Radiation Detection and
Counting Statistics
Please Read: Chapters 3 (all 3 parts),
8, and 26 in Doyle
Types of Radiation
• Charged Particle Radiation
– Electrons
• b particles
– Heavy Charged Particles
• a particles
• Fission Products
• Particle Accelerators
Can be easily
stopped/shielded!
• Uncharged Radiation
– Electromagnetic Radiation
• g-rays
• x-rays
– Neutrons
• Fission, Fusion reactions
• Photoneutrons
More difficult to
shield against!
Penetration Distances for Different
Forms of Radiation
a’s
b’s
g’s
n’s
Paper
Plastic
(few cm)
Lead
(few in)
Concrete
(few feet)
Why is Radiation Detection
Difficult?
•
•
•
•
•
Can’t see it
Can’t smell it
Can’t hear it
Can’t feel it
Can’t taste it
• We take advantage of the fact that radiation
produces ionized pairs to try to create an electrical
signal
Ideal Properties for Detection of
Radioactivity
Radiation
Ideal Detector Properties
a
Very thin/no window or
ability to put source inside
detector
Same as above, can be low or
high density, gas, liquid, or
solid
High density, high atomic
number materials
Low atomic number materials,
preferably hydrogenous
b
g
neutrons
How a Radiation Detector Works
• The radiation we are interested in detecting all
interact with materials by ionizing atoms
• While it is difficult (sometime impossible) to
directly detect radiation, it is relatively easy to
detect (measure) the ionization of atoms in the
detector material.
– Measure the amount of charge created in a detector
• electron-ion pairs, electron-hole pairs
– Use ionization products to cause a secondary reaction
• use free, energized electrons to produce light photons
– Scintillators
– We can measure or detect these interactions in many
different ways to get a multitude of information
General Detector Properties
• Characteristics of an “ideal” radiation detector
– High probability that radiation will interact with the detector
material
– Large amount of charge created in the interaction process
• average energy required for creation of ionization pair (W)
– Charge must be separated an collected by electrodes
• Opposite charges attract, “recombination” must be avoided
– Initial Generated charge in detector (Q) is very small (e.g.,
10-13C)
• Signal in detector must be amplified
– Internal Amplification (multiplication in detector)
– External Amplification (electronics)
• Want to maximize V
Q
V
C
Types of Radiation Detectors
• Gas Detectors
– Ionization Chambers
– Proportional Counters
– Geiger-Mueller Tubes (Geiger Counters)
• Scintillation Detectors
– Inorganic Scintillators
– Organic Scintillators
• Semiconductor Detectors
– Silicon
– High Purity Germanium
Gas Detectors
• Most common form of radiation detector
– Relatively simple construction
• Suspended wire or electrode plates in a container
• Can be made in very large volumes (m3)
– Mainly used to detect b-particles and neutrons
• Ease of use
– Mainly used for counting purposes only
• High value for W (20-40 eV / ion pair)
• Can give you some energy information
• Inert fill gases (Ar, Xe, He)
• Low efficiency of detection
– Can increase pressure to increase efficiency
– g-rays are virtually invisible
Ionization Chambers
• Two electric plates
surrounded by a metal case
• Electric Field (E=V/D) is
applied across electrodes
• Electric Field is low
– only original ion pairs
created by radiation are
collected
– Signal is very small
• Can get some energy
information
– Resolution is poor due to
statistics, electronic noise,
and microphonics
Good for detecting heavy charged
particles, betas
Proportional Counters
• Wire suspended in a tube
– Can obtain much higher
electric field
– E a 1/r
• Near wire, E is high
• Electrons are energized
to the point that they can
ionize other atoms
– Detector signal is much
larger than ion chamber
• Can still measure energy
– Same resolution limits as
ion chamber
• Used to detect alphas,
betas, and neutrons
Examples of Proportional Counters
Geiger Counters
• Apply a very large voltage
across the detector
– Generates a significantly
