COVARIANCE ANALYSIS AND FITTING OF GERMANIUM GAMMA-RAY DETECTOR EFFICIENCY CALIBRATION DATA

The measurement of neutron-induced reaction cross sections often requires detection of either prompt gamma rays or gamma rays emitted during the decay of radio nuclides. This paper describes the analytical procedures we use to generate calibrations for germanium gamma-ray detector full-energy-peak efficiency ε{lunate} versus photon energy E, and to predict the associated uncertainties. Our method, which involves fitting a parameterized regression formula to measured data by the principle of least squares, is widely applicable beyond the specific problem considered here. It differs from most commonly used methods in that comprehensive use is made of available information on all known sources of random and systematic (correlated) error associated with the calibration process. This is accomplished through the formation and application of a calibration-data covariance matrix. Objective prediction of the errors in subsequently derived quantities (e.g., detector efficiencies at energies not directly represented in the calibration data) is then achieved through error propagation. Specifically, this paper discusses our experiences in fitting the particular empirical formula In ε{lunate} = Σk-1m pk(InE)k-1 to measured calibration data at gamma-ray energies from just above 200 keV to several MeV. A numerical example is provided to demonstrate the utility of this approach. © 1990.