Methods for obtaining characteristic γ-ray net peak count from interlaced overlap peak in HPGe γ-ray spectrometer system*

Methods for obtaining characteristic γ-ray net peak count from interlaced overlap peak in HPGe γ-ray spectrometer system* 1 first-author 1 corresp Corresponding author, zhoufq03@126.com Corresponding author, zhoufq03@126.com zhoufq03@126.com 1 1 1 School of Electrical and Mechanical Engineering, Pingdingshan University, Pingdingshan 467000, China School of Electrical and Mechanical Engineering, Pingdingshan University, Pingdingshan 467000, China For a characteristic γ-ray with interlaced overlap peak, and the case where its reliable and credible net count cannot be obtained using the current high-purity germanium (HPGe) multichannel γ-ray spectrum software, two new methods are proposed herein to obtain the γ-ray net peak count from the interlaced overlap peak in the HPGe γ-ray spectrometer system, of which one is the symmetric conversion method based on Gaussian distribution and the other is where the energy average value of two close γ-rays is regarded as the γ-ray energy. The experimental results indicate that the two methods mentioned above are reliable and credible. This study is significant for the development of better γ-ray spectrum processing software for measuring complex γ-ray spectra concerning the nuclear reaction cross section, neutron activation analysis, and analysis of transuranium elements, using an HPGe detector. Peak count Interlaced overlap peak High-purity germanium (HPGe) γ-ray spectrometer system 1 INTRODUCTION 1 Owing to its advantages of good energy resolution, high detection efficiency, and good stability, the high-purity germanium (HPGe) detector has been used widely in nuclear physics, particle physics, astrophysics, radiation chemistry, neutron activation analysis, environment monitoring, safety inspection, and national security [ 1 1 - 6 6 1-6 ] . In measuring the complex γ-ray spectrum concerning the nuclear reaction cross section, the neutron activation analysis, and the analysis of transuranium elements using an HPGe detector, a staggered overlap peak still exists between the characteristic γ-ray and other γ rays. For instance, in the measurement of the nuclear reaction cross section, the following two cases exist. The first case is where a small interlaced overlap exists between the characteristic γ-ray full-energy peak (FEP) and another γ-ray FEP (as shown in Fig. 1 Fig. 1 below). The second is that an interlaced overlap exists (as shown in Fig. 2 Fig. 2 below). In these two cases, the typical methods used are as follows. One method is that isotope separation is used to avoid the effect of γ rays with the same or close energies produced by other isotopes. The other is that the samples are measured after having cooled for an adequate period of time to avoid the effect of γ rays with the same or close energies produced by other reactions, on the condition that the half-life of the radionuclides produced by the measured reaction is much longer than that of the radionuclides produced by other reactions. However, the interlaced overlap of the γ-ray FEP is sometimes inevitable in the actual measurement of the nuclear reaction cross section after performing the two measures above. In this case, the typical practice in the past is as follows. If a small interlaced overlap exists (as shown in Fig. 1 Fig. 1 below), the effect of other γ rays can be ignored. If significant interlaced overlap occurs (as shown in Fig. 2 Fig. 2 ), the cross-section measurement is abandoned because the correct γ-ray net peak count cannot be obtained by the current HPGe γ-ray spectrometer system. To