Detection efficiency calculation for photons, electrons and positrons in a well detector. Part I: Analytical model

An analytical model is presented to calculate the total detection efficiency of a well-type radiation detector for photons, electrons and positrons emitted from a radioactive source at an arbitrary position inside the well. The model is well suited to treat a typical set-up with a point source or cylindrical source and vial inside a NaI well detector, with or without lead shield surrounding it. It allows for fast absolute or relative total efficiency calibrations for a wide variety of geometrical configurations and also provides accurate input for the calculation of coincidence summing effects. Depending on its accuracy, it may even be applied in 4π–γ counting, a primary standardisation method for activity. Besides an accurate account of photon interactions, precautions are taken to simulate the special case of 511 keV annihilation quanta and to include realistic approximations for the range of (conversion) electrons and β−- and β+-particles.