A new FSA approach for in situ $gamma$-ray spectroscopy

An increasing demand of environmental radioactivity monitoring comes both from the scientific community and from the society. This requires accurate, reliable and fast response preferably from portable radiation detectors. Thanks to recent improvements in the technology, $\gamma$-spectroscopy with sodium iodide scintillators has been proved to be an excellent tool for in-situ measurements for the identification and quantitative determination of $\gamma$-ray emitting radioisotopes, reducing time and costs. Both for geological and civil purposes not only $^{40}$K, $^{238}$U, and $^{232}$Th have to be measured, but there is also a growing interest to determine the abundances of anthropic elements, like $^{137}$Cs and $^{131}$I, which are used to monitor the effect of nuclear accidents or other human activities. The Full Spectrum Analysis (FSA) approach has been chosen to analyze the $\gamma$-spectra. The Non Negative Least Square (NNLS) and the energy calibration adjustment have been implemented in this method for the first time in order to correct the intrinsic problem related with the $\chi ^2$ minimization which could lead to artifacts and non physical results in the analysis. A new calibration procedure has been developed for the FSA method by using in situ $\gamma$-spectra instead of calibration pad spectra. Finally, the new method has been validated by acquiring $\gamma$-spectra with a 10.16 cm x 10.16 cm sodium iodide detector in 80 different sites in the Ombrone basin, in Tuscany. The results from the FSA method have been compared with the laboratory measurements by using HPGe detectors on soil samples collected in the different sites, showing a satisfactory agreement between them. In particular, the $^{137}$Cs isotopes has been implemented in the analysis since it has been found not negligible during the in-situ measurements.

💡 Research Summary

The paper presents a comprehensive improvement to in‑situ gamma‑ray spectroscopy using a portable NaI(Tl) detector by integrating a full‑spectrum analysis (FSA) framework with two key enhancements: a non‑negative least‑squares (NNLS) constraint and an energy‑calibration adjustment. Traditional FSA solves the linear model N(i)=∑ C_k S_k(i)+B(i) by minimizing χ², but without constraints the solution can assign negative counts to some energy channels, producing non‑physical sensitive spectra and cross‑talk between isotopes. By enforcing NNLS, all channel counts are forced to be zero or positive, eliminating these artifacts and yielding physically realistic spectra, especially for the anthropogenic isotope ¹³⁷Cs whose peak lies in a region crowded by Compton background and neighboring natural peaks.

The authors also address the systematic energy shift that occurs in field measurements due to temperature, detector aging, or environmental conditions. During calibration they introduce an adjustable energy‑scale parameter that aligns measured peaks with reference energies, thereby improving the fidelity of the fundamental spectra S_k(i) used in the linear model.

A novel calibration strategy replaces the conventional concrete or KCl pads with a set of carefully selected field sites. Each calibration site is chosen for a dominant concentration of one radionuclide (K, U, Th, or ¹³⁷Cs) while satisfying criteria such as planar geometry, homogenous secular equilibrium, and minimal vegetation or moisture variation. At each site 5–12 soil samples are collected within a 10 m radius, dried, homogenized, sealed for radon equilibrium, and analyzed with a high‑resolution, dual‑HPGe “MCA‑Rad” system. These laboratory measurements provide the true concentrations C_k that are fed into the matrix equation