Utilization of different radionuclides for high-energy extended efficiency calibration of a HPGe for improved determination of calcium and sulfur using k0-INAA

The present study reports on the performance of three reactor-produced radionuclides (24Na, 56Mn, and 72Ga) and one accelerator-produced radionuclide (56Co) for extending the full-energy peak efficiency calibration of a coaxial HPGe detector up to ~ 3100 keV at different detector to source distances. The differences between the efficiency curves obtained with and without the use of high-energy gamma emitters radionuclides have a considerable impact on the accuracy of the Na, Ca, and S determination by the k0-INAA as evidenced by analysis results of reference materials. The results revealed that 24Na is the most suitable radionuclide for high-energy efficiency calibration due to its reasonable availability, low production cost, simple decay scheme, and well-defined decay properties.


Introduction
In instrumental neutron activation analysis (INAA), the full energy peak efficiency is one of the most important parameters that has a direct impact on the accuracy of the results obtained using k 0 -standardization method (k 0 -INAA). Commonly, most elements are determined by measuring radionuclides emitting their main γ-rays in the energy range of ~ 60-1800 keV [1]. Thus, a commercially available set of radioactive standard sources (ex: 241 Am, 133 Ba, 109 Cd, 139 Ce, 57 Co, 60 Co, 137 Cs, 152 Eu, and 88 Y) which have accurate emission probabilities of their γ-rays in the energy range from 59.5 keV ( 241 Am) up to 1836.2 keV ( 88 Y), is sufficient to obtain a well-fitted full energy peak efficiency curve for the HPGe detector. However, for determination of elements with analytical radionuclides emitting only high-energy γ-rays (ex: 49 Ca (E = 3084.4 keV) and 37 S (3103.4 keV)) or the high-energy line of a multi-line radionuclide is well separated and has a good counting statistics precision (ex: 24 Na), accurate efficiency calibration over a wide energy range is necessary. It was reported that extrapolation of efficiency curves to a higher energy region may yield significantly biased results for γ-ray energies beyond the available experimental data points [1][2][3]. Therefore, researchers' attention has been directed to use calibration radioactive standard sources that emit γ-rays with energy above 2000 keV. However, the commercial use of high-energy gamma-emitter radionuclides for efficiency calibration of HPGe has been hindered so far by their relatively short physical half-lives and/or limited certification bodies [1]. On the other hand, application of long-lived naturally occurring radionuclide 226 Ra (and its daughter 214 Bi) for high-energy extended efficiency calibration is hampered due to its limited availability and disparate nuclear data in various databases [3].
In the absence of commercial radioactive standard sources with high-energy γ-rays, several high-energy γ-ray emitters can be produced and used as in-house standards provided that they also emit at least one γ-ray with lower energy in the energy region of the above-mentioned radioactive standards in order to accurately quantify their activities [3,4].
Radionuclides that meet this criterion can be produced by activation with thermal neutrons in a nuclear reactor (ex: 72 Ga, 24 Na, and 56 Mn) or by charged particles reactions in a cyclotron facility (ex: 56 Co and 66 Ga). Reactor-produced radionuclides offer the advantages of the availability to INAA users' community and the simplicity of production procedures at low additional cost.
Numerous researchers have produced high-energy gamma emitter radionuclides and applied them to calibrate their HPGe detectors in the high energy region. Soilman et al., [5], Mohamed [6], and others reported on the application of 24 Na (as in-house standard) for extended-high energy efficiency calibration of HPGe in k 0 -INAA. Precise efficiency calibration of an HPGe up to 3.5 MeV was achieved by a combination of experimental measurements (using different sources) and computational calculations [7]. Kucera and his co-researchers [1] showed that the use of 56 Co for efficiency calibration along with commonly used calibration sets improves the accuracy of Ca determination by k 0 -INAA via the analytical radionuclide 49 Ca. Since the γ-rays emitted from these radionuclides are generally in cascade, their use was limited to calibrate the HPGe detectors at high detectorsource distances to minimize the true coincidence effect. In turn, this hinders the measurement of INAA samples at a large counting solid angle, which is required for measuring low concentration levels, unless sophisticated true coincidence corrections are made.