higher electric field than
proportional counters
– Multiplication near the
anode wire occurs
• Geiger Discharge
• Quench Gas
• Generated Signal is
independent of the energy
deposited in the detector
• Primarily Beta detection
• Most common form of
detector
No energy information! Only
used to count / measure the
amount of radiation. Signal is
independent of type of
radiation as well!
Examples of Geiger Counters
Geiger counters generally come in compact, hand carried
instruments. They can be easily operated with battery
power and are usually calibrated to give you radiation
dose measurements in rad/hr or rem/hr.
Scintillator Detectors
• Voltage is not applied to these types of detectors
• Radiation interactions result in the creation of
light photons
– Goal is to measure the amount of light created
– Light created is proportion to radiation energy
• To measure energy, need to convert light to
electrical signal
– Photomultiplier tube
– Photodiode
• Two general types
– Organic
– Inorganic
} light  electrons
Organic Scintillators
• Light is generated by fluorescence of molecules
• Organic - low atomic numbers, relatively low
density
– Low detection efficiency for gamma-rays
• Low light yield (1000 photons/MeV) - poor signal
– Light response different for different types of radiation
• Light is created quickly
– Can be used in situations where speed (ns) is necessary
• Can be used in both solid and liquid form
– Liquid form for low energy, low activity beta
monitoring, neutrino detection
– Very large volumes (m3)
Organic Scintillators Come in Many Forms
Inorganic Scintillators
• Generally, high atomic number and high density
materials
– NaI, CsI, BiGeO, Lithium glasses, ZnS
• Light generated by electron transitions within the
crystalline structure of the detector
– Cannot be used in liquid form!
• High light yield (~60,000 photons / MeV)
– light yield in inorganics is slow (ms)
• Commonly used for gamma-ray spectroscopy
– W ~ 20 eV (resolution 5% for 1 MeV g-ray)
– Neutron detection possible with some
• Can be made in very large volumes (100s of cm3)
Inorganic Scintillators
Solid State (Semiconductor) Detectors
• Radiation interactions yield electron-hole pairs
– analogous to ion pairs in gas detectors
• Very low W-value (1-5 eV)
– High resolution gamma-ray spectroscopy
• Energy resolution << 1% for 1 MeV gamma-rays
• Some types must be cooled using cryogenics
– Band structure is such that electrons can be excited at
thermal temperatures
• Variety of materials
– Si, Ge, CdZnTe, HgI2, TlBr
• Sizes < 100 cm3 [some even less than 1 cm3]
– Efficiency issues for lower Z materials
NaI Scintillator
Ge Detector
Ideal Detector for Detection of Radiation
Radiation
Ideal Detector
a
Thin Semiconductor Detectors
Proportional Counters
Organic Scintillators
Geiger Counters
Proportional Counters
Inorganic Scintillators
Thick Semiconductor Detectors
Plastic Scintillators
Proportional Counters (He, BF3)
Lithium Glass Scintillators
b
g
neutrons
Excellent table on Page 61 shows numerous different technologies used in
safeguards
Counting Statistics
Three Specific Models:
1. Binomial Distribution – generally applicable to all
constant-p processes. Cumbersome for large
samples
2. Poisson Distribution – simplification to the
Binomial Distribution if the success probability “p”
is small.
3. Gaussian (Normal) Distribution – a further
simplification permitted if the expected mean
number of successes is large
The Binomial Distribution
n = number of trials
p = probability of success for each trial
We can then predict the probability of counting exactly
“x” successes:
n!
nx
x
Px  
p 1  p 
n  x ! x!
P(x) is the predicted
“Probability Distribution Function”
Example of the Binomial Distribution
“Winners”:
3,4,5, or 6
P = 4/6 or 2/3
10 rolls of the die: n=10
Results of the Binomial Distribution
p = 2/3
n =10
x  pn
2
6
3
Some Properties of the
Binomial Distribution
n
It is normalized:
 Px   1
x 0
Mean (average) value
n
x   x  Px 
x 0
x  pn
Standard Deviation
“Predicted variance”
n


