Linear classes of Ge(Li) detector efficiency functions

The statistical and computational advantages which arise from using a linear rather than a non-linear class of fitting functions are discussed. Two linear classes of Ge(Li) detector efficiency functions are constructed, and their range of applicability assessed using a large number of independent efficiency data sets. One of these classes, defined by ϵ(E, p) = [p1 + p2ln(E) + p3ln2(E) + p4ln3(E) + p5ln5(E) + p6ln7(E)]E , where E represents energy in MeV, is shown to provide a satisfactory representation of Ge(Li) detector efficiency over the energy range (80/120–1850) keV, for efficiency measurements with standard deviations greater than 1%. It is shown that when the full covariance matrix of the measured efficiency values is not used, the goodness-of-fit test based on the chi-square approximation is no longer valid, and the likelihood of inconsistencies between measured and fited efficiency values remaining undetected is increased.