further development of the spectral deconvolution analysis tool

FURTHER DEVELOPMENT OF THE SPECTRAL DECONVOLUTION ANALYSIS TOOL (SDAT) TO IMPROVE COUNTING STATISTICS AND DETECTION LIMITS FOR NUCLEAR EXPLOSION

RADIONUCLIDE MEASUREMENTS

K. M. Foltz Biegalski, S. R. Biegalski, and D. A. Haas

The University of Texas at Austin

Sponsored by Army Space and Missile Defense Command

Contract No. W9113M-05-1-0017

ABSTRACT The Spectral Deconvolution Analysis Tool (SDAT) software was developed to improve counting statistics and detection limits for nuclear explosion radionuclide measurements. SDAT utilizes spectral deconvolution spectroscopy techniques and can analyze both β−γ coincidence spectra for radioxenon isotopes and high-resolution HPGe spectra from aerosol monitors. Spectral deconvolution spectroscopy is an analysis method that utilizes the entire signal deposited in a γ-ray detector rather than the small portion of the signal that is present in one γ-ray peak. This method shows promise to improve detection limits over classical γ-ray spectroscopy analytical techniques; however this hypothesis requires study. To address this issue, three tests were performed utilizing HPGe spectra to compare the detection ability and variance of SDAT results to those of commercial-off-the-shelf (COTS) software that utilizes a standard peak search algorithm. To test the applicability of the SDAT to β−γ coincidence spectra, Monte Carlo N-Particle eXtended (MCNPX) is used to simulate the detector response in an Automated Radioxenon Sampler-Analyzer (ARSA) detector for all the electrons and photons emitted from 131mXe, 133Xe, 133mXe, 135Xe, and 137Cs. A MatLab code was written to incorporate the MCNPX results in the calculation of β-γ coincidence spectra. These will aid in the development of the SDAT and to calibrate β-γ coincidence systems. The models developed for this work include improvements over previous models in their ability to address Compton scattering in the β cell, and the β distribution offset in the 30 keV γ-ray region for 133Xe.

28th Seismic Research Review: Ground-Based Nuclear Explosion Monitoring Technologies

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OBJECTIVES

This work aims to develop a spectral analysis tool that utilizes deconvolution to quantitatively calculate fission product concentrations in nuclear explosion monitoring radionuclide samples. The project was divided into two tasks for the year. The first task was to develop the Spectral Deconvolution Analysis Tool (SDAT). The second task was to develop models of both β−γ coincidence radioxenon spectra and HPGe fission product spectra in MCNP. These MCNP models were used to calibrate and test the SDAT code.

RESEARCH ACCOMPLISHED

SDAT Development

A good portion of the main SDAT analysis algorithm was written and discussed during the last SRR. This year, the focus was on testing, documentation, and development of peripheral software to improve analysis results.

Testing

The purpose of the first tests was to evaluate how well SDAT improves counting statistics and detection limits for explosion radionuclide measurements compared to COTS software that uses a standard peak-search and peak integration algorithm. SDAT results were compared with those from Canberra’s Genie-PC program. Three experiments were performed. In the first test, the variance properties of several sparse 137Cs spectra were determined. For the second test, small 137Cs peaks were superimposed on the Compton continuum of a 60Co spectrum and we compared how well each software package detected the small peaks. For the third test, 137Cs spectra of varying count times were superimposed onto 60Co spectra of varying count times such that the 137Cs peak occurs at the first gamma-line of 60Co: 1172 keV. In this case, the ability of each software package to deconvolve the multiplet peak signal was studied. For experimental details of these tests, see the Foltz-Biegalski, Biegalski, and Haas paper presented at the Methods and Applications of Radioanalytical Chemistry conference in Kona, Hawaii in April 2006. Conclusions of the test results were as follows. First, SDAT performs better than standard peak search and peak integration routines when the total spectrum count rates are relatively low, e.g., as in the ARSA histograms. This result was expected, but tests were needed to confirm this hypothesis. Not expected was the poor performance seen from the spectral deconvolution algorithm for spectra with high total counts. In these cases, peak-weighting significantly improved SDAT results; however, not consistently enough to achieve better results than the standard peak search and peak integration routine in cases of multiplet interference. The standard peak search and peak integration routine outperformed SDAT in these cases and gave more accurate results with lower errors. Consequently, we cannot recommend spectral deconvolution to replace standard peak search and peak integration algorithms, but to serve as a supplementary tool for analyzing atmospheric samples with low count rates or for analyzing samples with higher backgrounds when multiplets are not a concern. In the latter case, peak weighting must be used in conjunction with the with the spectral deconvolution algorithm.