The objectives of the present work are to report on the performance of various in-house prepared radioactive standard sources for extending the efficiency calibration of HPGe up to 3.1 MeV at different counting solid angles. The tested sources are 24 Na, 56 Co, 66 Ga, and 56 Mn. The performance of each calibrant will be evaluated based on the accuracy of Na, Ca and S determination using k 0 -INAA of samples with known concentrations. This could form the basis of a more simplified and advanced calibration procedures for the HPGe detectors in k 0 -INAA.

Preparation of radioactive standards
Quasi-point sources of 24 Na, 56 Mn, and 72 Ga were prepared by irradiation of tiny amounts of each corresponding natural target with a thermal neutron flux of 3.17 × 10 12 cm −2 s −1 for 5 min at Kyoto University Research Reactor. A quasi-point source of 56 Co was prepared by irradiation of a 0.05 mm thick nat Fe foil target with a proton beam at the cyclotron facility at Osaka University. The measured activities of 24 Na, 56 Mn, 72 Ga, and 56 Co were 26.7 ± 1.1, 50.3 ± 2.0, 12.9 ± 0.5, and 31.2 ± 1.3 kBq respectively. One or more gamma lines in the energy range below 1836 keV were used to accurately quantify the activity of each source. Na and Mn are monoisotopic elements. For Ga, two hours of cooling time allowed 70 Ga (t 1/2 = 21.15 min) to decay out completely. It was noted that the 56 Co source contained negligible activities of 57 Co and 58 Co, which did not affect the use of the 56 Co radionuclide for efficiency calibration in the high-energy region.
The measurement of the radioactivities was carried out using a well calibrated coaxial HPGe detector (EG&G Ortec, 35% relative efficiency, 1.85 keV FWHM at 1332.5 keV, peak to Compton ratio 73:1) at a detector to sample distance of 161 mm to minimize the effect of true coincidence. The full energy peak efficiencies of the detector at different counting position were calibrated up to 1836.06 keV using a multi-radionuclide standard source (provided by Eckert & Ziegler) consisting of 241 Am, 109 Cd, 139 Ce, 57 Co, 60 Co, 137 Cs, 203 Hg, 113 Sn, 85 Sr, and 88 Y. Higher energy gamma-rays of 24 Na, 56 Mn, 72 Ga, and 56 Co were then used for the extension of the efficiency calibration to the high energy region, beyond 1836 keV. The nuclear data of the four radionuclides used for extending the efficiency calibrations are listed in Table 1.
The full energy peak efficiency in the high energy region, was estimated using the following equation: where N p , , and refer to net peak area, full energy peak efficiency, and gamma-ray emission probability, respectively, and the subscripts "l" and "h" refer to the low-and high-energy gamma-lines of the calibrant radionuclide, respectively.

The applied k 0 -INAA procedures
To confirm the validity of the obtained efficiency calibration of the HPGe, concentrations of Na, Ca, and S were determined in several commercial and in-house reference materials analyzed by k 0 -INAA. The commercial certified reference materials were NIST SRM-1515 Apple Leaves and INCT-OBTL-5 Oriental Basma Tobacco Leaves, while the in-house reference material was 10.1 mg of S, prepared from stock a standard solution (10,007 mg/l). The detailed analytical procedures were presented in previous work [5]. Simply, the reference materials sealed in polyethylene bags along with flux monitors (Au-Zr set) were irradiated for 5 min with a thermal neutron flux of 3.17 × 10 12 cm −2 s −1 for 5 min using the pneumatic irradiation tube Pn-1 of Kyoto University Research Reactor. The irradiated reference materials were allowed to decay for 2-3 min before they were counted at different sample to detector distances, varying from 4 to 161 mm. Neutron flux monitors were measured for 10 h at a position of 161 mm from the detector end-cap. The γ-ray spectra of the irradiated samples were measured using the HPGe detector described above.
