Introduction

The methods based on gamma-ray measurements are frequently applied for the determination of activity or for nuclide identification. For precise determinations these methods must be validate in conformity to national, regional or international standards or in the absence of the above on the base of validated calibration methods [1, 2].

The validation of the measurement method is based on the determination of the performance parameters of the global method. These parameters are obtained during the development of the method and the inter-laboratory study, or by obeying internal validation protocols [3].

As it is known, the calibration of a gamma-ray spectrometry system evolves three main aspects:

  1. (1)

    The energy as a function of the number of the channel;

  2. (2)

    FWHM as a function of the number of the channel;

  3. (3)

    The efficiency as a function of the energy correlated with the acquisition geometry of the radiation spectrum.

In addition to these aspects, in the case of applied geometries the correlation with the coincidental standard (TCC) can be made. The energy as a function of the number of the channel and the FWHM as a function of the number of the channel do not interfere with the initial calibration in efficiency of the measuring system [4].

This paper presents the energy and efficiency calibration of gamma-ray spectrometry systems with HPGe detector on the base of internal procedures of laboratories.

The measurements and the studies were conducted on two ORTEC, gamma-ray spectrometry systems in two accredited laboratories: SALMROM (Life Science and Environmental Physics Dept.) and LAS, (Radioactive Waste Management Dept.) from the “Horia Hulubei”—National Institute for Physics and Nuclear Engineering, Bucharest (IFIN-HH), Romania.

The gamma-ray spectrometry systems

Two gamma-ray spectrometry systems have been used in this study. System 1 (ORTEC, United States) consist in a cooled GEM HPGe detector, 59.1 mm diameter and 54.1 mm length, with a Pop Top vertical cryostat configuration. The detector associated electronics is all digitally implemented. A detector interface module (DIM-ORTEC) includes the high voltage power supply, controlled by a high performance, portable multichannel analyzer, DigiDART and assures the connections for preamplifier. The DigiDART is fully integrated with software Gamma Vision 32 v-6 which can download setup parameters of the high voltage power supply, spectroscopy amplifier and analog digital converter.

The energy range of the HPGe spectrometric system is 50 ÷ 3000 keV and the operational parameters of the detector measured for a shaping time of 6 μs and high voltage of +4400 V are: relative efficiency: 30% at 1332 keV (60Co); 1.85 keV resolution at 1332 keV (60Co) and 0.85 keV resolution at 122 keV (57Co) [5].

System 2 (ORTEC, United States) consist in a HPGe germanium detector model GEM40P4 with a diameter of 69.5 mm and a length of 48.7 mm, HV = +4000 V; multichannel analyzer DigiDART, acquisition and data transformation software Vision 32 v-6.01. The energetic interval of the gamma-ray spectrometry system with GeHP detector is 50–2000 keV, and the installation parameters are: HPGe parameters (supplier specifications) obtained with a time constant of 12 μs, relative efficacy 40% at 1332 keV (60Co), 1.85 keV resolution at 1332 keV (60Co); 0.87 keV la 122 keV (57Co) [5].

Results and discussions

System calibration

Energy and resolution calibration

The energy calibration of the System 1 was performed in the energy range of interest, 50 ÷ 3000 keV, using certified spectrometric etalon sources, namely, 133Ba, 137Cs, 60Co, 152Eu, 22Na, 241Am. The energetic lines of the natural radionuclides, 40K and 208Tl, of 1460 keV, respectively, of 2614 keV, have been also considered for a more accurate energy calibration in the work energy interval.

The settings of the System 1 parameters made for the HPGe system calibration were: HV(+) = 4400 V; Gain = 2.2; Rise time: 6 μs; Flat Top: Width = 0.8, Tilt = −0.0396; ADC Conversion Gain = 16384; LLD = 100; ULD = 16383. From the height amplitude spectra of the etalon sources were obtained the peak positions of their energy lines mentioned in Table 1.