obtain reliable cross-section experimental data, the reliable and credible net count of the characteristic γ-ray FEP is a key factor in the nuclear reaction cross-section measurement. Typically, the γ-ray FEP is isolated in the γ-ray spectrum (as shown in Fig. 3 Fig. 3 ); therefore, it is easy to obtain the count or the net count of the γ-ray FEP using the HPGe multichannel γ-ray spectrum software. However, the software mentioned above cannot offer the reliable and credible net counts of characteristic γ-ray FEP (as shown in Fig. 1 Fig. 1 or Fig. 2 Fig. 2 above). To solve this problem, effective methods are proposed and their reliabilities are verified by our experimental results, which is of great significant for the development of better γ-ray spectrum processing software. 2 PROCESSING METHODS with THE INTERLACED OVERLAP PEAK 1 2.1 Processing method in the case of small interlaced overlap peak 2 In Fig.1 Fig.1 above, a small interlaced overlap exists between the FEP of the characteristic γ-ray, 615.3 keV, and the FEP of 618.3 keV. The net count of the 615.3-keV γ-ray FEP is calculated using the symmetric conversion method based on the Gaussian distribution law because the change in the net count of the γ-ray FEP with the energy or channel address approximately obeys the Gaussian distribution law. Therefore, the total net count of the 615.3-keV γ-ray FEP should be equal to twice the net count of its left half side. The specific steps are as follows: First, the background count of each channel in the left-half area covered by the 615.3-keV FEP is calculated using the method below: the background count of any channel in the left-half area is equal to the count of this channel that is thrice the half high-width of the FEP away from the center of the same FEP, plus the counts of two channels before it and those of two channels after it; and subsequently, the total counts are divided by 5. [ 7 7 ] Next, the net count in the left-half area of the 615.3-keV γ-ray FEP is calculated. For the calculation, the sum of the count of each channel in the left-half area of the 615.3 keV γ-ray FEP subtracts the background count of any channel calculated above. Finally, the total net count of the 615.3-keV γ-ray FEP is equal to twice the net count in its left half side. 2.2 Processing method in the case of significant interlaced overlap 2 As is shown in Fig. 2 Fig. 2 above, the two γ-rays of 737.5 keV and 739.2 keV are from the radioactive nuclei generated by the same reaction, and significant overlap occurs between them. For this case, the following two methods can be employed. Method 1: As mentioned above, i.e., the net count of the 737.5-keV FEP is calculated using symmetric conversion method based on the Gaussian distribution. Method 2: The energy weighted average (intensity as weight) value of two close γ-rays is regarded as the characteristic γ-ray energy, namely the characteristic γ-ray energy 737.94 keV=(737.5×29%+739.2×10%)/(29%+10%) keV. The intensity of 737.94 keV is equal to the total intensities of 737.5 keV and 739.2 keV (namely the total intensities 39%=29%+10%) and the net count of 737.94 keV is the total net count of the area covered by the FEPs of 737.5 keV and 739.2 keV. It is noteworthy that method 2 can be applied only when the two γ-rays are from the radioactive nuclei generated by the same reaction. 