The results of Na, Ca, and S determinations in the tested reference materials were calculated using the efficiency curves of the HPGe obtained with and without the inhouse prepared four calibration sources. The concentrations of the elements of interest (Na, Ca and S) were determined according to the following equation [5]: where is the mass fraction of the element of interest (mg/ kg); N p is the net peak area of the photopeak in the γ-ray spectrum, T CC is the true coincidence correction factor; t m is the counting time; S, D and C are the saturation, decay and counting factors, respectively; f is ratio of thermal-toepithermal neutron flux; k 0 is the k 0 -factor; w and W are the weights of the sample (in kg) and the comparator gold (in mg), respectively; is the full-energy peak efficiency; Q 0 is the ratio of resonance integral to thermal cross-section, and α is the deviation factor of the epithermal neutron flux from the ideal 1/E distribution approximated by a 1/E 1+α . The subscripts "a" and "Au" refer to the analyte and the comparator Au standard, respectively.

High-energy extended efficiency calibration
The obtained experimental data using the commercial calibration set with or without 24 Na, 56 Mn, 72 Ga, or 56 Co placed at 161 mm from the detector end-cap were evaluated in several ways. Under our experimental conditions, corrections for truce coincidence (coincidence summing or loss) were estimated for the gamma lines of 24 Na, 56 Mn, 72 Ga and 56 Co as well as for the gamma lines of radionuclides in the commercial calibration set following the approach reported by De-Corte [8]. It was found that these corrections were less than 0.5%. These results compared well with our previously published data for most of these radionuclides [5]. Figure 1 shows the efficiency curves as fitted by Gamma Vision software. In comparison with the efficiency curve obtained with the commercial calibration set, efficiency curves obtained with in-house calibration sources 24 Na, 56 Mn, 72 Ga, and 56 Co show a noticeable drop in the high energy region, > 2000 keV. On the other hand, there is a markable consistency between the curves obtained with the in-house standards as seen from insert in the top-right corner of Fig. 1. Gamma Vision software employs a six-term polynomial function to fit the natural logarithm of efficiency to the energy according to the following formula: where ɛ is the full energy photopeak efficiency; a i is the fitting coefficients; E is the γ-ray energy in MeV.
The polynomial coefficients obtained for the fitting of experimental data points are presented in Table 2. These coefficients are specific and valid only for the giving detection system and counting geometry. Table 3 shows the relative differences of full energy peak efficiency of some interesting high-energy γ-rays (namely: 2754.0 keV for 24 Na, 3084.4 keV for 49 Ca, and 3103.4 keV for 37 S) obtained with the use of in-house calibration sources placed at 161 mm from the detector end-cap. It is clear that the relative differences obtained by 24 Na, 56 Mn, 72 Ga, or 56 Co have negative values, and higher energies exhibit higher deviations. 56 Co and 56 Mn gave almost identical efficiency relative differences of − 7.60, − 9.52 and − 9.60% (for 56 Co), and − 7.64, − 9.62 and − 9.66% (for 56 Mn) at 2754.0, 3084.4, and 3103.4 keV, respectively. On the other hand, 24 Na and 72 Ga show slightly higher (< 1%) and slightly lower (~ 1%) deviations than the corresponding mean values of the results obtained with 56 Co and Mn. The observed deviations between the four sources are negligible and can be attributed to the disparate data of γ-ray emission probabilities [3].
