Determination of the age of highly enriched uranium

This paper describes the analytical methods (thermal ionization mass spectrometry, inductively coupled plasma mass spectrometry, and alpha spectrometry) that have been developed for determination of the age of uranium and discusses their advantages and limitations. With regard to potential application of the methods (e.g. Fissile Material Cut-off Treaty), the discussion focuses on highly enriched uranium, because this seems to be of highest strategic relevance.The different analytical methods were tested and validated by use of uranium reference materials of different (235)U isotope abundance and of known ages. The results show that thermal ionization mass spectrometry and alpha spectrometry are both very accurate and precise techniques for this application. Inductively coupled plasma mass spectrometry, on the other hand, although less precise, because of the different approach to the analytical problem, is still sufficiently accurate to be used as a rapid screening method.     

Development and validation of a methodology for uranium radiochronometry reference material preparation

The paper describes a methodology for a reference material preparation to be used for the determination of the production date (i.e. the time elapsed since the last chemical processing) of uranium materials based on the ²³⁰Th/²³⁴U radiochronometer. The reference material was prepared from highly enriched uranium by a complete separation of thorium decay products, thus zeroing the initial daughter nuclide concentration at known time. The complete elimination of thorium from the starting material was verified by gamma spectrometric measurements and by addition of a ²³²Th tracer to the material and its re-measurement in the final product after the separation. The validation of the methodology was carried out subsequently by comparing the ingrown daughter nuclide ²³⁰Th and the measured ²³⁰Th/²³⁴U ratio after recorded times following the last chemical separation with the calculated values obtained on the basis of their respective half-lives. The prepared reference material can be used as a quality control material for age determination of uranium in nuclear forensics and safeguards as well as for method validation.     

Identification of uranium signatures relevant for nuclear safeguards and forensics

The paper describes the applicability of different characteristics (signatures) in nuclear safeguards and forensics for assessment of uranium material provenance in terms of production process. The study follows a uranium ore concentrate production from an ore to a U₃O₈ product. It turned out that rare-earth elemental pattern, radiochronometry (age of ore body and material production date), sulphur and organic impurities are useful to find out the origin or history of the material, while certain trace-elements and isotopics of Pb or Sr were found to be inconclusive. The results will be important to understand the signatures in nuclear safeguards and forensics.     

Some Theory and an Approach to Solving Sequential Multiple-Criteria Decision Problems

This paper examines a sequential multiple-criteria decision problem. The problem arises when a decision-maker is unable to consider all possible decision alternatives simultaneously. The decision-maker evaluates only a subset of all decision alternatives, from which he chooses the most preferred solution. Obviously, this solution is not necessarily ‘globally’ best. An interesting question is: how good is the most preferred solution and what are the chances of finding a better solution by considering additional alternatives? A unified approach to solving this problem based on probability theory is presented and illustrated with numerical examples.     

Anion analysis in uranium ore concentrates by ion chromatography

In the present exploratory study, the applicability of anionic impurities for attributing nuclear material to a certain chemical process or origin has been investigated. Anions (e.g., nitrate, sulphate, fluoride, chloride) originate from acids or salt solutions that are used for processing of solutions containing uranium or plutonium. The study focuses on uranium ore concentrates (“yellow cakes”) originating from different mines. Uranium is mined from different types of ore body and depending on the type of rock, different chemical processes for leaching, dissolving and precipitating the uranium need to be applied. Consequently, the anionic patterns observed in the products of these processes (the “ore concentrates”) are different. The concentrations of different anionic species were measured by ion chromatography using conductivity detection. The results show clear differences of anion concentrations and patterns between samples from different uranium mines. Besides this, differences between sampling campaigns in a same mine were also observed indicating that the uranium ore is not homogeneous in a mine. These within-mine variations, however, were smaller than the between-mine variations.     

Muonic Atom Deexcitation via Formation of Metastable Molecular States, in Light of Experimental Verification

In a recent experiment performed at PSI, a peak in the time-of-flight distribution of pμ(1s) atoms could be identified with decay of ppμ^* molecular ions situated below the 2s threshold, providing 900 eV of kinetic energy to the pμ atom. This finding may be interpreted in terms of the side path model which suggests that metastable muonic molecules may form with high probability in resonant collisions between muonic hydrogen in the 2s state and hydrogen molecules, e.g. $$p\mu (2s) + {\text{H}}_{\text{2}} \to [(pp\mu ^* )_{vJ}^{pq} - pee]_{vK} \to [(pp\mu ^* )_{v'J'}^{p'q'} - pe]^ + + e^ - .$$ The Coulombic decay of the Auger stabilised ppμ^* molecular ion then leads to the formation of highly energetic pμ(1s) atoms. In the present paper calculations of resonant formation rates in pure hydrogen are presented and compared to the quenching rate of pμ(2s) atoms measured at low hydrogen density.     

Optimizing macroeconomic policy: A review of approaches and applications

In this paper the main approaches to optimizing macroeconomic policy problems are reviewed. These include the classical approaches of Tinbergen, Theil and Frisch as well as several mathematical programming methods, such as linear programming, goal programming, interactive multiple criteria optimization, and methods of optimal control. In addition, several applications are described. Finally, the usefullness and suitability of these approaches to solving macroeconomic policy problems in practice is discussed.     

Impact of the side-path model on the muon cycling rate density dependence in D-T mixtures

The side-path model previously suggested by us allows for muon transferfrom tritiumto deuterium via intermediate dtµ^* resonances formed in tµ(2s)-D₂ collisions. Taking this effect into account, the density dependence of the muon cycling rate in D-T mixtures at low temperatures is analysed. Compared with cascade models where only one-sided transfer is present, the predicted density dependence of _c is in better agreement with measurements.     

Student teachers’ concept definitions of area and their understanding about two-dimensionality of area

We examine what kind of concept definitions of area a group of Finnish primary and lower secondary student teachers (N = 82) use, and how the quality of the definitions is associated with the participants’ success in seven exercises involving area. We are especially interested in how the understanding of the two-dimensionality of area appears in the participants’ responses. Only six student teachers were able to give a mathematically precise and correct definition of area. Altogether 26 participants defined it as ‘the size of a figure’ and 20 respondents required that a figure must be bounded. Further, 22 of them associated area with a formula or an example and eight respondents gave an incorrect or nonsensical definition. On average, student teachers master rather well the area formulae of a circle and a rectangle but already the relationship between the surface area of a cube and its volume is less commonly perceived. Most student teachers associate the area of an irregular domain with the method of exhaustion but clearly fewer of them acknowledge the difference between the area and an approximation of it. Surprisingly, there is only a weak Spearman correlation between the participants’ scores in the test exercises and the qualitatively ordered categories of concept definitions.