Evaluation of energy efficiency fitting functions for HPGe detectors

Numerous and diverse mathematical methods have been used to model the full-energy photopeak (FEP) efficiency-to-energy relationship. All of the methods attempt to approximate this relationship using numerical analysis methods. Sophistication of the mathematics does not guarantee a meaningful and accurate determination of the physical relationships being modeled. This discrepancy stems from the fact that the data being modeled may suffer from spectral and nuclear effects which alter the counts in the full energy photopeak resulting from absorption and attenuation in the active volume of the diode, in the intervening materials between the detector diode and source, within the source itself, and in the shielding around the detector and source. Data must be free of these effects either as a result of acquiring the spectral data in geometries which minimize or eliminate these effects, or by pre-treatment of the net area counts to correct for these effects. If these corrections are not possible, then the choice of mathematical fitting method should be constrained to provide results which are consistent with physical-theoretical considerations of the energy-efficiency relationship being modeled. If possible, the method chosen should also provide a meaningful estimate of the uncertainty associated with the approximation of this function.