3 EXPERIMENT RESULTS AND DISCUSSION 1 In fact, two cases of interlaced overlap peak exist (as shown in Figs. 1 Figs. 1 and 2 2 ) in our experiments with regard to the cross-section measurement of the 186 W (n,p) 186 Ta reaction. The related experimental conditions and cross section obtained using the processing method of interlaced overlap peak mentioned above concerning the 186 W (n,p) 186 Ta reaction are described briefly as follows. The samples were irradiated at the K-400 Neutron Generator at the Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics. Neutrons in the 14 MeV region with a yield of approximately 5×10 10 n/s, were produced by the T(d,n) 4 He reaction with a deuteron beam energy of 255 keV and a beam current of 320 µA. The solid tritium–titanium (T–Ti) target used in the generator was approximately 2.19 mg/cm 2 thick. During irradiation, the neutron flux was monitored by the alpha-particles such that corrections could be made for small variations in the yield. Groups of samples were placed at 45° and 135° relative to the deuteron beam direction, and centered about the T–Ti target at distances of 3–5 cm. The neutron energies in the measurements were determined in advance by the method of cross-section ratios for the 90 Zr(n,2n) 89m+g Zr and 93 Nb(n,2n) 92m Nb reactions [ 8 8 ] . The natural tungsten foils of purity 99.99% and thickness 2.0 mm were made into circular samples of diameter 2.0 cm. Each of them was sandwiched between two disks of thin niobium(purity better than 99.99% and 1.0 mm thickness)of the same diameter, and was subsequently wrapped in a 1.0-mm-thick cadmium foil(purity better than 99.95%).The activated samples were studied for their γ-activities by γ-ray spectrometry, using a well-calibrated GEM-60P coaxial HPGe detector (crystal diameter 70.1 mm, crystal length 72.3 mm) with a relative efficiency of ~68% and an energy resolution of ~1.69 keV FWHM at 1.33 MeV. The efficiency of the detector was precalibrated using various standard γ sources. The decay characteristics of the product radionuclides and the natural abundance of the target isotopes under investigation are summarized in Table 1 Table 1 [ 9 9 ] . The abundance of 93 Nb are from Ref. [ 10 10 ] because no 93 Nb abundance is given in Ref. [ 9 9 ]. For the product radionuclide 186 Ta, the four γ rays with relatively large intensities and their intensities are all summarized in Table 1 Table 1 . The characteristic γ ray of 197.9 keV affected by the γ ray of 198.35 keV with intensity 1.465% is from the 182 W (n,p) 182(m+g) Ta+ 183 W (n,d) 182(m+g) Ta+ 184 W (n,t) 182(m+g) Ta reactions. The characteristic γ ray of 615.3 keV (from the 186 W (n,p) 186 Ta reaction) affected by the γ ray of 615.17 keV with intensity 0.23345% are from the 184 W (n,α) 181 Hf reaction. Simultaneously, a small interlaced overlap occurred between the FEP of 615.3 keV and the two FEPs of 618.37keV (with 7.57% of the intensity from the 186 W (n,γ) 187 W reaction) and 618.3 keV (with 28% of the intensity from the 186 W (n,p) 186 Ta reaction)(as shown in Fig.1 Fig.1 ), and significant interlaced overlap occurred between the FEPs of 737.5 keV and 739.2 keV (as shown in Fig. 2 Fig. 2 ). a Here, we used the value given by Ref. [ 10 10 ]. 1 1 Reaction 1 1 Abundance of target isotope (%) 1 1 Half-life of product 1 1 E γ (keV) 1 1 I γ (%) 1 1 186 W ( n , p ) 186 Ta 1 1 28.43 1 1 10.5m 1 1 197.9 1 1 50 1 1 1 1 1 1 1 1 615.3 1 1 28 1 1 1 1 1 1 1 1 737.5 1 1 29 1 1 1 1 1 1 1 1 739.2 1 1 10 1 1 93 Nb( n ,2 n ) 92m Nb 1 1 100 a 1 1 10.15d 1 1 934.44 1 1 99.15 The cross sections were calculated using the equation proposed by Xiangzhong Kong et al.