Efficiency calibration at low sample-detector distances is needed when the samples to be measured have weak levels of the induced radioactivity, low count-rate. Commercial software packages like k 0 -IAEA and KAYZERO for Windows can convert a reference efficiency curve (measured at a reference counting position) to an actual efficiency calibration for any given counting geometry [9,10]. When software packages are not available and/or analysts have not sufficient experiences to use them, calibration sources have to be measured at all possible counting positions to generate an efficiency curve for each counting position. So, beside the high detector-source distance (161 mm), the high-energy calibration sources under investigation were tested at a larger solid angle counting geometry (close to the detector), ranging from 4 to 126 mm. Effects of true coincidence must be considered for short detector-sample distances [5,10]. Also, at close sample-detector distances, an efficiency curve measured with calibration sources and corrected for coincidence effects may potentially give more accurate efficiencies than those obtained with an available software package. The relative difference of the efficiency obtained with the use of in-house calibration sources placed at selected positions, 4, 16, 36, 66, 96, 126 and 161 mm, from the detector end-cap are presented in Fig. 2 (To simplify the layout of the figure, only the data for 49 Ca γ-line is presented). It is clear from Fig. 2 that the use of any source of the tested high-energy radionuclides yields almost identical significant change in the high energy region of full energy peak efficiency curves obtained at detector to source distances of 161 mm down to 66 mm. The mean value of the relative difference is − 9.65 ± 0.39. At a closer detector to source distance (≤ 36 mm), all obtained efficiencies showed more negative relative differences. At detector to source distance of 4 mm, relative differences reached − 11.0, − 12.0, − 10.9 and − 12.3% for 24 Na, 56 Co, 56 Mn, and 72 Ga, respectively. The data presented in Fig. 2 show that, for smaller detector to source distances, the relative difference in the efficiency more strongly depends on the calibrant radionuclide and on the distance. The relative difference increased as the source moved closer to the detector. In addition, the radionuclides 56 Co and 72 Ga yield more relative differences than 24 Na and 56 Mn. This can be attributed to the true coincidence effects, and can be explained as the following. For a given radionuclide, the magnitude of true coincidence summing (summing in or summing out) is strongly dependent on the peak and total detection efficiencies as well as on the decay scheme of the radionuclide. The true coincidence summing, hence, becomes significant at close detector-to-source distances owing to a greater probability of two or more γ-rays reaching the detector within the resolving time of the detector [11]. In practice, measuring or computing peak and total detection efficiency for a close detector to source distance is cumbersome and complicated and might yield biased results [12]. In addition, the relatively large deviations observed for 56 Co and 72 Ga (compared to 24 Na and 56 Mn) at short detector to source distances can be attributed to improper estimation of true coincidence correction due to their complicated decay schemes and/or insufficient general confidence in their nuclear data [3,8,[13][14][15].

Analysis of reference materials
Reference materials were analyzed using the k 0 -INAA method in order to test the validity of the applied efficiency calibration procedure and its impact on the accuracy of Na, Ca, and S determination. The investigated reference materials were two commercial reference materials (NIST-SRM-1515 and INCT-OBTL-5) and one in-house reference material (10.1 mg of S). Three subsamples were analyzed for each reference material. The mean of the measured values as well as the reference values and the associated uncertainties are presented in Table S1 (supplementary data). The measured concentrations were evaluated based on the relative deviation from the reference value (Bias%) [16]. The evaluation results for the three reference materials are presented in Fig. 3. Because its concentration was below the limits of detection of the k 0 -NAA procedure employed for NIST-SRM-1515 and INCT-OBTL-5, S could not be determined in these two commercial reference materials. Although Na can be accurately determined by measuring the 1368.4 keV gamma-line of 24 Na, it was determined in the investigated samples through the high-energy gamma-line of 24 Na, 2754.0 keV, for the following two reasons. The first reason is to give more confidence in the extended efficiency calibration of the HPGe. The second reason is to avoid the possible interference that might have occurred due to 24 Sb [17]. As demonstrated in Fig. 3, the differences in the efficiency values obtained with and without different high-energy calibrant radionuclides have a significant impact on the accuracy of Na, Ca and S determination by k 0 -INAA. Extrapolation of the efficiency curve obtained with the commercial calibration set always yielded significant deviations (~ − 10%) from the assigned values for Na, Ca, and S for samples measured at all tested counting positions. On the other hand, the use 24 Na or 56 Mn for extending the efficiency calibration to high energy region yields a good accuracy (Bias% < 5) for samples measured at all counting positions, while the use of 56 Co or 72 Ga shows good results (Bias% < 5) for samples counted at positions ≥ 36 mm from the detector end-cap. In general, counting at positions close to the detectors yielded a systematic deviation from the assigned value (positive Bias% values), and relatively large deviations (~ + 10% at counting position of 4 mm) were observed when 56 Co or 72 Ga were used as calibrants. These observations match well with the results of efficiency calibration presented in Fig. 2.

