Monte Carlo calculation of geometry-dependent true coincidence summing correction factors for the gamma-rays of 214Bi in HPGe detectors

True coincidence summing (TCS) effects in gamma-ray spectrometry introduce significant systematic uncertainties in activity determinations, particularly for radionuclides with complex decay schemes such as 214Bi. This study presents a comprehensive Monte Carlo investigation of TCS correction factors (CFs) for seven major gamma-ray lines of 214Bi. The primary contribution of this study is the systematic decoupling of detector geometry effects: nine distinct HPGe detector configurations were simulated with varying crystal dimensions, dead layers, and hole geometries, followed by an isolated analysis of crystal radius versus crystal length contributions for both point and extended source geometries. The decay scheme of 214Bi was meticulously modeled using Nucleide 2000 data, incorporating all beta branches, gamma transitions, internal conversion coefficients, and cascade probabilities to ensure high-fidelity representation of the decay scheme. Results demonstrate that crystal radius exerts a substantially stronger influence on TCS CFs than crystal length, with point source values at 609.3 keV increasing by 18.2% across the radius range of 2.1–4.5 cm, compared to only 3.7% variation across the length range of 3–11 cm. Extended source geometries reduce TCS CFs by 5%–11% compared to point sources across all configurations, highlighting the mitigating effect of distributed sources. Energy-dependent behavior is also evident: the 609.3 keV line exhibits strong summing-in (CF > 1.3 for large detectors), while the 1377.7 keV line shows dominant summing-out (CF < 0.86). These findings provide gamma-ray spectrometrists with insight into the relative importance of detector dimensions for TCS effects, suggesting that crystal radius is the primary geometric parameter influencing coincidence summing corrections. The observed trends illustrate how TCS corrections vary with detector dimensions, offering spectrometrists a basis for understanding the relative sensitivity of these corrections to different geometric parameters.