Analytical formulae for borehole scintillation detectors efficiency calibration

The borehole scintillation detectors (with central borehole) are useful for the identification and quantification of unknown gamma-ray emitting radionuclides in geological and environmental samples due to the near 4π solid angle that can be obtained with them. In addition, the 4π gamma-ray-counting is a well-established method for direct activity measurements, and is especially suited for radionuclides with complex gamma-ray spectra. A straightforward theoretical approach was carried out to calculate the efficiencies (total, εT and geometrical, εg) of borehole scintillation detectors. The approach depends on the accurate calculation of two important factors: the path length, d, the photon traverses within the active volume of a gamma detector, and the geometrical solid angle, Ω, subtended by the source to the detector at the point of entrance. These two factors are theoretically derived through straightforward analytical formulae. Furthermore, the attenuation of photons by the source container and the detector housing materials is also treated by calculating the photon path length through these materials. The comparisons with the experimental and Monte Carlo method works reported in the literature indicate that the present approach is useful in the efficiency calibration of such complicated gamma-ray spectrometer.