Additional testing was performed using four detector response histograms created using the MCNPX ARSA model, one for each radioxenon isotope of interest. A weighting matrix was created using the SDAT program, “Create_weighted_matrix.m”. Several experimental sample histograms were created by combining the radioxenon detector response files in different amounts. The SDAT analysis program was then used to deconvolve the experimental samples. The coefficients calculated by SDAT were as expected with very low residual. Documentation

The SDAT software suite is described in a document titled “SDAT Software Documentation.” This document gives an overview of the software package, includes installation information, and describes basic procedures and detailed operations. Additional scientific documentation on the software can be found in the final report prepared for SMDC.


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Further Software Development

Two important additions were made to the SDAT software suite this year. These included the ability to calculate uncertainty values for the multiplier coefficients and the ability to determine a weighting matrix using the four radioxenon library files and a user-defined sensitivity index. The weighting matrix is used to improve the results of the deconvolution algorithm as discussed above in the section on software testing. The uncertainty of the multiplier coefficients was determined according to multiple linear regression theory as discussed in Statistical Analysis for Engineers and Scientists by J. Wesley Barnes, 1994 on page 250. The theory is summarized below. The [Coefficients] matrix will be referred to as β to match the reference. Other symbolic replacements that will be used in this discussion are listed below.

[Response] = Xnxp

[Sample] = y

öβ is an unbiased estimate of β. The variance-covariance matrix of

öβ is σ 2 ( öβ) = (XTX)−1σ 2 . The mean square of

errors, or MSE, is the best unbiased estimate of σ2. Therefore,

σ 2 = MSE = SSE

(n − p)

where SSE is the sum of squares for error, n is the number of samples in the data set, and p is the number of parameters in the model. In our case, n = 255 x 255 = 65025 and p = 4 for the four radioxenon isotopes (p =6 if radon background and detector background are included). SSE is determined using the equation below.

SSE = yTy-bTXTy-yTXb+bTXTXb.

Therefore

σ 2 = yT y-bTXT y-yTXb + bTXTXb

(n − p).

As mentioned in the Testing section, it was found that, in most cases, signal weighting reduced the residual of the [coefficients] matrix [Foltz Biegalski, Biegalski, and Haas, 2006]. To create a weighting histogram, a program that comes with the SDAT software called “Create_weighted_matrix.m” is used. This program uses all the detector response files to create the weighting histogram. For β-γ coincidence data, the weighting file contains a 255 x 255 matrix of zeroes and ones that is used to weight the areas of the sample spectrum in which a radioxenon signal is expected. The interesting areas of the sample histogram can be weighted in different amounts by changing a sensitivity number within the program. See the SDAT Software Documentation for more information on the setup and execution of this program.

MCNPX Model Development For the last SRR, MCNPX models for both the ARSA β−γ coincidence detector and a HPGe detector were created. This year, Compton scattering was added to the ARSA detector model as well as the 45 keV β energy shift at 30 keV on the γ energy scale caused by an additional coincident photon during conversion electron decay (Figure 1). All models were transferred to MCNPX this year due to improved decay libraries. As a result of the improved models, more accurate representations were made of the individual radioxenon histograms (Figures 1-5). A model was also produced for the β-γ coincidence response expected from Compton scattering of 137Cs–a proposed method for calibrating the energy vs. channel response of the ARSA. (Figure 6) In addition, decay signals of the four radioxenon isotopes of interest—131mXe, 133Xe, 133mXe, and 135Xe —and other fission products including 137Cs, 140Ba, and 140La were modeled using the HPGe detector model. (Figures 7–13) More information on the scientific details behind the creation of the radioxenon histograms can be found in the Haas, Biegalski, Foltz-Biegalski paper, “Modeling β-γ coincidence spectra of 131mXe, 133Xe, 133mXe, and 135Xe,” presented at the Methods and Applications of Radioanalytical Chemistry conference in Kona, Hawaii in April 2006. Additional details are provided in this year’s final report for this project provided to SMDC.


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Figure 1. β-γ coincidence data for 133Xe produced

through MCNPX simulation. Note the endpoint of the β spectrum coincident with the 30 keV X-ray is approximately 45 keV greater than that coincident with the 81 keV γ-ray.

