A fitting algorithm based on simulated annealing techniques for efficiency calibration of HPGe detectors using different mathematical functions

Abstract

In this work several mathematical functions are compared in order to perform the full-energy peak efficiency calibration of HPGe detectors using a 126 cm3 HPGe coaxial detector and gamma-ray energies ranging from 36 to 1460 keV. Statistical tests and Monte Carlo simulations were used to study the performance of the fitting curve equations. Furthermore the fitting procedure of these complex functional forms to experimental data is a non-linear multi-parameter minimization problem. In gamma-ray spectrometry usually non-linear least-squares fitting algorithms (Levenberg–Marquardt method) provide a fast convergence while minimizing w2 R, however, sometimes reaching only local minima. In order to overcome that shortcoming a hybrid algorithm based on simulated annealing (HSA) techniques is proposed. Additionally a new function is suggested that models the efficiency curve of germanium detectors in gamma-ray spectrometry