Efficiency calibration of HPGe detector without standard source based on surface point detection efficiency database

<bold>Background</bold>Efficiency calibration method without standard source has the advantages of convenience, rapidity, and low cost in the volume-source efficiency calibration of high-purity germanium (HPGe) detector. The detection efficiency of volume source can be obtained through numerical integration of point source detection efficiencies at different positions from a pre-prepared database. Nevertheless, this method is limited by the numerous positions of point sources, leading to a long computation time. For large volume-sources or distant sources, supplementary calculations to update the detection efficiency database are often required.<bold>Purpose</bold>This study aims to propose a new method for establishing a detection efficiency database and combines numerical integration to achieve efficient calculation of the volumetric source detection efficiency for HPGe detector without standard source.<bold>Methods</bold>Firstly, the Geant4 software was used to sample the position and direction of the γ ray incident on the detector surface, thus the detection efficiency database under different incident positions and directions was established. Then, the efficiency of γ rays reaching the detector surface after being self-absorbed by the bulk source medium was calculated through integration. Finally, by combining the efficiency of γ ray reaching the detector surface and the detection efficiency database, the bulk detection efficiency calibration for HPGe was realized through numerical integration.<bold>Results</bold>The volume-source calculation results indicate that the relative deviation of detection efficiency between this method and fully Geant4 simulation results is within 6%, while the maximum relative deviation for point sources is less than 8%. These findings are consistent with the commonly used efficiency calibration methods for volume sources. Furthermore, for the same precision, the time required to establish the database using this method has been reduced to one-tenth of the original.<bold>Conclusions</bold>This indicates the method can effectively improve the calculation speed of the mathematical efficiency calibration, and facilitate the development of sourceless efficiency calibration software. Comparison results show that the method proposed in this study can effectively improve the calculation speed of the mathematical efficiency calibration, and facilitate the development of sourceless efficiency calibration software.