Figure 3. β-γ coincidence data for 135Xe produced

through MCNPX simulation.

Figure 5. Plot of the γ spectra in coincidence with

β particles from the decay of 133Xe.

Figure 2. β-γ coincidence data for 131mXe and

133mXe produced through MCNPX simulation.

Figure 4. Plot of the β spectra in coincidence with

the 81 keV γ-ray of 133Xe from the real sample and MCNPX model.

131mXe 164 keV IC electron

133mXe 233 keV IC electron

81 keV γ-ray

30 keV X-ray


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Figure 6. β-γ coincidence spectrum of the 137Cs calibration source. Top - MCNPX model of the gamma

spectra coincident with different energy events in the β cell. Middle—interpolation of the top image gives a complete model. Bottom—an experimental result.


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HPGe Spectrum of Cs-137

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Energy (MeV)

No

rmal

ized

Co

un

ts

Figure 7. Modeled plot of 137Cs γ spectra acquired with a HPGe detector.

HPGe Spectrum of Xe-131m

1.00E-09

1.00E-08

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0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500

Energy (MeV)

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Co

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Figure 8. Modeled plot of 131mXe γ spectra acquired with a HPGe detector.


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HPGe Spectrum of Xe-133

1.E-09

1.E-08

1.E-07

1.E-06

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1.E-04

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0.000 0.100 0.200 0.300 0.400 0.500

Energy (MeV)

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ized

Co

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Figure 9. Modeled plot of 133Xe γ spectra acquired with a HPGe detector.

HPGe Spectrum of Xe-133m

1.E-09

1.E-08

1.E-07

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1.E-04

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0.000 0.100 0.200 0.300 0.400 0.500

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Co

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Figure 10. Modeled plot of 133mXe γ spectra acquired with a HPGe detector.


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HPGe Spectrum of Xe-135

1.E-09

1.E-08

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0.000 0.200 0.400 0.600 0.800 1.000 1.200

Energy (MeV)

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ized

co

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Figure 11. Modeled plot of 135Xe γ spectra acquired with a HPGe detector.

HPGe Spectrum of La-140

1.00E-09

1.00E-08

1.00E-07

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0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600 1.800 2.000

Energy (MeV)

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Co

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Figure 12. Modeled plot of 140La γ spectra acquired with a HPGe detector.


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HPGe Spectrum of Ba-140

1.00E-09

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0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700

Energy (MeV)

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Co

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Figure 13. Modeled plot of 140Ba γ spectra acquired with a HPGe detector.

CONCLUSIONS AND RECOMMENDATIONS

Future work will include purchase of a β-γ coincidence detector similar to what is utilized in an ARSA or Swedish SAUNA system. We have begun constructing equipment for creating and separating radioxenons. The radioxenon will be produced through irradiation of uranium in the 1.1 MW TRIGA Mark II research reactor at UT. The samples produced will provide greater activity samples for counting in the detector which will give better counting statistics. The goal will be the development of an accurate and reliable deconvolution tool for determining isotopic abundances of radioxenon for use in support of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). It is planned to incorporate the SDAT software into a user-friendly GUI during the summer of 2006. REFERENCES

Foltz-Biegalski, K. M. (2006). Spectral Deconvolution Assessment Tool (SDAT) software documentation, developed for SMDC as part of this contract.

Foltz-Biegalski, K. M., S. R. Biegalski, and D. A. Haas (2006). Performance evaluation of Spectral Deconvolution

Analysis Tool (SDAT) software used for nuclear explosion radionuclide measurements,” Methods and Applications of Radioanalytical Chemistry Conference, April 2006 (to be published in the 2008 J. Radioanal. Nucl. Chem.).

Foltz-Biegalski, K. M., D. A. Haas, and S. R. Biegalski (2006). SDAT final report, developed for SMDC as part of

this contract. Haas, D. A., S. R. Biegalski, and K. M. Foltz Biegalski (2006). Modeling β-γ coincidence spectra of 131mXe, 133Xe,

133mXe, and 135Xe signals, Methods and Applications of Radioanalytical Chemistry Conference, April 2006 (to be published in the 2008 J. Radioanal. Nucl. Chem.).


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Lawson, C. L. and R. J. Hanson (1974). Solving Least Squares Problems. Englewood Cliffs, New Jersey: Prentice-Hall.


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further development of the spectral deconvolution analysis tool

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