Calibration source selection and covariance uncertainty propagation in HPGe efficiency calibration

Efficiency calibration in high purity germanium (HPGe) spectroscopy is a process that must be performed before a measurement of source activity can take place. Any sources of error present in the efficiency calibration should be carefully propagated to subsequent measurements for applications in which high precision is important. This study examines how covariance analysis propagates dominant sources of uncertainty to the best-fit coefficients of a linear model and how the user’s selection of calibration isotopes shapes the uncertainty band around the model. To do this, a MCNP pulse-height tally (F8) simulation of nine hypothetical calibration sources was run against a validated model of a real-world coaxial HPGe detector, with 20 high-intensity gamma energies ranging from 88 to 1836 keV. Absolute efficiencies were fitted by method of generalized least squares to identify best-fit parameters for a linear model. A covariance matrix was carefully constructed to propagate dominant sources of uncertainty caused by counting statistics and correlated calibration activities to the best-fit coefficients of the model for 511 combinations of calibration isotopes. The data produced by this procedure was verified against the σ/N trend expected for N same-σ uncorrelated data.