Nuclear Forensics is recognized as a essential component in the nuclear non-proliferation verification sector by the international community. It is being advanced under the leadership of the IAEA, the U.S., and the EU. Both the U.S.’s Lawrence Livermore National Laboratory (LLNL) and the international collaborative organization, the Nuclear Forensics International Technical Working Group (ITWG), have proposed to establish a relationship between the production timing and radiochronometry of nuclear materials or samples to utilize in the field of nuclear forensics. Radiochronometry of nuclear materials is calculated based on the Bateman equation, incorporating factors with uncertainties derived from tests, experiments, and analyses. The results from the nuclear activity radiochronometry also encompass uncertainties, affecting their reliability. This study examined the mathematical uncertainty calculations related to the results of nuclear activity radiochronometry, focusing on calculation methods, contribution rates per factor, and sensitivities. Uncertainty factors for the Bateman equation-based radiochronometry were observed in the decay constants for each nuclide type and the uncertainty in the radioactive ratio of the tracer nuclide. The sensitivity for each factor revealed that the uncertainty in the radioactive ratio of the signature nuclide contributed more significantly than the uncertainty in decay constants for each nuclide type. Each factor displayed a distinct sensitivity curve relative to the radioactive ratio. As it approaches a radioactive equilibrium, the sensitivity tends to increase infinitely, indicating a corresponding trend of infinite increase in uncertainty. Because the time and curve shape to reach radioactive equilibrium vary depending on the signature nuclide, it’s essential to choose an appropriate signature nuclide based on the anticipated period and analysis requirements for nuclear activity radiochronometry. However, radiochronometry using mathematical methods is limited to the relationship between parent and daughter nuclides, presenting the potential for underestimation of uncertainty factors like decay constants. Future research will need to focus on uncertainty calculation methods through computational simulations, especially using the Monte Carlo method, to overcome the limitations of mathematical approaches and potential underestimations.

The parent and daughter nuclides in a radioactive decay chain arrive at secular equilibrium once they have a large half-life difference. The characteristics of this equilibrium state can be used to estimate the production time of nuclear materials. In this study, a mathematical model and algorithm that can be applied to radio-chronometry using the radioactive equilibrium relationship were investigated, reviewed, and implemented. A Bateman equation that can analyze the decay of radioactive materials over time was used for the mathematical model. To obtain a differential-based solution of the Bateman equation, an algebraic numerical solution approach and two different matrix exponential functions (Moral and Levy) were implemented. The obtained result was compared with those of commonly used algorithms, such as the Chebyshev rational approximation method and WISE Uranium. The experimental analysis confirmed the similarity of the results. However, the Moral method led to an increasing calculation uncertainty once there was a branching decay, so this aspect must be improved. The time period corresponding to the production of nuclear materials or nuclear activity can be estimated using the proposed algorithm when uranium or its daughter nuclides are included in the target materials for nuclear forensics.

Nuclear security event involving nuclear and other radioactive materials outside of regulatory control (MORC) has the potential to cause severe consequences for public health, the environment, the economy and society. Each state has a responsibility to develop national nuclear security measures including nuclear forensics to respond to such events. In Japan, national nuclear forensics capability building efforts mainly based on research and development (R&D) have been conducted since 2010, in accordance with national statement of Japan at the Nuclear Security Summit in Washington DC. Most of that work is undertaken at the Integrated Support Center for Nuclear Non-proliferation and Nuclear Security (ISCN) of the Japan Atmic Energy Agency (JAEA) in close cooperation with other competent authorities. The ISCN has made increased contributions to the enhancement of international nuclear security by establishing technical capabilities in nuclear forensics and sharing the achievements with the international community. The ISCN has mainly engaged in R&Ds for establishing and enhancing nuclear forensics technical capability. As for the laboratory capability, several new pieces of analytical equipment have been introduced for nuclear forensics R&D purposes. High-precise measurement techniques validated in the past nuclear forensics incidents have been established, and novel techniques that can contribute to the more timely and confident nuclear forensics signature analysis have been developed. The ISCN has been also developed a proto-type nuclear forensics library based on the data of nuclear materials possessed for past nuclear fuel cycle research in JAEA. These technical capability developments have been conducted based on the cooperation with international partners such as the U.S. Department of Energy and EC Joint Research Center, as well as participation in exercises organized by Nuclear Forensics International Technical Working Group (NF-ITWG). Recent R&D works have been mainly based on the needs of domestic competent authorities, such as first responders and investigators, and aim to develop technologies covering the entire spectrum of nuclear forensics processes from crime scene investigation to laboratory analysis and interpretation. One important key issue is the enhancement of technical capability for post-dispersion nuclear forensics. For instance, the ISCN has carried out the development of radiation measurement equipment coupled with the low-cost and mobile radiation detectors that uses machine-learning algorithms for quick and autonomous radioisotope identification to support first responders during crime scene investigations. Laboratory measurement techniques for samples collected at a post-dispersion crime scene are also among the important technical issues studied at the ISCN. The application of emerging technologies to nuclear forensics has also been studied. This includes the application of deep leaning models to nuclear forensics signature interpretation that could provide more confident results, as well as the development of contamination imaging technology that could contribute to the analytical planning on the samples in collaboration with conventional forensics. Many analytical techniques have been developed and the capability to analyze nuclear and other radioactive materials for nuclear forensics purposes has been considerably matured over the past decade. The challenges of post-dispersion samples, collaboration with conventional forensics and the development of novel signatures will be more important in the near future. Therefore, the ISCN will promote the R&Ds to further enhance the technical capabilities solving these issues. In addition, the ISCN is also promoting to expand the nuclear forensics research into universities and other research institutes in Japan. This is expected to contribute to the establishment of a domestic nuclear forensics network that enables to respond timely and flexibly to the MORC incidents, and to the maturation of nuclear forensics as a new academic field.