A new model calculation of the peak efficiency for HPGe detectors used in assays of radioactive waste drums

In this paper we present a new semi-empirical model calculation of the peak efficiency for unshielded HPGe detectors based on the virtual point detector and the attenuation factor concepts. The validity of the model calculation was checked by comparison with Monte Carlo efficiency values and experimental efficiencies determined for a HPGe detector type GEM 25P4 using a calibration drum. The discrepancy between experimental and calculated efficiencies is smaller than 10% in the energy range 122–1408 keV.     

Virtual point detector: Application to coincidence-summing correction in gamma-ray spectrometry

The use of an efficiency transfer method based on the virtual point detector approximation to evaluate coincidence-summing correction values for point and volume sources was examined. The method was validated by means of a comparison with experimental efficiency determinations.     

Precise measurement and calculation of coincidence summing corrections for point and linear sources

Point sources of (60)Co, (133)Ba, (134)Cs and (152)Eu, calibrated at Physikalisch-Technische Bundesanstalt were measured in 13 positions on the axis of a 50% relative efficiency p-type detector. The peak and total efficiencies were calibrated using single photon emitting nuclides. Precise experimental values of the coincidence summing corrections were evaluated in each geometry. Synthetic linear source data, as well as the corresponding peak and total efficiency curves, were prepared using the dependence of the count rates on the position of the emitting point. The coincidence summing corrections for the linear sources were computed, analyzed with respect to different approximations and compared with simulations carried out with GESPECOR.     

Transfer of the efficiency calibration of Germanium gamma-ray detectors using the GESPECOR software.

The GESPECOR software was extended to incorporate procedures for the computation of the efficiency transfer factor for cases of practical interest: (a) sources with identical geometry, but different matrices, (b) sources with similar (but not identical) geometry; and (c) transfer from a point source to a volume source. Fast and accurate algorithms. based on correlated sampling, were implemented for solving the first two cases. A procedure to take into account the imperfect charge collection in the detector was implemented.     

Application of GESPECOR software for the calculation of coincidence summing effects in special cases.

In this work, coincidence summing correction factors have been measured for 133Ba, 152Eu and 88Y point sources with a 50% relative efficiency p-type detector and a 25% relative efficiency n-type detector in two close-to-detector measurement geometries. The experimental data for 133Ba and 152Eu and the results obtained with the GESPECOR software reveal a complex structure of the conventional dead layer of the p-type detector. The high value of the coincidence summing correction factor for the 511 keV peak of 88Y, in agreement with the values computed by GESPECOR, in this case cautions against the application of the semiempirical method for evaluating coincidence summing effects.     

Efficiency calibration of high volume samples using the GESPECOR software.

In this paper the Monte Carlo simulation program GESPECOR is applied for the computation of the efficiency of an HPGe gamma-spectrometry system used for the measurement of high volume samples. The detector characterization required for Monte Carlo simulation is achieved by a trial and error procedure using the efficiency values measured with point sources placed in several positions. After detector characterization, the efficiency values appropriate for the assessment of 220l waste drums are computed and compared with experimental values.     

HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for Marinelli beaker sources using compact analytical expressions.

Direct mathematical methods to calculate total and full-energy peak (photopeak) efficiencies, coincidence correction factors and the source self-absorption of a closed end coaxial HPGe detector for Marinelli beaker sources have been derived. The source self-absorption is determined by calculating the photon path length in the source volume. The attenuation of photons by the Marinelli beaker and the detector cap materials is also calculated. In the experiments gamma aqueous sources containing several radionuclides covering the energy range from 60 to 1836 keV were used. By comparison, the theoretical and experimental full-energy peak efficiency values are in good agreement.     

ETNA software used for efficiency transfer from a point source to other geometries

The quality of the results of gamma spectrometry measurement depends directly on the accuracy of the detection efficiency in the specific measurement conditions. The purpose of this work is to examine the applicability of the efficiency transfer method using ETNA software for the computation of the efficiency in various measurement geometries on the basis of the measured efficiency for reference point source geometry located at 100 mm distance from the high purity germanium (HPGe) detector.     