Table 1 Peak position of energy lines of calibration sources
Full size table

The energy calibration of the HPGe detector of the System 2 has been made in the energetic range of 50 ÷ 2000 keV with standard punctiform sources of 60Co, 133Ba, 137Cs, 241Am taking into consideration the energetic line of 40K of 1460 keV. The parameters of the system and their settings were: HV(+) = 4000 V; Coarse Gain = ×4, Fine Gain = 0.7645 formation time constant = 12 μs ADC Conversion Gain = 8192; Digital offset = Automatic; LLD = 180; ULD = 8190.

The energy calibration of the System 1 has been made in the mentioned experimental conditions by measuring on 18 channels, and for the System 2 only eight channels were measured (Table 1).

Taking into account these results from Table 1, the energy calibration curve has been obtained, being described by the following 2° polynomial function [6, 7]:

$$ {\text{Energy }}\left( {\text{keV}} \right) = a_{0} + a_{ 1} \times {\text{channel}} + a_{ 2} \times \left( {\text{channel}} \right)^{ 2} $$

where the coefficients, a i bear the values: a 0 = −0.291, a 1 = 0.163, a 2 = 2.155 × 10−9, for the System 1 and a 0 = 0.240, a 1 = 0.250, a 2 = −1.086 × 10−9 for System 2. The energy calibration curves obtained for the two gamma-ray spectrometry systems are presented in Fig. 1.

Fig. 1
figure 1

The energy calibration curve of the gamma-ray spectrometry systems

Full size image

The resolution calibration of both systems have been conducted with calibration sources of 57Co, 137Cs, 60Co, 133Ba, 241Am, and the values of efficiencies obtained for the two detectors are presented in Table 2.

Table 2 Measured values of the resolution
Full size table

The resolution (FWHM) calibration curve is also described, by a 2° polynomial function, as follows [6, 7]:

$$ {\text{FWHM}}\left( {\text{keV}} \right) = a_{0} + a_{ 1} \times {\text{canal}} + a_{ 2} \times \left( {\text{canal}} \right)^{ 2} $$

where the coefficients a i bear the values a 0 = 4.7361, a 1 = 0.000653, a 2 = −4.2255 × 10−9 for the System 1 and a 0 = −0.2912, a 1 = 0.163542, a 2 = 2.15548 × 10−9 for the System 2. These are the coefficients of the fitting curve, represented in Fig. 2.

Fig. 2
figure 2

The resolution calibration curve

Full size image

Efficiency calibration

The efficiency calibration of the System 1 has been done using the same certified spectrometric etalon sources, 241Am, 133Ba, 137Cs, 60Co, 152Eu, 22Na. The efficiency values were determined using the amplitude spectra acquired for every radioactive source, namely, from the net area in the region of interest of the energy peak of interest, divided by the activity of the sources, acquisition time and intensity of the energy line. The standard radioactive sources were positioned at 11 cm distance from the end cap of the detector, using a special distance piece (Table 3).

Table 3 Efficiency measurements—System 1
Full size table

These results emphasize the capability of the System 1 to measure complex spectra and to identify radionuclides with very close energy lines, in the limits of the values calculated for the resolutions. The efficiency calibration of the System 2 has been conducted with punctiform sources at a distance of 30 cm from the detector. The efficiency values are presented in Table 4.

Table 4 Efficiency measurements—System 2
Full size table

The efficiency fitting curve is described by a 6-term polynomial function to fit the natural logarithm of efficiency to the energy [8]:

$$ {\text{Ln}}\left( \varepsilon \right) = \sum\limits_{i = 0}^{5} {a_{i} } E^{2 - i} $$

where ε is the efficiency at energy E (MeV) and a i is the fitting coefficients.

Using the determinated values of the fitting coefficients from the System 1: a 0 = −0.3821104, a 1 = −6.343216, a 2 = 0.5304888, a 3 = −0.05512359, a 4 = 0.002084932, a 5 = −0.3127718 × 10−4 and the System 2: a 0 = −0.412965, a 1 = −4.983256, a 2 = 0.782049, a 3 = −0.0712944, a 4 = 0.0120845, a 5 = −0.5723974 × 10−4, we obtained the in efficiency calibration curves presented in Fig. 3.

