Nuclear Attribution and Forensics

Firas Abuzaid
March 17, 2011

Submitted as coursework for Physics 241, Stanford University, Winter 2011


As the threat from nuclear Armageddon has only heightened in the past decade, much has been discussed in the foreign policy arena about the use of nuclear attribution and forensics as an anti-proliferation measure. Since the beginning of the 1990s, cases of illicit trafficking involving nuclear material were started being reported. [1] As a result, nuclear material has become a part of the forensic investigations and this new discipline of nuclear forensic science was developed. Essentially, the theory is that nuclear attribution technologies can be used to dissuade rogue governments and rogue individuals from using nuclear weapons irresponsibly. To see this, a more in-depth look at this technology is warranted.

Techniques: Age Determination

One technique that's often used in nuclear forensics and nuclear attribution is age determination: calculating the age of the fissile material (typically uranium) that's been obtained. To do this, one must first analyze the ratio of isotopes in the fissile material and then analyze the half-lives of each of these isotopes.

For example, say uranium is the fissile material. Two determine the isotope composition, either thermal ionization mass spectroscopy or an inductively coupled plasma mass spectrometer with multi-collector detection system can be used, although the former is more often used.

Uranium has three candidate parent/daughter relationships for the age determination - U-234/Th-230, U-235/Pa-231, and U-236/Th-232. [2] The latter relationship is valid only for irradiated and reprocessed U, because the U-236 is not a naturally occurring isotope. The second limitation on the use of this relationship is that Th-232 occurs in nature, which leads to non-negligible Th-232 blank levels in the chemical reagents and solvents.

From there, the age of uranium material is calculated from the equation of basic radioactive decay, N = N0 exp(-λt). An examination of the U-234/Th-230 ratio would like this for example:

= N0U-234 exp(-λU-234t)
(N0U-234 - NU-234) × exp(-λTh-230 t)

where t and λ are derived from other factors specific to the material.

Gamma Ray Spectroscopy

An alternative to this traditional approach is gamma spectroscopy, which is widely used to determine isotopic composition of radioactive materials. Upon decay, each radioisotope emits characteristic gamma rays with particular energies, essentially providing a fingerprint for the isotope. Relative line intensities can then be used to determine isotope ratios and infer sample age, origin, and processing history. [3] Traditionally, high-purity germanium (HPGe) detectors operating at liquid nitrogen temperatures have been used, but these typically exhibit an error of about 1%. On the other hand, cryogenic gamma ray spectrometers operating at 0.1 degrees Kelvin are a good alternative, with an error of magnitude improvement in energy resolution. This has a significant benefit in the case of analyzing uranium enrichment. While standard measurements of enrichment rely on measuring the magnitude of the 186 keV line from U-235 above the Compton background, which can be done even with NaI scintillators, high-precision measurements are based on the Th-234 lines at 92.38 and 92.80 keV as a measure of the U-238 abundance, and the Th X-ray at 93.35 keV as a measure of the U-235 abundance This analysis relies on the fact that the strong 186 keV Gamma emission from U-235 excites X-rays from the Th daughter of U much more efficiently than radiation released in the decay of U-238. Note that these lines provide a measure of enrichment accurate to 0.1% only in samples at least 170 days old because they require an equilibrium between the Th-234 daughter (τ1/2 = 24 days) and the U-238 parent, but they are still preferred for analysis because of their spectral proximity.

© Firas Abuzaid. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] M. Wallenius, K. Mayer and I. Ray, "Nuclear forensic Investigations: Two Case Studies," Forensic Science International 156, 1 (2006).

[2] M. Wallenius et al., "Determination of the Age of Highly Enriched Uranium," Analytical and Bioanalytical Chemistry 374, 3 (2002).

[3] S. F. Terracol et al., "Ultra-High Resolution Gamma-Ray Spectrometer Development for Nuclear Attribution and Non-Proliferation Applications," Nuclear Science Symposium Conference Record, 2004 IEEE 2, 1006 (2004).