Small-angle Compton Scattering to Determine the Attenuation of ...

2011 ANS Winter Meeting in Washington, D.C. October 30 – November 3, 2011
Small-angle Compton Scattering to
Determine the Attenuation of Gamma Rays
from HEU
Rick B. Oberer
Cynthia A. Gunn
Lisa G. Chiang
Michael C. Mattmann

Disclaimer
This report was prepared as an account of work sponsored by an agency of
the United States Government. Neither the United States Government nor
any agency thereof, nor any of their employees, makes any warranty,
express or implied, or assumes any legal liability or responsibility for the
accuracy, completeness, or usefulness of any information, apparatus,
product, or process disclosed, or represents that its use would not infringe
privately owned rights. Reference herein to any specific commercial
product, process, or service by trade name, trademark, manufacturer, or
otherwise, does not necessarily constitute or imply its endorsement,
recommendation, or favoring by the United States Government or any
agency thereof. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the United States Government or any
agency thereof.

Acknowledgement:
Rick .B. Oberer
Cynthia A. Gunn
Lisa G. Chiang
Robert E. Valiga
Julia A. Cantrell
Funded by Nuclear Safety Research and Development
(NSRD)

Gamma Non Destructive Analysis
• Gamma NDA measurements are dependant on:
– Geometry
• Distance of source to detector
• Physical Dimensions (containers, measurement distance)
– Attenuation
• Process Knowledge (matrix composition, bulk density, net
weight)
• Matricies (material interfering with gamma rays of
interest)
• Material Forms
• Self-Shielding of material
• Many of these can be theoretically estimated or calculated
• At Y-12 gamma emitting radiation is present in a variety of
forms and myriad locations
• Departure from reliance on ‘representative standards’
– Development of Theoretical corrections, such as the use of
Small Angle Compton Scattering

Nuclear criticality issue
• HEU Chemical Processing Floors
– At Y-12, HEU solution has been spilled and absorbed into
the concrete floors of chemical processing areas.
– The amount of HEU estimated by NDA is significant.
– The estimated quantity is highly dependent on the depth
distribution of the HEU in the floor.

Quantifying Radioactivity and Attenuation
To quantify the amount of radioactivity, need to know
• geometry and
• amount of attenuation of gamma rays.
– Differential Attenuation
• For HEU, use of U-235 gamma rays
– (144keV, 168keV, 186keV, and 205keV)
• Can also use higher energy gamma rays from Tl-208 from U-232 in HEU *
– (277keV, 511keV, 583keV, 860keV, 2614keV)
*
Y-12 innovation. R. B. Oberer, L. G. Chiang, M. J. Norris, C. A. Gunn, B. C. Adaline, "The use of Tl-208
gamma rays for safeguards, nondestructive-assay (NDA) measurements," INMM Central Regional Chapter,
2009 Fall Meeting, Oak Ridge, Tennessee, November 3-4, 2009, Y/EN-8270 May 26, 2009.
http://www1.y12.doe.gov/search/library/documents/pdf/yen-8270.pdf

Differential attenuation
Uncorrected
Corrected

Small-angle Compton scattering discontinuity

Experimental setup
HEU solution absorbed on paper between Hardy board (1-15) and patio
blocks (16, 17).
Monte Carlo U-235 planar source at a
discrete depth,
Monte Carlo U-235 planar source at a
continuous distribution to depth,

Count rate (cps)
Count rate
Gamma Ray Attenuation
N
x N 0
Experimental
e
x
Monte Carlo
120
7.E-06
100
y = 155.75e -0.126x
R² = 0.9993
6.E-06
y = 6E-06e -0.328x
80
5.E-06
60
4.E-06
3.E-06
40
2.E-06
20
1.E-06
0
0 10 20 30 40
Density thickness (ρx) concrete (g/cm2)
0.E+00
0 2 4 6 8 10 12
Concrete depth x (cm)

Small-angle Compton scattering is calculated from the
spectrum as follows:
N sa
x
ROI
E
ROI
1 2

Klein-Nishina (for computing fraction of interactions that
are small angle Compton scatters, k)
k
d
dE
0
The differential cross-section for θ = 0
depends only on the atomic-number Z of the
material and the energy Eγ of the gamma ray.
The total cross-section σ taken from
XCOM [1] data.
d
dE
0
254.9
Z
keV
b
2
E
Berger, M.J., Hubbell, J.H., Seltzer, S.M., Chang, J., Coursey, J.S.,
Sukumar, R., Zucker, D.S., and Olsen, K. (2010), XCOM: Photon
Cross Section Database (version 1.5). National Institute of Standards
and Technology, Gaithersburg, MD.
http://physics.nist.gov/xcom