Analytical approach for radioactivity correlation of disc sources with HPGe detector efficiency

The HPGe detector efficiency is measured as a function of source to detector separation using disc sources of ¹³¹I with diameter ranging from 10 to 400 mm. Detector efficiencies are characterized using single photon point-like standard sources at different distances; the calculated efficiencies for disc sources were analyzed by utilizing the double point detector model (DPDM) and the efficiency transfer method. The developed approach provided satisfactory results. The axial variation and radial dependence for disc sources efficiency determination in gamma-ray spectrometry were described with both gamma ray standard sources and measured samples as their extended sources.     

Analytical calculations of the solid angles subtended by a well-type detector at point and extended circular sources.

Knowledge of the solid angle (and consequently, the geometrical efficiency) is essential in all absolute measurements of the strengths of radioactive materials and to calibrate detectors. The method of high-efficiency gamma counting by means of well-type HPGe and NaI (Tl) detectors is widely used and has proved a powerful tool, particularly when low-activity, small-volume environmental samples are to be analyzed by gamma-ray spectrometry. In the present work, we introduce a direct analytical method for calculating the solid angle subtended by a well-type detector at axial point, non-axial point, extended circular disk and cylindrical sources. The validity of the derived analytical expressions was successfully confirmed by the comparisons with some published data (experimental and Monte Carlo).     

Calculation of total counting efficiency of a NaI(Tl) detector by hybrid Monte-Carlo method for point and disk sources.

This paper presents results on the total gamma counting efficiency of a NaI(Tl) detector from point and disk sources. The directions of photons emitted from the source were determined by Monte-Carlo techniques and the photon path lengths in the detector were determined by analytic equations depending on photon directions. This is called the hybrid Monte-Carlo method where analytical expressions are incorporated into the Monte-Carlo simulations. A major advantage of this technique is the short computation time compared to other techniques on similar computational platforms. Another advantage is the flexibility for inputting detector-related parameters (such as source-detector distance, detector radius, source radius, detector linear attenuation coefficient) into the algorithm developed, thus making it an easy and flexible method to apply to other detector systems and configurations. The results of the total counting efficiency model put forward for point and disc sources were compared with the previous work reported in the literature.     

Calibration of the 4π γ-ray spectrometer using a new numerical simulation approach

The 4π γ-counting system is well suited for analysis of small environmental samples of low activity because it combines advantages of the low background and the high detection efficiency due to the 4π solid angle. A new numerical simulation approach is proposed for the HPGe well-type detector geometry to calculate the full-energy peak and the total efficiencies, as well as to correct for the coincidence summing effect. This method depends on a calculation of the solid angle subtended by the source to the detector at the point of entrance, (Abbas, 2006a). The calculations are carried out for non-axial point and cylindrical sources inside the detector cavity. Attenuation of photons within the source itself (self-attenuation), the source container, the detector’s end-cap and the detector’s dead layer materials is also taken into account. In the Belgium Nuclear Research Center, low-activity aqueous solutions of ⁶⁰Co and ⁸⁸Y in small vials are routinely used to calibrate a γ-ray p-type well HPGe detector in the 60–1836 keV energy range. Efficiency values measured under such conditions are in good agreement with those obtained by the numerical simulation.     

Monte Carlo determination of full energy peak efficiency for a HPGe detector.

The Monte Carlo method was used to determine full energy peak efficiency of a high-purity germanium (HPGe) co-axial detector within the energy range of 59.5-1836 keV. Plotted ratios of the experimentally derived efficiency data over the fitted values showed oscillations at certain energies attributed to the characteristics of the detector. Results obtained by the Monte Carlo yielded deviations between 0.2 to 12% from the experimental data.     

Experimental and MC determination of HPGe detector efficiency in the 40-2754 keV energy range for measuring point source geometry with the source-to-detector distance of 25 cm.

A precise model of a 40% relative efficiency p-type HPGe detector was created for photon detection efficiency calculation using the MCNP code. All detector parameters were determined by different experiments. No experimental calibration points were used for the modification of detector parameters. The model was validated by comparing calculated and experimental full energy peak efficiencies in the 40-2754 keV energy range, for point-source geometry with the source-to-detector distance of 25 cm.     

