Recently, there have been several significant improvements in the area of the
radiation detection system and its instruments, especially those using
scintillation or semiconductor gamma ray detectors. Scientists and
technicians are interested in studying this progress, which can be useful
for the detector's operation and its basic properties, such as energy,
shape, and efficiency calibration. In this work, an extended study of
various mathematical formulas was conducted to obtain the efficiency
best-fitting function, that covers the measured values from low to high
energy regions. They can be used to represent the efficiency of a
high-purity germanium detector in the regions where accuracy and maximum
speed in optimizing the calibration process are very important for gamma
spectroscopy. Determination of the activity of environmental samples
mainly depends on the efficiency calibration curve of the detection
system. The gamma ray energy in the range from 59.54 up to 1408.01 keV used
in this work was obtained by using a set of standard radioactive gamma ray
sources of certified intensity. The current data analysis shows that most of
the mathematical formulas, which represent the fitting curve for the
detector full-energy peak efficiency, were quite agreeable with the experimental results.