2
2   x  x  Px 
x 0
“Standard Deviation”
  var iance

 is a “typical” value for x  x

For the Binomial Distribution:
n!
nx
Px  
p x 1  p 
n  x ! x!
where n = number of trials and p = success probability
Predicted Variance:
n


2
2   x  x  Px 
x 0
Standard Deviation:
 np 1  p   x 1  p 
  x 1  p 
For our Previous Example
p = 2/3
n = 10
x  np  6 2
3
20 1
  x 1  p  
  2.22
3 3
2
  2  2.22  1.49
The Poisson Distribution
Provided p << 1
x

pn  e  pn
Px  
x!
pn  x

x e
Px  
x
x!
x
For the Poisson Distribution
n
 Px   1
x 0
n
Predicted Mean:
x   x  Px 
x 0
x  pn
Predicted Variance:
n

2   x  x  Px 
x 0
 pn  x
Standard Deviation:

2
 x
Example of the Application
of Poisson Statistics
“Is your birthday today?”
p
1
365
x
x ex
Px  
x!
x  pn  2.74
Example: what is the probability that 4 people out of 1000
have a birthday today?

2.74  e 2.74
P4  
4
4  3 2
 0.152
Discrete Poisson Distribution
Gaussian (Normal) Distribution
p << 1
Binomial
Poisson
x l arg e
Poisson
Px  
1
2x
x  pn
e
2

x x 

2x
Gaussian
n
 Px   1
x 0
2  x
 x
Example of Gaussian Statistics
What is the predicted distribution in the number of people
with birthdays today out of a group of 10,000?
p
1
365
n  10000
Px  
1
e
2  27.4
  x  5.23
x  27.4

x  27.4 2

54.8
Distribution Gaussian Distribution
The Universal Gaussian Curve
to
f(to)
0
0
0.674
0.500
1.00
0.683
1.64
0.900
1.96
0.950
2.58
0.990
Summary of Statistical Models
For the Poisson and Gaussian Distributions:
Predicted Variance:
2  x
Standard Deviation:
 x
CAUTION!!
We may apply   x only if x
represents a counted number of
radiation events
Does not apply directly to:
1. Counting Rates
2. Sums or Differences of counts
3. Averages of independent counts
4. Any Derived Quantity
The “Error Propagation Formula”
Given: directly measured counts
(or other independent variables)
x, y, z, …
for which the associated standard
deviations are known to be
x, y, z, …
Derive: the standard deviation of any
calculated quantity
u(x, y, z, …)
2
 u 
 u 
2u    2x    2y  
 x 
 y 
2
Sums or Differences of Counts
u=x+y
or u = x - y
2
 u 
 u 
2u    2x    2y  
 x 
 y 
2
Recall:
u
1
x
u
1
y
u
1
x
u
 1
y
2u  2x  2y
u  2x  2y  x  y
Example of Difference of Counts
total = x = 2612
background = y = 1295
net = u = 1317
 u  2612  1295
 u  3907  62.5
Therefore, net counts = 1317 ± 62.5
Multiplication or Division by a
Constant
Example of Division by a Constant
Calculation of a counting rate
r
x = 11,367 counts
x
t
t = 300 s
11367
r
 37.89 / s
300 s
r 
x
11367

 0.36 / s
t
300 s
 rate r = 37.89 ± 0.36 s-1
Multiplication or Division of Counts
Example of Division of Counts
Source 1:
Source 2:
N1 = 36,102 (no BG)
N2 = 21,977 (no BG)
R = N1/N2 = 36102/21977 = 1.643
2
2
2

N1 N 2
 R    N1    N 2 







 2

 
2



N1 N 2
 R   N1   N 2 
 R 
3

  8.56  10
 R 
 R 
5

  7.32  10
 R 
2
 
 R   R   R  0.014
 R 
 R = 1.643 ± 0.014
Average Value of Independent Counts
Sum:  = x1 + x2 + x3 + … + xN
  2x1  2x 2    2x N  x1  x 2    x N
  
x 
Average:




N
N
Single measurement:
“Improvement Factor”:
Nx

N
x
x
N
x  x
1
1

N
N

N
For a single measurement based
on a single count:
Fractional error:
x
x
1


x
x
x
x
100
1000
10,000
Fractional
Error
10%
3.16%
1%
Limits of Detection
• In many cases within non-proliferation, you
are required to measure sources that have a
small signal with respect to background
sources of radiation
• Thus, we need to assess the minimum
detectable amount of a source that can be
reliably measured.
• Let’s look at an example of testing the limits
of detection
Limits of Detection
Two basic cases:
No Real Activity Present
Real Activity Present
NS  N T  N B
N s  Counts from source
N T  Measured Counts
N B  Counts from background
2N s  2N T  2N B
Limits of Detection – No Source
Goal: Minimize the number of false positives (i.e., don’t want to holdup many
containers that do not contain anything interesting)
2Ns  2N T  2N B
2N T  2N B
2Ns  22N B
 Ns  2 N B  2 N B if only fluctuatio ns from counting statistics

Want to set critical counting level (LC) high enough such that the probability
that a measurement Ns that exceeds Lc is acceptably small. Assuming
Gaussian distribution, we are only concerned with positive deviations from
the mean. If we were to accept a 5% false positive rate (1.645σ or 90% on
distribution), then
LC  1.645 NS  2.326 N B
Limits of Detection – Source Present
Goal: Minimize the number of false negatives (i.e., don’t want to let many
containers that contain radioactive materials get through). Let ND be the
minimum net value of NS that meets this criterion. We can then determine our
lower critical set point. Let’s assume an acceptable 5% false negative rate.
N D  LC  1.645 N D
But , N D  N B , we can use the approximat ion
 N D  2 N B
N D  LC  2.326 N B
N D  4.653 N B
Assumes the width of the distribution of the source + background is approximately
the same as that of the background only. In reality, these widths are not the same.
Limits of Detection – Source Present
ND  2N B  N D
ND
 4.653 N B