The applicability of the sum-peak formula to extended sources

When the “sum-peak” formula is used for the calculation of the disintegration rate of radioisotopes, the results are too low for extended sources, whereas the true disintegration rate is obtained for a point source. This effect is not a consequence of absorption in an extended source, but is due to the fact that the detector does not have the same efficiency for all the positions in the source. Estimates of the magnitude of the effect are derived.     

Uncertainty analysis of in-situ gamma spectrometry measurements of air cleaning filter cartridges and 200 L drums by a HPGe detector

This work deals with most significant sources of uncertainty in determination of radionuclides massic activity in 200 L drums with radioactive waste (RAW) from decommissioning of nuclear power plant (NPP) A1 and operational air cleaning filters coming from different parts of NPP's ventilation system. It turned out that the most significant source of uncertainty is determination of photo peak detection efficiency, in particular measurement geometry. The detection efficiency of HPGe detector has been determined by calculation using ISOCS software (In Situ Object Counting System) and detector characteristics delivered by the manufacturer (LABSOCS). The detector efficiency is influenced by various factors like measurement geometry, deviation from standard geometry, environmental characteristics, sample properties (density, material composition), used collimator etc. Mentioned factors and their contributions to the uncertainty of detection efficiency and thus to the total uncertainty of massic activity determination have been individually evaluated in the paper. The main part of the work consists of evaluation of maximum uncertainty factor due to presence of hypothetical point source in measurement volume for both types of measurement geometry.     

Analytical formulae for well-type NaI (Tl) and HPGe detectors efficiency computation.

A straightforward analytical formulae for the computation of total and full-energy peak efficiencies of NaI (Tl) and HPGe well-type detectors are deduced. In addition, the attenuation of photons by the source container and the detector end cap materials is presented in a direct mathematical expression. Results are compared with previous treatments.     

Application of PENELOPE code to the efficiency calibration of coaxial germanium detectors.

The code PENELOPE is applied here to the efficiency calibration exercise described in the EUROMET project 428 [Lépy et al., 2001. Appl. Radiat. Isot. 55, 493]. We evaluated the peak efficiencies for a coaxial HPGe detector in the range 60-2000 keV, for point sources located at various distances from the detector and for a cylindrical box containing two different matrixes: a low-density silica and a hydrochloric acid solution. After an optimization of several detector parameters, the results were in good agreement with the experimental values.     

Automated construction of detector models for efficiency interpolation in gamma-ray spectrometry.

A method was developed for automated construction of detector models in gamma-ray spectrometry, which can be used in Monte Carlo calculations of efficiency calibration curves. Full-energy peak efficiencies were first measured for different gamma-ray energies and for a given sample-detector arrangement and then calculated by the Monte Carlo method. For these calculations a detector model was employed along with a computer algorithm, which seeks agreement between the experimental efficiencies and the calculated ones by automatically determining the parameters of the model. The resulting agreement of the calculated data with the experimental one was within the relative uncertainty of the latter (3-4%) and the parameters of the detector models obtained were close to the values specified by the manufacturers. The detector models thus constructed can then be used for interpolation of calibration curves.     

An analytical calculation of the peak efficiency for cylindrical sources perpendicular to the detector axis in gamma-ray spectrometry.

An analytical expression for the so-called full-energy peak efficiency epsilon(E) for cylindrical source with perpendicular axis to an HPGe detector is derived, using point-source measurements. The formula covers different measuring distances, matrix compositions, densities and gamma-ray energies; the only assumption is that the radioactivity is homogeneously distributed within the source. The term for the photon self-attenuation is included in the calculation. Measurements were made using three different sized cylindrical sources of 241Am, 57Co, 137Cs, 54Mn, and 60Co with corresponding peaks of 59.5, 122, 662, 835, 1173, and 1332 keV, respectively, and one measurement of radioactive waste drum for 662, 1173, and 1332 keV.