Theoretical basis for long-term measurements of equilibrium factors using LR 115 detectors

In this paper, we propose a method to determine the equilibrium factor using a bare LR 115 detector. The partial sensitivities ρ_i of the LR 115 detector to ²²²Rn and its alpha-emitting short-lived progeny, ²¹⁸Po and ²¹⁴Po, were investigated. We first determined the distributions of lengths of major and minor axes of the perforated alpha tracks in the LR 115 detector produced by ²²²Rn, ²¹⁸Po and ²¹⁴Po through Monte Carlo simulations. The track parameters were calculated using a track development model with a published V function, by assuming a removed active layer of 6.54 μm. The distributions determined for different alpha emitters were found to completely overlap with one another. This implied equality of partial sensitivities for radon and its progeny, which was also confirmed through analytical considerations. Equality of partial sensitivities makes possible convenient measurements of the proxy equilibrium factor F_p, which is defined in the present work as (F₁+F₃) and is equal to the ratio between the sum of concentrations of the two alpha emitting radon progeny (²¹⁸Po+²¹⁴Po) to the concentration of radon gas (²²²Rn). In particular, we have found F_p=(ρ/ρ_itC₀)?1, where ρ (track/m²) is the total track density on the detector, ρ_i=0.288×10^?2 m, t is the exposure time and C₀ (Bq/m³) is the concentration of ²²²Rn. If C₀ is known (e.g. from a separate measurement), we can obtain F_p. The proxy equilibrium factor F_p is also found to be well correlated with the equilibrium factor between radon gas and its progeny through the Jacobi room model. This leads to a novel method for long-term determination of the equilibrium factor.