To understand the nuclear structure for most elements, it is essential to
investigate the nuclear excitations by using high precision gamma-ray
spectroscopy in which intensive measurements should be carried out. This is
becoming a new challenge for the radiation scientific community nowadays,
where the instrumentations and technical advances must be developed to be
used in a wide range of applications. To discover the weakest nuclear
reaction, the maximum probability of the detection system of the total
energy of any released individual photon must be determined. In this work, a
new mathematical method to calculate the absolute full-energy peak
efficiency of asymmetrical polyhedron germanium detector is presented. This
type of detector can be arranged in array, forming ?complex detectors of
encapsulated germanium crystals?, with the solid angle reaching 82 % of
total solid angle coverage, i. e., with the highest possible efficiency and
with a good quality of spectral response. In addition, the photon path
length was enclosed in the mathematical method to determine its attenuation
through different materials such as, the detector active medium
and any other material in-between source-detector system during the
measuring process. The comparison between the efficiency calculated in this
work and that of the published Monte Carlo simulation showed a good
agreement and a small variation. However, the method discussed in the
current work can be useful in nuclear safeguards, in overcoming the huge
difficulties in identification of the energy range of radioactive isotopes
and their quantities in nuclear waste.