Count rate (cps/keV)
Count rate
Small-angle count rate for discrete case
N
sa
x
x
kN0xe
Experimental
1.2
Monte Carlo
4.E-08
1
3.E-08
0.8
3.E-08
0.6
2.E-08
0.4
2.E-08
0.2
1.E-08
5.E-09
0
0 10 20 30 40
0.E+00
0 5 10 15
Density thickness (ρx) concrete (g/cm 2 )
Concrete depth x (cm)

A linear relationship
For a radioactive source at a discrete depth x, the ratio of the small-angle Compton
scattering discontinuity to the peak is linear and directly proportional to the product (μρx)
Primary gamma
rays
Small angle scattered gamma
rays
N
N
sa
x
x
N 0
e
x
x
kN0xe
Ratio
N sa
N
x
x
kx

Step/Peak
Step/Peak
Discrete Depth (x)
Experimental
N sa
N
x
x
kx
Monte Carlo
0.08
5.0E-02
0.07
4.5E-02
0.06
4.0E-02
0.05
3.5E-02
3.0E-02
0.04
2.5E-02
0.03
2.0E-02
0.02
0.01
1.5E-02
1.0E-02
5.0E-03
0.00
0 10 20 30 40
0.0E+00
0 5 10 15
Density thickness (ρx) concrete (g/cm2)
Concrete depth x (cm)

Step/Peak
Continuous distribution (x)
Step/Peak
N
N
sa
x
x
x
k 1
e
1
e
1
x
x
Experimental
0.14
0.12
0.10
0.08
Monte Carlo
0.014
0.012
0.010
0.008
0.06
0.006
0.04
0.004
0.02
0.002
0.00
0 10 20 30 40
0.000
0 2 4 6 8 10 12
Density thickness concrete (g/cm 2 )
Concrete depth x (cm)

Measurement results with and without small angle
Spreadsheet
Actual depth
Actual Areal Density = 0.085 gU235/cm 2
Spreadsheet
Assumed 4" depth
ISOTOPIC
Assumed 4" depth
Small
Angle
Case 1 0.072 0.096 0.129 0.079
Case 2 0.084 0.103 0.121 0.089
Case 3 0.083 0.086 0.107 0.087
Case 8 0.085 0.085 0.077 0.082
Average: 0.081 0.092 0.108 0.084
Standard deviation: 0.006 0.009 0.023 0.004
Actual Areal Density = 0.052 gU235/cm 2
Case 4 0.052 0.070 0.070 0.051
Case 5 0.045 0.052 0.069 0.050
Case 6 0.048 0.052 0.065 0.052
Case 7 0.051 0.054 0.065 0.046
Case 9 0.040 0.045 0.041 0.054
Average: 0.047 0.055 0.062 0.050
Standard deviation: 0.005 0.009 0.012 0.003

Measured areal density (gU235/cm2)
Measurement results with and without small angle
0.15
0.13
ISOTOPIC
Small angle
Spreadsheet
0.11
0.09
0.07
0.05
0.03
0.03 0.04 0.05 0.06 0.07 0.08 0.09
True areal density (gU235/cm2)

Summary of equations
The small-angle Compton scattering differential
cross-section is determined from the atomicnumber
Z and gamma-ray energy E γ
according to
d
dE
0
254.9
Z
keV
b
2
E
Dividing this differential cross-section by the total
cross-section σ gives the fraction k of interactions
which are small-angle Compton scatters
Multiplying this fraction k by the mass-attenuation
coefficient μ density ρ and depth x of a discrete
gamma-ray source gives the magnitude of smallangle
scattering discontinuity divided by the peak
height
k
d
dE
N sa
N
x
x
0
kx
A continuous, uniform distribution in a matrix
to a depth x is given from the same variables
(μρx)
N
N
sa
x
x
x
k 1
e 1
x
x
1
e
*
R.B. Oberer, C.A. Gunn, L.G. Chiang, R.E. Valiga, J.A. Cantrell, "Small-angle Compton
Scattering to Determine the Depth of a Radioactive Source in Matter," Technical Report RP
900000-0006, Y-12 National Security Complex, April 2011.
http://www1.y12.doe.gov/search/library/documents/pdf/RP-900000-0006.pdf

Conclusion
• The small-angle Compton-scattering discontinuity can be
used to determine the amount of intervening matter
between a gamma-ray source and detector.
• It can be used in addition to differential attenuation, or
• when differential attenuation cannot be used such as a
single gamma ray source such as Cs-137.
• This depth is useful in estimating the attenuation of the
gamma rays