Mathematical approach to determine the linear attenuation coefficient without collimator in gamma-ray spectrometry.

The linear attenuation coefficient is an important factor in the correction of self-attenuation. In this study, a cone beam from a source of ∼1 µCi was utilised, not equipped with the collimator, and a complete geometric configuration was mathematically modelled. Samples of NaCl, Na2CO3 and (NH4)2SO4 were used to verify the mathematical model. The linear attenuation coefficient can be calculated within ∼4 % of difference in the cylindrical sample at energies of 59.5, 121.8, 244.7, 344.2 and 444.0 keV.