Comparison between the four calibration radionuclides
There are several radionuclides which can be used for extending the efficiency calibration to high-energy region, which are reviewed in the Introduction section of the present article. Based on the above-shown results, comparison between reactor produced radionuclides (ex: 24 Na, 56 Mn, and 72 Ga) and accelerator-produced radionuclides (ex: 56 Co) as high-energy calibration sources are summarized in Table 4.
It is clear from the comparison presented in Table 4 that the four radionuclides are good candidates for efficiency calibration of HPGe in the high-energy region. Although it has a reasonable half-life and emits γ-rays over a wide energy range (up to 3253 keV), accelerator-produced radionuclide, 56 Co, is not generally available for the community of NAA. 56 Co and 72 Ga have a complicated decay scheme which might affect the accuracy of estimating the true coincidence correction factors required when the calibration is performed at a close detector to sample distance. In addition, their cost of production is not cheap. Due to its short half-life, 56 Mn decays significantly between two subsequent detector calibration campaigns. With 56 Mn, counting positions far from the detector can be calibrated first and then as the source decays it can be used for the positions close to the detector and the activity will be low enough that it doesn't saturate the detector. On the other hand, 24 Na possesses characteristics that make it the nuclide of chose for the purpose of routine HPGe calibration. The advantages of using 24 Na include: • Simplicity of its decay scheme and the well-defined nuclear data allow for accurate estimation of true coincidence correction factors, if needed. • Reasonable availability to NAA community. Natural sodium is easily activated by thermal neutrons and rou-tine NAA samples can be used as a calibration source. No need for special preparations. • Low production cost

Conclusions
The use of high-energy gamma emitter radionuclides for efficiency calibration in addition to the commonly employed calibration set significantly changed the full energy peak efficiency curves in the high-energy region compared to  Half-life + + + + + + + + Availability to NAA community + + + + + + + + + + Cost + + + + + + + Simplicity of correction + + + + + + + Accuracy of results + + + + + + + + + + those obtained with the commercial calibration set only. This change yielded a significant improvement in the accuracy of Na, Ca, and S determination using k 0 -INAA by measuring their high energy analytical radionuclides, 24 Na, 49 Ca, and 37 S, respectively. The performance of three reactor-produced radionuclides ( 24 Na, 56 Mn, and 72 Ga) and one accelerator-produced radionuclide ( 56 Co) was examined for extending the full energy peak efficiency calibration of a coaxial HPGe detector as a function on detector to source distance,. The performance of each calibration radionuclide has been evaluated based on the accuracy of Na, Ca and S determination as demonstrated by analysis results of reference materials. In general, the use of 24 Na, 56 Mn, 56 Co, or 72 Ga yielded almost identical change in the efficiency curve at large detector to source distances. The use of radionuclides with complex decay schemes may result in biased estimation of the full-energy peak efficiency at lower counting positions due to inaccurate prediction of true coincidence correction factors. It can be concluded that 24 Na is the best among the tested radionuclides due to its availability, well-known nuclear data, and the simplicity of its decay scheme. In the present case, a measurement of only 24 Na in a reference position would have been enough to update the efficiency of all counting positions.