Nuclear material accountancy

1. Passive Non-Destructive Assay
Gamma-Spectrometry
Comparison of Approach to Quantification Methods

2. Approach Based on
Attenuation Correction
Factor

3. Assay Procedure
TCR = total corrected rate
RR = raw rate of data acquisition
CF(EL) = correction factor due to
electronic
CF(AT) = correction factor due to
self attenuation of sample
Electronic
K = calibration constant
M = mass of the assayed isotope
Electronic
CF(EL)=0
K is determined by use of appropriate physical
standard(s) and includes the effects of detector
efficiency, subtended solid angles, and gamma-ray
emission rates.
• Compute the total corrected rate, which is
proportional to the mass of the isotope
being assayed.
• Determine the constant of proportionality,
the calibration constant
The procedure:
• Measure the raw data acquisition rate
• Determine the correction for electronic losses
• Determine the correction for gamma-ray
self-attenuation

4. Raw Data Acquisition Rate
n1
n n2
Count
rate
Channel
1. Region of Interest
(ROI)
2. Function Fitting
a, b, c 🡪 real arbitrary constant
a defines highest peak
b defines center location of highest peak
c is standard deviation that controls bell width

5. Correction for Deadtime & Pileup
1. Purely electronic method 🡪 fast timing circuitry
2. Pulser Injection
3. Reference source method
Electronic
Pulser
Electronic
source
FEIR = full energy interaction rate in the
detector

6. Determination of Sample
Attenuation Coefficient
1. Representative Standards identical
in size, shape and composition to
the unknowns with varying
concentrations 🡪 calibration curve
2. Computation from Knowledge of
Composition
Counting
Concentration
Compound or mixture:

7. 3. Gamma Ray Intensity Ratio
4. Transmission Method
x
I0
I
t
E1
E2

8. Analytical Solution for CF(AT)
SLAB
X
2
Y
2Z
D
Detector
x
z
y
Far-Field assumption:
CYLINDER (far-field assumption):
SPHERICAL (far-field assumption):

9. Near-Field Example
One-Dimensional Model
D
d
D
d
cylindrical
sample
cylindrical
detector
linear
sample
point
detector

10. Approach Based on
Infinite Thickness
Method

11. Quantification Method Based On
Uranium-Enrichment Meter*
Infinite Sample
Measurement
Method
Photon energy of
interest: 185.7 keV
MFPU-metal
: 0.037 cm
Infinite thickness criterion:
If the depth of the sample along the collimation axis is much larger than the mean free
path (MFP) of the gamma energy of interest in the sample material, all samples of the
same physical composition would present the same visible volume.
For the implementation of this technique, the sample must be isotopically uniform, thus
the surface sample will resemble the total material.
* Hasting A. Smith, Jr., The Measurement of Uranium Enrichment, NUREG/CR-5550, 1981.
Visible
volume
dx
D
Sample
Detector
Collimator

12. Basic
analytical
formula
Fraction of 235
U in U:
Count rate of photon with energy of interest:
dx
D
Sample
Detector
Collimator
Projected
volume
FEIR
TCR
CF(AT)

13. Basic analytical formula derivation
Integration over the sample thickness gives the
total photon (at energy of interest) count rate:
Mass fraction of nuclide of interest in the sample:
PHITS calculations
(or direct measurement/element data)

14. Correction for additional shieldings
Canister
[thickness tC
]
t2
t1
dx
D
Projected
volume
Fe Filter
Sample
Detector
Collimator
Count rate of photon with energy of interest:
Mass fraction of nuclide of interest in the sample:

15. Infiniteness Criterion
for 185.7 keV Gamma-Ray of 235
U
if D e-μρD
≈ 0
X is no longer a function of sample
thickness
U-metal UF6
D [cm] e-μρD
D [cm] e-μρD
1 MFP 0.037 0.367879 0.190 0.367879
3 MFP 0.110 0.049787 0.570 0.049787
5 MFP 0.183 0.006738 0.950 0.006738
7 MFP 0.256 0.000912 1.330 0.000912
9 MFP 0.329 0.000123 1.710 0.000123
12 MFP 0.439 0.000006 2.280 0.000006
Common
accepted value

