Validation of the ray-tracing Monte-Carlo code tRAYcy for geometry and coincidence-summing corrections in environmental gamma-ray spectrometry.

Accurate determination of radionuclide activities in environmental samples requires the detector response to be known for the specific detector-sample geometry, and requires correction for the matrix and density differences between calibration and sample as well as for true coincidence summing (TCS). We demonstrate the scientific validity and practical applicability of the ray-tracing Monte-Carlo code tRAYcy for these tasks by analysing two international proficiency-test materials with assigned reference activities: a soil matrix (ρ=1.70gcm-3) and a ground green-tea matrix (ρ=0.62gcm-3), both measured in 1l Marinelli geometry on a 40% relative-efficiency N-type HPGe detector calibrated with an aqueous mixed-γ source. Activities were evaluated under successive correction strategies - no correction, geometry (efficiency-transfer) correction, TCS correction, and the two combined - and, additionally, using a sourceless mathematical calibration in which the full-energy-peak efficiency was simulated directly for the sample geometry rather than transferred from the measured source. Uncorrected analyses showed systematic deviations of both signs, with absolute deviations reaching approximately 11%. Fully corrected results agree with the assigned reference values within 4% for 40K, 60Co, 133Ba, 134Cs, and 137Cs. Larger deviations were observed for 241Am in the soil sample (6.6%) and 210Pb in the green-tea sample (-7.7%). The mathematically calibrated activities reproduce the assigned reference values, showing that a physically modelled efficiency can replace a matched calibration source. Finally, complete synthetic spectra generated for both samples in single simulations reproduce the principal measured spectral structures across the investigated energy range, including nuclide-specific contributions, summing features, escape structures, and the Compton continua. Localised discrepancies remain in the low-energy X-ray region and below prominent high-energy peaks. The results show that physically motivated Monte-Carlo modelling delivers accuracy consistent with the assigned reference values for real environmental matrices.