Radiation Detection and Counting Statistics

1
Radiation Detection and Counting Statistics

• Please Read Chapters 3 (all 3 parts), 8, and 26
  in Doyle

2
Types of Radiation

• Charged Particle Radiation
• Electrons
• b particles
• Heavy Charged Particles
• a particles
• Fission Products
• Particle Accelerators
• Uncharged Radiation
• Electromagnetic Radiation
• g-rays
• x-rays
• Neutrons
• Fission, Fusion reactions
• Photoneutrons

Can be easily stopped/shielded!
More difficult to shield against!
3
Penetration Distances for Different Forms of
Radiation
as
bs
gs
ns
Paper
Plastic (few cm)
Lead (few in)
Concrete (few feet)
4
Why is Radiation Detection Difficult?

• Cant see it
• Cant smell it
• Cant hear it
• Cant feel it
• Cant taste it
• We take advantage of the fact that radiation
  produces ionized pairs to try to create an
  electrical signal

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Ideal Properties for Detection of Radioactivity
6
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

7
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

8
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

9
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

10
Ionization Chambers

• Two electric plates surrounded by a metal case
• Electric Field (EV/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
11
Proportional Counters

• Wire suspended in a tube
• Can obtain much higher electric field
• E ? 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

12
Examples of Proportional Counters
13
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!
14
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.
15
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
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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)

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Organic Scintillators Come in Many Forms
18
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)

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Inorganic Scintillators
20
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 ltlt 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 lt 100 cm3 some even less than 1 cm3
• Efficiency issues for lower Z materials

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NaI Scintillator
Ge Detector
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(No Transcript)
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Ideal Detector for Detection of Radiation
Excellent table on Page 61 shows numerous
different technologies used in safeguards
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Counting Statistics
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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

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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
P(x) is the predicted Probability Distribution
Function
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Example of the Binomial Distribution
Winners 3,4,5, or 6
P 4/6 or 2/3 10 rolls of the die n10
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Results of the Binomial Distribution
p 2/3 n 10
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Some Properties of the Binomial Distribution
It is normalized
Mean (average) value
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Standard Deviation
Predicted variance
Standard Deviation
s is a typical value for
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For the Binomial Distribution
where n number of trials and p success
probability
Predicted Variance
Standard Deviation
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For our Previous Example
p 2/3 n 10
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The Poisson Distribution
Provided p ltlt 1
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For the Poisson Distribution
Predicted Mean
Predicted Variance
Standard Deviation
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Example of the Application of Poisson Statistics
Is your birthday today?
Example what is the probability that 4 people
out of 1000 have a birthday today?
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Discrete Poisson Distribution
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Gaussian (Normal) Distribution
p ltlt 1
Binomial
Poisson
Poisson
Gaussian
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Example of Gaussian Statistics
What is the predicted distribution in the number
of people with birthdays today out of a group of
10,000?
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Distribution Gaussian Distribution
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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
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Summary of Statistical Models
For the Poisson and Gaussian Distributions
Predicted Variance
Standard Deviation
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CAUTION!!
Does not apply directly to

1. Counting Rates
2. Sums or Differences of counts
3. Averages of independent counts
4. Any Derived Quantity

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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
sx, sy, sz,
Derive the standard deviation of any calculated
quantity
u(x, y, z, )
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Sums or Differences of Counts
u x y or u x - y
Recall
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Example of Difference of Counts
total x 2612 background y
1295 net u 1317
Therefore, net counts 1317 62.5
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Multiplication or Division by a Constant
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Example of Division by a Constant
Calculation of a counting rate
x 11,367 counts t 300 s
? rate r 37.89 0.36 s-1
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Multiplication or Division of Counts
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Example of Division of Counts
Source 1 N1 36,102 (no BG) Source 2 N2
21,977 (no BG)
R N1/N2 36102/21977 1.643
? R 1.643 0.014
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Average Value of Independent Counts
Sum S x1 x2 x3 xN
Average
Single measurement
Improvement Factor
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For a single measurement based on a single count
Fractional error
x 100 1000 10,000
Fractional Error 10 3.16 1
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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.
• Lets look at an example of testing the limits of
  detection

