A semi-empirical approach to estimate the parameters determining the LR-115 detector response in radon measurements

One way to estimate the calibration factor (CF) of an LR-115 detector within a diffusion chamber by Monte Carlo (MC) simulation requires as input parameters the energy window (ΔE), the dependence of critical angle with energy [θ_c = f(E)] or mean critical angle (<θ_c>), and the air fraction of ²¹⁸Po atoms (f₁). Using simulated tracks and MC techniques, it was demonstrated that <θ_c> can replace θ_c = f(E) relatively accurate. Results of numerical examples validate the correct performance of developed MC code. A semi-empirical approach to estimating the parameters E_min, E_max, <θ_c> and f₁ is presented. The method is based on the calculation of the CFs by means of MC simulations (S_sim) for the range of expected input parameters values and their comparison with the experimental CF (S_exp). Parameters that minimized the deviations between S_exp and S_sim were obtained through successive iterations. <θ_c> was the parameter with the most marked and differentiated tendency to converge. The energy window and mean critical angle for our etching conditions, track counting method, and environmental conditions during exposure of LR-115 detectors were [1.5 ± 0.3, 4.0 ± 0.2]MeV and (56.1 ± 6.6)° respectively. The air fraction f₁ was found to be 0.1 for most of the used diffusion chambers. The comparison of radon concentrations obtained with the reference and test monitors, using in the latters the CFs simulated with the mean values of found parameters, demonstrate that the proposed method is applicable if uncertainties around 20% are accepted.