In the gamma-ray spectroscopy field, the radiometric examination for small
quantities of natural samples is extremely significant. Therefore, the
gamma-ray spectrometry calibration process must be prepared with good
precision for several energies, matrices of sources or samples, and
source-to-detector shapes. This manuscript considers a new uncomplicated
analytical computation technique to calculate the effective geometrical
solid angle and the efficiency of cubic scintillation crystal with a side
cylindrical hole. The computations can be done by using a simple method,
with a few essential limitations, that describes radioactive point sources
located inside the side cylindrical hole and a high-efficiency cubic NaI(Tl)
detector, come together with a low background as well. The technique
stands on a trouble-free solid angle analytical formula for the detection
system, using an accurate relation for the detector cavity, united with
rough formulas controlling the interactions in the gamma-ray source and the
materials introduced in between the source and the gamma-ray spectrometry.
This new technique is not restricted to certain sources, because several
source shapes can correspond to a homogeneous huge number of point sources
and the detector geometry can be represented as a set of border points. The
technique simply can be useful to obtain the full-energy peak efficiency
in the future, challenging developments for low-energy gamma-ray
spectroscopy.