New approaches for analyzing the dynamics of the Rn-222 emanation behavior from Ra-226 sources by means of spectrometric measurement series

For the low activity range, conventional standards (consisting of gaseous Rn‑222) are not suited to the realization and dissemination of the Bq/m³ unit with respect to Rn‑222. An alternative is found in Ra‑226 sources whose physicochemical properties are such that a certain fraction of the direct progeny, Rn‑222, emanates from the source. The process observed here is in most cases a diffusion process, so the emanation behavior correlates to the physicochemical properties and hence nearly always to the climate parameters of the environment. At PTB, a procedure for characterizing the emanation behavior of such sources has been established on the basis of the emanation‑induced disturbance of equilibrium between the Rn‑222 progenies remaining in the source and the Ra‑226 itself, as determined by γ-spectrometry [1].

More elaborate measurements have demonstrated that the established technique — given that it requires continuity of the Rn‑222 remaining in the source — can only deliver reliable results in cases where a state of equilibrium has been attained. The reason for this is that with each change in the emanation behavior, the amount of Rn‑222 found in the source must first decay back to a state of equilibrium, or must be replenished through the decay of Ra‑226, before the formula underlying the original methodology becomes applicable. However, if the emanation behavior follows its own dynamics, the measurand will represent the convolution of this dynamic signal with the impulse response of the radioactive system. As such, estimating the emanating Rn‑222 based on measuring the Rn‑222 found in the source is an inverse problem. Drawing on this insight, new statistical methods based on the Bayesian filters (Kalman filter, assumed density filtering [2]) have been developed that will in the future allow an approximated probability distribution to be calculated for the emanated Rn‑222 from a time series of spectrometric data even before radioactive equilibrium has been attained. At the same time a determination will be made of the probability that the source is currently in a stable regime. Figure 1 shows an example of raw data gathered from measured γ-spectra of an Ra‑226 source, the activity estimated from this data of the Rn‑222 remaining in the source and of the emanated Rn‑222, and the probability for stable regimes. For each point in time, analysis was done using only the data available up to that time, making this method suitable for online applications as well.

Fig. 1: The top diagram shows the integral count rate above the highest energy Ra-226 emission (E_γ = 186.1 keV). This count rate includes only events of Rn-222 and its progenies. The variation in the count rates is due to variation in the environmental parameters. The next graph shows the thus-determined residual Rn-222 activity in Bq in the source. The pale blue band marks the 90 % confidence interval of uncertainty. The third graph shows the equivalent representation of the emanated Rn‑222 in atoms/s from the source – the very quantity we are looking to determine here. The bottom graph presents the probability for the stability of emanation from the source over a period of nearly 100 days.

Literature

[1]    Linzmaier, D., Röttger, A.: Development of a low-level radon reference atmosphere, Applied Radiation and Isotopes, 2013; DOI: 10.1016/j.apradiso.2013.03.032

[2]    Barber, D.: Expectation Correction for Smoothed Inference in Switching Linear Dynamical Systems, Journal of Machine Learning Research, 2006

Contacts:

F. Mertes, Department 6.1, Working Group 6.13

S. Röttger, Department 6.1, Working Group 6.13