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Limits of Detection
Two basic cases No Real Activity Present Real
Activity Present
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Limits of Detection No Source
Goal Minimize the number of false positives
(i.e., dont want to holdup many containers that
do not contain anything interesting)
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 (1.645s or 90 on distribution), then
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Limits of Detection Source Present
Goal Minimize the number of false negatives
(i.e., dont 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. Lets assume an acceptable 5
false negative rate.
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.
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Limits of Detection Source Present
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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

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Neutron DetectionNeutron Coincidence Counting
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Neutron Energy Classification
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Slow Neutron Detection
Need exoenergetic (positive Q) reactions to
provide energetic reaction products
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Useful Reactions in Slow Neutron Detection
10B (n, a) 7Li 6Li (n, a) 3H 3He (n, p) 3H (n,
fission)
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The 10B(n,a) Reaction
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10B (n, a) 7Li
Conservation of energy Eli Ea Q 2.31
MeV Conservation of momentum
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Other Reactions
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Detectors Based on the Boron Reaction

1. The BF3 proportional tube
2. Boron-lined proportional tube
3. Boron-loaded scintillator

66
The BF3 Tube

• Typical BF3 pressure lt 1 atm
• Typical HV 2000-3000 V
• Usual 10B enrichment of 96

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BF3 Pulse Height Spectrum
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Boron-Lined Proportional Tube

• Conventional proportional gas
• Detection efficiency limited by boron thickness

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Boron-Lined Proportional Tube Pulse Height
Spectrum
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Fast Neutron Detection and Spectroscopy

• Counters based on neutron moderation
• Detectors based on fast neutron-based reactions
• Detectors utilizing fast neutron scattering

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Moderated Neutron Detectors
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Moderating Sphere
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Moderating Sphere
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Neutron Rem Counter
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Long Counter
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Long Counter Sensitivity
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Application of the 3He(n,p) reaction the 3He
Proportional Tube
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3He Proportional Counter
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Detectors that Utilize Fast Neutron Scattering

• Proton recoil scintillator
• High (10 50) detection efficiency, complex
  response function, gamma rejection by pulse shape
  discrimination
• Gas recoil proportional tube
• Low (.01 - .1) detection efficiency, can be
  simpler response function, gamma rejection by
  amplitude
• Proton recoil telescope
• Very low ( .001) detection efficiency, usable
  only in beam geometry, simple peak response
  function
• Capture-gated spectrometer
• Modest (few ) detection efficiency, simple peak
  response function

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Proton Recoil Scintillators
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Recoil Proton Spectrum Distortions
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Recoil Proton Detector Efficiency
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Proton Recoil Telescope
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Proton Recoil Telescope Response Function
Ep Encos2 ?
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Capture-Gated Proton Recoil Neutron Spectrometer
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Capture-Gated Spectrometer Timing Behavior
Accept first pulse for analysis if followed by
second pulse within gate period
87
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.)

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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

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Neutron Distribution from Pu Fission
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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

91
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
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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
• 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

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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
  mass-spectroscopy or gamma-ray spectroscopy, and
  is then used to calculate the quantity

94
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

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NCC Counters
96
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

97
NCC Parameters to Consider

1. Spontaneous fission rate
2. Induced fission
3. (a,n) reaction rate
4. Energy spectrum of (a,n) neutrons
5. Spatial variation of multiplication
6. Spatial variation of detection efficiency
7. Energy spectrum effects on efficiency
8. Neutron capture in the sample
9. Neutron die-away time in the detector

Clearly, there can be more unknowns than can be
determined in conventional NCC
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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

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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

100
Design of NMC

• 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

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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

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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

103
Examples

• In-Plant NMC measurement system

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Examples

• 30-gallon drum measurement system

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Examples

• High efficiency neutron counter