Eur. Phys. J. Spec. Top.
https://doi.org/10.1140/epjs/s11734-026-02278-y

Regular Article

Evaluating geometrical parameters in defined solid-angle alpha spectrometry for absolute Radon-222 activity measurement

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116, Brunswick, Germany

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Received: 23 July 2025
Accepted: 14 March 2026
Published online: 29 March 2026

Abstract

Defined Solid Angle (DSA) alpha spectrometry is a primary method for absolute activity determination of Radon-222, in which radon is cryogenically depositing onto a polished cold disk under vacuum and counted in a fixed source–detector geometry. In this approach, the detection efficiency is determined exclusively by the normalized solid angle, expressed as the Geometry Factor $G$. The accuracy of activity determination therefore depends directly on the precise evaluation of $G$ and its associated uncertainty. This work presents a comprehensive numerical investigation of the sensitivity and uncertainty of $G$ with respect to the governing geometrical parameters: source–diaphragm distance $z$, diaphragm radius $a$, source radius $b$, and eccentricity $e$. Calculations were performed using both the Knoll (Radiation detection and measurement, 4th ed. Wiley, New York, S120, 2010) and Curtis (Nucleus 13:38, 1955. https://doi.org/10.1016/S0168-9002(96)80029-5) analytical extensions, enabling systematic parameter variation and direct model comparison. The results show excellent agreement between the two models for concentric configurations ($e$ = 0 mm). The Geometry Factor is found to be most sensitive to variations in $z$ and $a$; however, uncertainty propagation analysis demonstrates that the dominant contribution to the combined uncertainty arises from $z$, accounting for approximately 88% – 97% of the total variance under typical National Metrology Institute (NMI) conditions. In contrast, the influence of $b$ is significantly smaller, and eccentricities up to 1 mm produce only minor variations in $G$. These findings quantitatively identify the source–diaphragm distance as the critical parameter limiting uncertainty reduction in DSA-based primary standardization of Radon-222. The study provides a clear metrological framework for optimizing geometry control and supports the harmonization of high-accuracy activity measurements across NMIs, enabling more stable and reliable transfer standards for secondary laboratories and end-users.