Towards the definition of the optimum height of voluminous cylindrical sources in gamma-ray spectroscopy

We show that for cylindrical voluminous sources in gamma-ray spectroscopy the relative error of the spectral intensity of a low-energy spectral line, as the height of the source increases, saturates faster than the spectral intensity itself. This significantly reduces the quantity of the required sample material as compared to that based on the usual considerations of the spectral intensity only. We also demonstrate that there exists a weakly pronounced height of the source (the source size) which minimizes the relative error of the intensity of a given low-energy spectral line. Due to the smallness of the effect the benefit of introducing the concept of the truly optimum size of the source is more on a psychological side, one should feel easier using an optimum quantity of the source material than merely a sufficient one, as is otherwise the case