Analytical calculations of the solid angles subtended by a well-type detector at point and extended circular sources

Knowledge of the solid angle (and consequently, the geometrical efficiency) is essential in all absolute measurements of the strengths of radioactive materials and to calibrate detectors. The method of high-efficiency γ counting by means of well-type HPGe and NaI (Tl) detectors is widely used and has proved a powerful tool, particularly when low-activity, small-volume environmental samples are to be analyzed by γ-ray spectrometry. In the present work, we introduce a direct analytical method for calculating the solid angle subtended by a well-type detector at axial point, non-axial point, extended circular disk and cylindrical sources. The validity of the derived analytical expressions was successfully confirmed by the comparisons with some published data (experimental and Monte Carlo).