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

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 $$G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> . The accuracy of activity determination therefore depends directly on the precise evaluation of $$G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> and its associated uncertainty. This work presents a comprehensive numerical investigation of the sensitivity and uncertainty of $$G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> with respect to the governing geometrical parameters: source–diaphragm distance $$z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> </mml:math> , diaphragm radius $$a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>a</mml:mi> </mml:math> , source radius $$b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>b</mml:mi> </mml:math> , and eccentricity $$e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>e</mml:mi> </mml:math> . 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 ( $$e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>e</mml:mi> </mml:math> = 0 mm). The Geometry Factor is found to be most sensitive to variations in $$z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> </mml:math> and $$a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>a</mml:mi> </mml:math> ; however, uncertainty propagation analysis demonstrates that the dominant contribution to the combined uncertainty arises from $$z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> </mml:math> , accounting for approximately 88% – 97% of the total variance under typical National Metrology Institute (NMI) conditions. In contrast, the influence of $$b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>b</mml:mi> </mml:math> is significantly smaller, and eccentricities up to 1 mm produce only minor variations in $$G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> . 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.