Fig. 3
figure 3

The efficiency calibration curve of the gamma-ray spectrometry systems

Full size image

The relative errors of the measuring interval obtained after the efficiency calibration are presented in Table 5, taking into account the measuring conditions: the dead time correction made by the system, measurements of the calibration defined geometry, the used sources are radioactive punctiform standard sources, with the characteristics described in the calibration certificates.

Table 5 Measurements of radioactive standard sources
Full size table

Method validation

The activity measurement of punctiform standard sources

For the method validation, gamma-ray spectrometric measurements were carried out using standard sources such as 60Co, 133Ba, 137Cs and 241Am. Minimum Detectable Activity (MDA), the stability and repeatability of the energetic resolution, Peak to Compton Ratio and the peak shape parameters were determinate.

The activities measured for the punctiform standard sources are presented in Table 5.

Note that the values of the activity of measured sources with both systems are in close connection with the true conventional values, the relative measurement errors being situated within tenths of percent.

Minimum detectable activity

The MDA for the two systems (Table 6) was determined for 137Cs and 60Co using the formula:

$$ {\text{MDA }}\left( {\text{Bq}} \right) = ( 2. 7 1+ 4. 6 5\surd {\text{B}})/{\text{Eff}}. \times P_{\gamma } \times t_{m} $$

where B is the background in the energy region of interest; t m (s) the measuring time; Eff. (cps/Bq) the peak efficiency; and P γ is the radiation intensity.

Table 6 The Minimum Detectable Activity (MDA) of the systems
Full size table

The results obtained by the two gamma-ray spectrometry systems were very good and in concordance with the standard sources used.

The stability and repeatability of the energetic resolution

The stability of the energetic resolution (energetic repeatability) for the 122 keV peak of the 57Co source and for the 1.33 MeV peak of the 60Co source was monitored with System 1.

In addition 10 measurements for each measuring were made with an acquisition time of 1,800 s for each measurement without modifications of the parameters. The average calculated values for the resolutions of the gamma-ray spectrometry systems for the 60Co and 57Co are 1.674 keV at the 1.33 MeV line and 0.808 keV at the 122 keV line. These values are lower than the maximum values guaranteed by the producer and mentioned in the technical documentation/specification of the HPGe detector for the same energy lines: 1.85 keV at the 1.33 MeV line of 60Co and 0.85 keV at the 122 keV line of 57Co. (Table 7).

Table 7 Repeatability measurements—System 1
Full size table

The time stability of the peaks position has been determined with System 2 for the 137Cs peak by repeated measurements on a period of 6 h and a measuring time of 600 s without ups or downs of the high tension on the detector (Table 8).

Table 8 Repeatability measurements—System 2
Full size table

Peak to Compton Ratio and the peak shape parameters

Other parameters of the HPGe system, determined as part of the validation method, were the Peak to Compton Ratio and the peak shape parameters FWTM/FWHM and FWFM/FWHM, [9]. These parameters have acquired, using a certified standard point source of 60Co.

The result of 67:1, for the Peak to Compton Ratio calculated using the values from Table 8, confirm the value of 67:1, calculated and declared in the HPGe detector technical documentation (Table 9).

Table 9 Peak to Compton Ratio
Full size table

This result emphasizes another important characteristic of the HPGe spectrometric system, namely, that, to distinguish low energy lines in the presence of high energy sources.

The values calculated for the peak shape parameters, FWFM/FWHM and FWTM/FWHM, of 1.6 and 1.9, respectively, are less than those warranted in the HPGe detector technical documentation, namely, 1.9 and 2.43, respectively (Table 10) [5].

Table 10 Peak shape parameters
Full size table

Inter-laboratory comparisons

An important part of the measurement validation was the inter-comparison of the results obtained with both systems. The results obtained are presented in Table 11, indicating comparable activity values, with low errors respecting with those for conventionally true activities.

Table 11 Inter-comparison results
Full size table

Conclusions

The validation of the results and of the calibration method was made in a series of measurements to check the values of the parameters declared in the HPGe detector technical documentation, using certified standard point sources and respecting the initial measuring conditions. The results obtained validate the measuring method, emphasizing the fact that the new gamma spectrometric system with HPGe detector is correctly calibrated in energy and efficiency, respecting the measuring geometry.