16. Original Method for Uranium
Enrichment Measurement
Sample to detector distance is large compared with
the depth of visible volume:
Integration over the sample thickness gives the
total photon (at energy of interest) count rate:
(matrix effects)
where,
where,
dx
D
Sample
Detector
Collimator
Projected
volume
Canister
[thickness tC
]
Matrial composition correction factors (F/Fs)

17. Original Application
Detector count rate:
where f is determined by calibration
where b = -a.f
If the measurement is performed on materials of
the same type packaged in the same container,
then can be included in the calibration
constant. Thus,
Rearranging previous equation gives
Calibration constants a and b are determines by
measurement of standards of known enrichment

18. Mathematical formula modification
Inclusion of aperture effect
dV
dx
Sample volume subtended
by solid angle seen from
detector through
collimator
tF
Fe Filter
y
x2
y
x
0
-0.1
-5.1
Cylindrical collimator
radius 1 cm
x1
y=ax+b
x
y
z

19. Modification Results
Correction factors
by Fe filter, air
inside collimator
and Al casing of
detector
X
or
mass
Detector count rate, R

20. Comparison
First Method of Quantification
(Correction Factor)
Second Method of Quantification
(Modified Infinite Thickness Criterion)
Sample homogeneity Sample homogeneity
Focus on Correction factor Focus on Direct Calculation of TCR
In principle CF is comparing
non-attenuated to attenuated
gamma-ray
In principle is transmitting gamma-ray
through attenuating sample
No constraint on sample thickness Constraint on sample thickness
No need for detector efficiency Need detector efficiency
Near-field assay requires numerical
calculation
Simple analytical formula with closed
form solution by elementary functions

21. Reference
1. J.L. Parker, “The Use of Calibration Standards and the Correction for
Sample Self-Attenuation in Gamma-Ray Nondestructive Assay”, Los
Alamos National Laboratory report LA-10045, 1984.
2. T.D. Reilly and J.L. Parker, “A Guide to Gamma-Ray Assay for Nuclear
Material Accountability”, Los Alamos National Laboratory report
LA-5794-M, 1975.
3. D. Reilly, N. Ensslin, H. Smith, S. Kreiner, “Passive Nondestructive Assay
of Nuclear Materials”, US NRC report NUREG/CR-5550, 1991.
4. J. H. Hubbell, “Photon Cross Sections, Attenuation Coefficients, and
Energy Absorption Coefficients from 10 keV to 100 GeV,” National
Bureau of Standards report NSRDS-NBS 29, 1969.
5. Y. Peryoga, H. Sagara, “Study on Classification Method of Nuclear
Waste by Passive Gamma Spectrometry,” Laboratory for Advanced
Nuclear Energy, Tokyo Institute of Technology internal report, 2017.

22. THANK YOU

23. Inverse Square Law

24. Results for Umetal
with modified formula
Sample thickness:
1 cm
Sample thickness:
5 cm
Sample thickness:
10 cm
Un-Modifi
ed
Formula
Modified
Formula
Un-Modi
fied
Formula
Modified
Formula
Un-Modifi
ed
Formula
Modified
Formula
Sample weight [g] 467.5 2,337.5 9,163
U-235 content [g] 23.38 116.88 458.15
Counting [γ/s]* 9.63 9.66 9.66
U-235 content by
Formula [g]
24.52 23.24 123.08 116.62 482.45 457.11
Difference [C/T-1] 4.92% -0.59% 5.31% -0.22% 5.30% -0.23%
Application to Umetal
*HPGe detector counting on 185.7 keV photon simulated by PHITS

25. Correction for additional shieldings
Mass fraction of nuclide of interest in the sample:
t2
t1
dx
D
Projected
volume
Fe Filter
Sample
Detector
Collimator
Count rate of photon with energy of interest: