Theoretical and experimental estimation of self-attenuation corrections in determination of $^{210}Pb$ by gamma-spectrometry with well Ge detector

This paper aims at giving a practical method for routine measurements of the activity of 210Pb in solids by γ-spectrometry with a well Ge crystal. Since the γ-rays emitted by 210Pb have a low energy, 46.5 keV, the proportion of pulses counted in the crystal depends strongly on the sample composition trough self-attenuation within the sample itself. Self-attenuation can be calculated by use of a Monte Carlo method based on a model. In the present work two codes, namely GEANT 4 and a Laboratory code, gave results in agreement. However, both necessitate a good knowledge of the sample composition, of the detector geometry and of the computing programs. In order to circumvent such drawbacks, an experimental technique was developed, where the overall counting efficiency can be derived directly from the transmission of 46.5 keV γ-rays through the sample, by means of a linear relationship. Such correlation was observed experimentally with samples of known activity and the approach was validated by verification that a linear relation preliminary exists between the transmission and the calculated self-absorption.