An artificial neural network with analytical self-attenuation correction for rapid efficiency calibration of HPGe detectors

Abstract

Abstract Efficiency calibration of HPGe detectors for environmental gamma-ray spectrometry requires knowing the full energy peak efficiency (FEPE) for each combination of photon energy, sample geometry and material composition. We present a hybrid model, combining an artificial neural network with a fixed analytical correction layer, that decouples this problem into a multilayer perceptron—trained on a single reference material to learn FEPE as a function of energy and sample height—and the analytical layer, which corrects for self-attenuation using XCOM mass attenuation coefficients. Two levels of geometric correction are evaluated: the classical parallel beam (PB) formula and a geometric ray-tracing (RT) approach with solid-angle weighting. The methodology is validated on two HPGe detectors of fundamentally different geometry—a well-type and a planar extended-range (XtRa) detector—using characterised PENELOPE Monte Carlo models as the data source. For each detector, the model is trained with IAEA-RGU-1 and tested against eight materials spanning densities from $${1.0}\,\text {g cm}^{-3}$$ (water) to $${2.7}\,\text {g cm}^{-3}$$ (ilmenite), at unseen energies and unseen sample heights. The solid-angle weighted ray-tracing correction is universally superior to the parallel beam formula for both detector geometries, achieving a mean pipeline MAPE across all eight test materials of 2.7% ( $$R^2 = 0.994$$ ) for the well-type detector and 1.8% ( $$R^2 = 0.999$$ ) for the XtRa, compared to 4.0% and 2.4% with the parallel beam formula. With the ray-tracing correction, the pipeline MAPE remains below 5% for all materials on both detectors, including ilmenite ( $$\rho = {2.7}\,\text {g cm}^{-3}$$ ). Once trained, the model yields FEPE predictions in under one second for any sample height and material, compared to tens to hundreds of seconds per Monte Carlo simulation, depending on sample size and the statistical precision required.