Theoretical full-energy peak efficiency determination for LaBr₃:Ce detectors

Lanthanum bromide scintillators doped with cerium, LaBr₃:Ce, are widely used as room-temperature detectors for gamma-ray spectroscopy because of their good energy resolution, high detection efficiency, and fast timing response. Accurate modeling of their efficiency is therefore important for activity determination, efficiency calibration, and quantitative gamma-ray spectrometry. In this work, an analytical-semi-empirical formulation is presented for the full-energy peak efficiency of cylindrical LaBr₃:Ce detectors. The efficiency is evaluated as the product of the total detection efficiency and the peak-to-total ratio. The total efficiency is calculated using analytical radiation-transport integrals for point, disk, and cylindrical volumetric sources positioned along the detector symmetry axis, building on classical total-efficiency formulations for cylindrical detectors. The peak-to-total ratio is described by a semi-empirical mean-chord-length formalism, with an energy-dependent parameter representing the average number of photon interactions inside the detector volume. The main contribution of the present approach is the combination of these analytical total-efficiency calculations with a peak-to-total formalism adapted to LaBr₃:Ce detectors, together with an explicit self-attenuation correction for cylindrical volumetric sources. The resulting framework provides a computationally efficient and physically transparent tool for estimating full-energy peak efficiencies in well-defined axial geometries. The calculated efficiencies show good agreement with Monte Carlo simulations and experimental data reported in the literature.