M. Korun

A semi-empirical model of the efficiency curve for extended sources in gamma-ray spectrometry

Abstract A semi-empirical formula for the full energy peak efficiency of extended sources in the range from 4 to 3000 keV is presented, taking into account self-absorption in the sample. The formula is based on physically sound premises and features a low number of free parameters, which exhibit physically viable values. Along with very good fits it furnishes, this makes the model suitable for extrapolation of the efficiency values towards the energies where measurements are not available. The model we use is based on the assumption of independence of the intrinsic peak-to-total ratio on the emission point of the gamma-ray. For extended sources, it features a term which takes into account the attenuation of gamma-rays in the sample. The proposed model was tested against a number of experimental efficiency curves measured with point and extended sources on n- and p-type HPGe detectors, as well as against data sets obtained from Monte Carlo calculations using the GEANT and MCNP codes.

Close-geometry efficiency calibration in gamma-ray spectrometry using radio-nuclides with a two-step cascade decay

Abstract When efficiency calibration is performed in gamma-ray spectrometry with point sources in close geometry, radio-nuclides emitting photons of a single energy are usually utilized in order to avoid problems arising from true coincidence summing. Radio-nuclides emitting gamma-rays in a simple two-step cascade are therefore not considered suitable for such measurements. It is, namely, not possible to determine the full-energy-peak and total efficiencies for the gamma-rays such radio-nuclides emit from the system of equations which determine the number of counts registered in individual peaks in their spectra. A method was developed to overcome this difficulty by making use of additional constraints, based upon sound physical grounds, which can be imposed on these equations to render the combined system solvable. The accuracy of the method was successfully tested with point sources of 60 Co , 46 Sc and 94 Nb . The method provides six additional energies in the range between 700 and 1400 keV for which full-energy-peak and total efficiencies can be determined, which is important in view of the fact that only seven single-energy emitters are generally available for close-geometry calibration. We applied the method to several distances of the point source from the detector and studied the influence of angular correlations on the determination of the efficiencies. The effect is significant for total efficiencies and larger distances of the source from the detector, which has not been noted before.

Reliability of the peak-analysis results in gamma-ray spectrometry for high relative peak-area uncertainties.

When measurement results with values near the decision threshold are being considered, a relative uncertainty of 60% is expected. Since such measurement results can be reported, the performance of the peak-analysing software for gamma-ray spectra needs to be examined for peaks that have a large relative uncertainty. The investigation was performed on a series of spectra measured with a HPGe detector under identical counting conditions. It was found that under a limit value of the relative peak area uncertainty the peak-analysis results are reliable with respect to both the peak location and the peak area evaluation. At relative uncertainties exceeding this uncertainty, the probability of type-II errors increases and a systematic influence on the peak area occurs, which originates in fluctuations of the continuous background in the vicinity of the peak. For the counting conditions used in this investigation, the limit relative uncertainty is about 35%, and whereas a systematic influence can be taken into account by a correction factor, the frequency of the type-II errors can only be reduced at the expense of increasing the frequency of the type-I errors.

Calculation of the decision thresholds in gamma-ray spectrometry.

A method was developed for calculating the decision thresholds for gamma-ray spectrometric measurements. At the energies where gamma-ray emitters that are present in the nuclide library, but were not identified in the spectrum, radiate, peaks are supposed to appear. The peak areas are calculated by fitting, using the method of least squares, the spectral region of the supposed peaks with a continuous background and the spectrometer response function at the gamma-ray energies where the supposed peaks are positioned. The null measurement uncertainty of a gamma-ray emitter is obtained as the uncertainty of the weighted average of the activities calculated from the areas of the supposed peaks in a spectrum where the specified activity of the gamma-ray emitter is zero. For the calculation of the decision threshold the null measurement uncertainty is used. These decision thresholds overestimate the critical limits calculated with the Currie formula by about 10% in the case of single gamma-ray emitters. For multi-gamma-ray emitters the decision thresholds yield smaller values than the Currie formula. The presence of a peaked background or peaks that are near the supposed peaks increases the decision threshold considerably.

An analysis of the causes of discrepant results in proficiency tests in a testing laboratory

We present an analysis of the results reported in the framework of proficiency tests performed in the years 2003-2007 in a gamma-ray spectrometry laboratory. Measurements of 102 samples and 622 results reporting the activities or activity concentrations of 39 gamma- or X-ray emitters are included in the study. A total of 61 results were found to be in disagreement with their target values. The cause of the disagreement was not found for only 21 discrepant results.

Quality control of gamma-ray spectrometry measurements

Specific techniques have been implemented to assess the quality of routine gamma-ray measurements and the associated analysis procedures. Appropriate steps monitor three factors influencing the quality of performance: the performance of the spectrometer, the quality of the measurement and the quality of the peak analysis. In order to illustrate the approach, time dependencies of parameters describing the performance of the spectrometer, the quality of the measurements and the sample activities are presented.

Quality assurance of automated gamma-ray spectrometric analysis

Fully automatic gamma-ray spectrometric analysis procedures perform complete processing of the spectrum without intervention of the operator. In order to maintain the reliability of the final results the analysis checks the intermediate results automatically. When a disagreement is identified by such a check the uncertainty of the intermediate results is increased in order to accommodate the disagreement. The increased uncertainty is propagated into the uncertainty of the final results in order to take into account the disagreement. This approach was implemented in Canberras Genie ESP gamma-ray spectrometry package for examining the results of the peak analysis. In addition to this intermediate check also a-posteriori checks of the final results can be performed by statistical analysis. Such analysis shows whether the results are under statistical control and can discover sources of variability which are not taken into account in the uncertainty budget.

Calculation of the correlation coefficients between the numbers of counts (peak areas and backgrounds) obtained from gamma-ray spectra.

Two simple methods for calculating the correlations between peaks appearing in gamma-ray spectra are described. We show how the areas are correlated when the peaks do not overlap, but the spectral regions used for the calculation of the background below the peaks do. When the peaks overlap, the correlation can be stronger than in the case of the non-overlapping peaks. The methods presented are simplified to the extent of allowing their implementation with manual calculations. They are intended for practitioners as additional tools to be used when the correlations between the areas of the peaks in the gamma-ray spectra are to be calculated. Also, the correlation coefficient between the number of counts in the peak and the number of counts in the continuous background below the peak is derived.

Probability of Type-I errors in the peak analyses of gamma-ray spectra.

The probability density of Type-I errors in the peak-locating step of the spectra-analyzing procedure was empirically determined at a low value of the sensitivity parameter for peak recognition as a function of the height of the continuous spectral background and peak width. On the basis of this probability density, the number of Type-I errors for any spectral shape and FWHM calibration can be estimated. A criterion that is based on the relative peak-area uncertainty and the relative difference between the peak width obtained from the FWHM calibration and the width reported by the peak-analyzing program, as a measure of the believability that a located peak presents a Type-I error, is established. In addition, we demonstrate that the peaks having the largest believability are most likely to originate from Type-I errors. Using this criterion, the number of peaks, not identified in the identification step of the spectra analyzing procedure, to be checked for their origin can be reduced in accordance with the number of estimated Type-I errors.

Calculation of the detection limits by explicit expressions

A method for calculating the approximate value of the detection limit for measurements of ionizing radiation is presented. The method can be applied when the indication corresponding to the detection limit and its uncertainty are given as explicit functions. Then also the detection limit can be calculated explicitly, which means that the iteration procedure for its calculation can be avoided. The advantage of the method becomes apparent when the iteration process for calculating the detection limit is difficult to apply.