Correction factors for the self-absorption of gamma-rays in a cylindrical sample

A distribution of distances was calculated which a gamma-ray will travel in order to escape from a cylindrical sample with a radius of 5 mm and a length of 20 mm in a solid angle of 2 sr. From this distribution, attenuation factors were calculated for linear attenuation coefficients varying from 0.001 to 9 (mm^?1) and from these corrections the self-absorption of gamma-rays can be calculated for different gamma-ray energies and for different chemical compositions of the sample. The self-absorption in iron and lead was measured for different energies and the measured values are in a good agreement with the calculated ones.