ND 
  2 N B 1 
 2 N B 1 

4N B
 4N B 

 N D  2 N B  1.645
N D  4.653 N B  2.706 (Currie Equation )
ND
a  min imum det ectable activity 
fT
f  radiation yield per decay
  absolute det ection efficiency
T  measuremen t time




Two Interpretations of Limits of
Detectability
• LC = lower limit that is set to ensure a 5%
false-positive rate
• ND = minimum number of counts needed from
a source to ensure a false-negative rate no
larger than 5%, when the system is operated
with a critical level (or trigger point) LC that
ensures a false positive rate no greater than 5%
Neutron Detection
Neutron Coincidence Counting
Neutron Energy Classification
Slow Neutron Detection
Need exoenergetic (positive Q) reactions to provide
energetic reaction products
Useful Reactions in Slow Neutron
Detection
10B
(n, a) 7Li
6Li
(n, a) 3H
3He
(n, p) 3H
(n, fission)
The 10B(n,a) Reaction
Q MeV 
7

Li  a
10
B  n  7 *
 Li  a
2.792
2.310
[10B (n, a) 7Li*]
Conservation of energy:
Eli + Ea = Q = 2.31 MeV
Conservation of momentum:
m Li v Li  m a v a
2 m Li E Li  2 m a E a
E Li  0.84 MeV
E a  1.47 MeV
Other Reactions
Q MeV 
6
Li  n He  a
3
He  n3 H  p
X n, fission 
3
4.78
0.765
~ 200
Detectors Based on the Boron Reaction
1. The BF3 proportional tube
2. Boron-lined proportional tube
3. Boron-loaded scintillator
The BF3 Tube
•
•
•
Typical BF3 pressure < 1 atm
Typical HV: 2000-3000 V
Usual 10B enrichment of 96%
BF3 – Pulse Height Spectrum
Boron-Lined Proportional Tube
• Conventional proportional gas
• Detection efficiency limited by boron thickness
Boron-Lined Proportional Tube –
Pulse Height Spectrum
Fast Neutron Detection and
Spectroscopy
• Counters based on neutron moderation
• Detectors based on fast neutron-based
reactions
• Detectors utilizing fast neutron scattering
Moderated Neutron Detectors
Moderating Sphere
Moderating Sphere
Neutron “Rem – Counter”
Long Counter
Long Counter Sensitivity
Application of the 3He(n,p) reaction –
the 3He Proportional Tube
3He
Proportional Counter
Detectors that Utilize Fast Neutron
Scattering
1. Proton recoil scintillator
High (10 – 50%) detection efficiency, complex response
function, gamma rejection by pulse shape discrimination
2. Gas recoil proportional tube
Low (.01 - .1%) detection efficiency, can be simpler response
function, gamma rejection by amplitude
3. Proton recoil telescope
Very low (~ .001%) detection efficiency, usable only in beam
geometry, simple peak response function
4. Capture-gated spectrometer
Modest (few %) detection efficiency, simple peak response
function
Proton Recoil Scintillators
Recoil Proton Spectrum Distortions
Recoil Proton Detector Efficiency
Proton Recoil Telescope
Proton Recoil Telescope Response
Function
Ep = Encos2 θ
Capture-Gated Proton Recoil Neutron
Spectrometer
Capture-Gated Spectrometer:
Timing Behavior
Accept first pulse for analysis if followed by
second pulse within gate period
Capture-Gated Spectrometer:
Response Function
• Only events ending in capture deposit the full neutron
energy
• Energy resolution limited by nonlinearity of light output
with energy (Two 0.5 MeV protons total yield less than
one 1 MeV proton.)
Neutron Coincidence Counting
• Technique involving the simultaneous measurement
of neutrons emitted from a fission source (in
“coincidence” with each neutron)
• Used to determine mass of plutonium in unknown
samples
– Most widely used non-destructive analysis technique for Pu
assay, and can be applied to a variety of sample types (e.g.,
solids, pellets, powders, etc.)
– Requires knowledge of isotopic ratios, which can be
determined by other techniques
– Also used in U assay
Neutron Distribution from Pu
Fission
Neutron Coincidence Counting
• Makes use of the fact that plutonium isotopes
with even mass number (238, 240, 242) have a
high neutron emission rate from spontaneous
fission
– Spontaneous fission neutrons are emitted at the
same time (time correlated), unlike other neutrons
(a,n), which are randomly distributed in time
– Count rate of time correlated neutrons is then a
complex function of Pu mass
Fission Emission Rates for Pu isotopes
Isotope
Spontaneous Neutron
Emission Rate
(neutrons/sec-g)
Pu-238
2.59 x 103
Pu-239
2.18 x 10-2
Pu-240
1.02 x 103
Pu-241
