Photo-electric absorption
(Photo-effect)
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 / (cm2/g)
Interaction of Gamma Rays
7
Photo-Absorption Coefficient
Absorption coefficient
  (1/cm)
“Mass absorption” is
measured per density 
Pt
 / (cm2/g)
“Cross section” is
measured per atom
  (cm2/atom)
Wave Length  (Å)
Probabilities for
independent processes
are additive:
PE = PE(K)+PE(L)+…
W. Udo Schröder, 2007
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
Photon Scattering (Compton Effect)
Relativistic E 2  ( pc) 2  (m0c 2 ) 2 photons : m0  mg  0
 Eg   g  pg c

8

f
Momentum balance :
pe  pg  pg 
pe2 c 2  Eg2  Eg2  2 Eg Eg   cos 
Energy balance :
Eg  me c  Eg  
Interaction of Gamma Rays
2
     C  1  cos  
" Compton wave length C "
2
C 
 2.426 pm
me c
W. Udo Schröder, 2007
pe c   pg  pg  c
2
Eg  
 pec 
Eg
2
  mec

2 2
1   Eg mec 2  1  cos  
me c 2  0.511MeV
2
Compton Angular Distributions
Intensity as function of 
Klein-Nishina-Formula (a =Eg/mec2)
Forward scattering for high-energy
photons, symmetric about 900 for
low-energy
d C r  Eg  
 

d
2  Eg 
9
2
0
2


 Eg Eg 
2 

 sin  

 Eg  Eg



Interaction of Gamma Rays
“Classical e- radius” r0 = 2.818 fm.
Alternative formulation:
3


d C r
1


 1  cos  
 
d
2

1  a 1  cos   

2
0
2
2


a
1

cos





 1 

2
1

cos

1

a
1

cos








 

Total scattering probability: C  Z (number of e-)
W. Udo Schröder, 2007
Compton Electron Spectrum
Actually, not photons but
recoil-electrons are detected
Compton Energy Sp ectrum
Recoil-espectrum
0.6
Cross Section (b)
0.5
Nexp( E)
true
0.4
ddE( E)
0.3
0.2
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 me c 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 mec 2 
Pair Creation by High-Energy g-rays
g-rays
{e+, e-,e-} triplet and one doublet in
H bubble chamber
A
Magnetic field provides
momentum/charge analysis
e-
e+
11
Event A) g-ray (photon) hits atomic
electron and produces {e-,e+} pair
Event B) one photon converts into a
{e-,e+} pair
Interaction of Gamma Rays
B
e-
e+
e
Magnetic field
W. Udo Schröder, 2007
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
Energy
normally empty
e-particle
12
+[mec2+Ekin
+mec2
]
0
-mec2
Interaction of Gamma Rays
-[mec2+Ekin]
e-hole
normally filled
Fermi Sea
Dirac theory of electrons and holes:
World of normal particles has positive
energies, E ≥ +mc2 > 0
Fermi Sea is normally filled with
particles of negative energy, E ≤-mc2 < 0
Electromagnetic interactions can lift a
Eg 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
W. Udo Schröder, 2007
The Nucleus as Collision Partner
recoil
nucleus
e-
g
Eg  EThreshold  2me c 2


Actually converted : Eg  2me c 2  Ekin
 Ekin
 ....
Interaction of Gamma Rays
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e+
Pb
Excess momentum requires presence of
additional charged body, the nucleus
2
 P( Z , Eg )
d PP
2 1  e
Z


2 
dEkin
137  me c  Eg  2me c 2
2
5.81028 cm2
Eg  2 me c 2
P slowly varying
1barn = 10-24cm2
W. Udo Schröder, 2007
Increase with Eg because interaction
sufficient at larger distance from nucleus
Eventual saturation because of screening
of charge at larger distances
Efficiencies of g-Induced Processes
Different processes are dominant at
different g energies:
Photo absorption at low Eg
Interaction of Gamma Rays
14
Pair production at high Eg
Compton scattering at intermediate Eg.
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, 2007
Detection for Incomplete Absorption
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
15
Ge
crystal
Interaction of Gamma Rays
e-
g
511
keV
W. Udo Schröder, 2007
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!
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 Gamma Rays
16
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, 2007
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
High-Eg can lead to e+/epair production,
FE
e-: stopped in the detector
measured intensity
Interaction of Gamma Rays
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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, 2007
Interaction of Gamma Rays
18
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, 2007
Interaction of Gamma Rays
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Spectrum of g Rays from Nuclear Decay
W. Udo Schröder, 2007
Spectrum of g Rays from Nuclear Decay
Interaction of Gamma Rays
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g1
W. Udo Schröder, 2007
Spectrum of g Rays from Nuclear Decay
Interaction of Gamma Rays
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g1
W. Udo Schröder, 2007
g2
Spectrum of g Rays from Nuclear Decay
Interaction of Gamma Rays
22
g1
W. Udo Schröder, 2007
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Interaction of Gamma Rays
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g1
W. Udo Schröder, 2007
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Interaction of Gamma Rays
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g1
W. Udo Schröder, 2007
g2
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
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g1
g2
Interaction of Gamma Rays
511
keV
W. Udo Schröder, 2007
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
BSc
Interaction of Gamma Rays
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g1
W. Udo Schröder, 2007
g2
511
keV
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Pb X-rays
BSc
Interaction of Gamma Rays
27
g1
W. Udo Schröder, 2007
g2
511
keV
DE
g2
SE
g2
CE
g2
Spectrum of g Rays from Nuclear Decay
Pb X-rays
BSc
Interaction of Gamma Rays
28
g1
W. Udo Schröder, 2007
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 Gamma Rays
29
g
W. Udo Schröder, 2007
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 Gamma Rays
30
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, 2007
Interaction of Gamma Rays
31
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, 2007
Modern g Detectors: “Gammasphere”
Interaction of Gamma Rays
32
Compton
Suppression
W. Udo Schröder, 2007
Interaction of Gamma Rays
33
e
n
d
W. Udo Schröder, 2007