5 x 10-2
Pu-242
1.72 x 103
In reactor fuel, Pu-240 signal dominates over Pu-238 and Pu-242 due to
abundance
Neutron Coincidence Counting
• In neutron coincidence counting, the primary quantity
determined is the effective amount of Pu-240, which
represents a weighted sum of the three even numbered
isotopes
m240eff  a  m238  m240  c  m242
• Coefficients for contributions from Pu-238 and Pu-242
are determined by other means, such as knowledge of
burnup of reactor fuel. Without additional information,
calculation will have errors but will give a good
estimate of Pu mass due to relative abundance of the
three isotopes. Generally, a ≈2.52, c ≈ 1.68
Neutron Coincidence Counting
• In order to determine the total amount of Pu, mPu,
the isotopic mass fractions (R) must be known.
These can be easily determined through massspectroscopy or gamma-ray spectroscopy, and is
then used to calculate the quantity
240
Pu eff  aR 238  R 240  cR 242
m Pu 
m 240eff
240
Pu eff
NCC Technique
• Utilize He-3 detectors, which can moderate and detect
spontaneous fission neutrons
• He-3 detectors usually embedded in neutron moderating
material to further slow down neutrons
– Increases detection efficiency
• Most common measurement is the simple (2-neutron)
coincidence rate, referred to as doubles
– If other materials present in the material contribute to neutron signal, or
impact neutron multiplication, other effects may become significant,
producing errors
– Generally carried out on relatively pure or well characterized materials,
such as Pu-oxides, MOX fuel pins and assemblies
NCC Counters
NCC Sources of Uncertainty
• Counting statistics (random)
– Can be a significant issue since efficiency can be
low
• Calibration parameters and uncertainties
associated with reference materials
(systematic)
• Correction for multiplication effects, detector
dead time, other neutron emission (systematic)
• Nuclear data
NCC Parameters to Consider
1.
2.
3.
4.
5.
6.
7.
8.
9.
Spontaneous fission rate
Induced fission
(a,n) reaction rate
Energy spectrum of (a,n) neutrons
Spatial variation of multiplication
Spatial variation of detection efficiency
Energy spectrum effects on efficiency
Neutron capture in the sample
Neutron die-away time in the detector
Clearly, there can be more unknowns than can be determined in conventional NCC
NCC Parameters
• We want to determine 1,2,3
• 4 and 5 can be determined with proper use of
modeling and simulation
• 6 and 7 can be determined through proper
calibration
• 8 and 9 are usually unknown, but in general,
are of minor consequence
• Traditional NCC can end up indeterminate –
only 2 equations, but three unknowns
Neutron Multiplicity Measurements
• In neutron multiplicity counting (NMC), one utilizes
triple coincidence rates (in addition to single and
double counting rates) to provide a third
measurement such that all parameters can be
determined
• Thus, we are solving three equations with three
unknowns – solution is self contained and complete
• One significant advantage of NMC is that there is no
need for careful calibration with Pu standards
– Also, can measure samples where there may be significant
uncertainties in composition
Design of NMC
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Maximize detection efficiency
Minimize signal processing
time
Minimize detector die-away
time to decrease accidental
coincidences
Minimize geometry effects to
efficiency
Minimize spectral effects on
efficiency
Advantages of NMC
• Greater accuracy in Pu mass determination
• Self-multiplication and (a,n) rates are directly
determined
• Calibration does not necessarily require
representative standards
• Measurement time on the order of a few thousand
seconds, shorter than the 10,000s typical of NCC
• Higher efficiency NMC systems can provide even
shorter measurement times with improved accuracy
Disadvantages of NMC
• Cost
• More floor space required
• Some other techniques can provide shorter
measurement times
• Some biases can remain if there is a high
degree of uncertainty in measured samples
• Running out of He-3
Examples
• In-Plant NMC measurement system
Examples
• 30-gallon drum measurement system
Examples
• High efficiency neutron counter