(1999) [ 11 11 ] . The cross-section values of the 186 W(n,p) 186 Ta reaction were obtained relative to those of the 93 Nb(n,2n) 92m Nb reaction. The cross-section values of the 186 W (n,p) 186 Ta reaction were obtained using the equation [ 11 11 ] and net count of the FEP of 197.9 keV (using multichannel γ spectrum processing software). In this process, the effects from the 182 W(n,p) 182(m+g) Ta+ 183 W(n,d) 182(m+g) Ta+ 184 W(n,t) 182(m+g) Ta reactions have been deducted using the method in literature [ 12 12 ]. The obtained result with the superscript b is shown in Table 2 Table 2 and plotted in Fig.4 Fig.4 . b The cross-sectional values were obtained using net count of the FEP of 197.9 keV (using multichannel γ spectrum processing software) c,d The cross-sectional values were obtained using the net count of FEP of 615.3 keV, which was obtained using multichannel gamma spectrum processing software and the symmetric conversion method based on Gauss distribution mentioned above, respectively e The cross-sectional values were obtained using the net count of FEP of 737.5 keV (with the symmetric conversion method based on Gauss distribution mentioned above) f The cross-sectional values were obtained using the characteristic γ-ray of 737.94 keV whose intensity is 39%, and the net count of FEP is the total net count of the area covered by FEPs of 737.5 keV and 739.2 keV 1 1 Reaction 1 1 This work  E n (MeV) 1 1 σ (mb) 1 1 Literature Values  E n (MeV) 1 1 σ (mb) 1 1 Reference 1 1 186 W( n , p ) 186 Ta 1 1 13.5±0.2 1 1 1.01±0.05 b 1 1 13.48 1 1 0.80±0.10 1 1 [ 13 13 ] 1 1 1 1 14.4±0.2 1 1 1.52±0.07 b 1 1 13.65 1 1 0.93±0.11 1 1 [ 13 13 ] 1 1 1 1 1 1 1 1 13.88 1 1 1.02±0.12 1 1 [ 13 13 ] 1 1 1 1 13.5±0.2 1 1 0.56±0.03 c 1 1 14.04 1 1 1.25±0.15 1 1 [ 13 13 ] 1 1 1 1 14.4±0.2 1 1 1.11±0.06 c 1 1 14.27 1 1 1.55±0.19 1 1 [ 13 13 ] 1 1 1 1 1 1 1 1 14.46 1 1 1.59±0.18 1 1 [ 13 13 ] 1 1 1 1 13.5±0.2 1 1 0.83±0.04 d 1 1 14.67 1 1 1.83±0.21 1 1 [ 13 13 ] 1 1 1 1 14.4±0.2 1 1 1.41±0.07 d 1 1 14.82 1 1 1.97±0.22 1 1 [ 13 13 ] 1 1 1 1 1 1 1 1 14.5 1 1 1.64±0.12 1 1 [ 14 14 ] 1 1 1 1 13.5±0.2 1 1 0.79±0.04 e 1 1 14.7 1 1 1.4±0.2 1 1 [ 15 15 ] 1 1 1 1 14.4±0.2 1 1 1.40±0.07 e 1 1 14.1 1 1 1.33±0.10 1 1 [ 16 16 ] 1 1 1 1 1 1 1 1 14.8 1 1 11±4 1 1 [ 17 17 ] 1 1 1 1 13.5±0.2 1 1 0.87±0.04 f 1 1 13.4 1 1 0.59±0.14 1 1 [ 18 18 ] 1 1 1 1 14.4±0.2 1 1 1.44±0.07 f 1 1 13.65 1 1 1.2±0.35 1 1 [ 18 18 ] 1 1 1 1 1 1 1 1 13.88 1 1 1.31±0.31 1 1 [ 18 18 ] 1 1 1 1 1 1 1 1 14.28 1 1 1.78±0.54 1 1 [ 18 18 ] 1 1 1 1 1 1 1 1 14.58 1 1 1.84±0.41 1 1 [ 18 18 ] 1 1 1 1 1 1 1 1 14.87 1 1 2.31±0.48 1 1 [ 18 18 ] 1 1 1 1 1 1 1 1 14.5 1 1 2.6 1 1 [ 19 19 ] 1 1 1 1 1 1 1 1 14.5 1 1 2.9±0.58 1 1 [ 20 20 ] 1 1 93 Nb( n ,2 n ) 92m Nb 1 1 1 1 1 1 13.5±0.3 1 1 457.9±6.8 1 1 [ 22 22 ] 1 1 1 1 1 1 1 1 14.4±0.3 1 1 459.8±6.8 1 1 [ 22 22 ] The cross-section values of the 186 W(n,p) 186 Ta reaction were obtained using the equation in literature [ 11 11 ] and the net count of the FEP of 615.3 keV. In the process, the net count of the FEP of 615.3 keV was obtained using multichannel gamma spectrum processing software and the symmetric conversion method based on the Gaussian distribution mentioned above, respectively. Simultaneously, the effect from the 184 W (n,α) 181 Hf reaction was deducted using the method in literature [ 12 12 ]. The obtained results that are marked with the superscripts c and d are shown in Table 2 Table 2 and plotted in Fig. 4 Fig. 4 . The cross-section values of the 186 W(n,p) 186 Ta reaction were obtained using the equation [ 11 11 ] and the net count of the FEP of 737.5 keV (with the symmetric conversion method based on Gaussian distribution mentioned above). The obtained result with the superscript e is shown in Table 2 Table 2 and plotted in Fig. 4 Fig. 4 . The cross-section values of the 186 W(n,p) 186 Ta reaction were also obtained using the equation [ 11 11 ] and characteristic γ-ray of 737.94 keV whose intensity is 39%, and the net count of the FEP is the total net count of the area covered by the FEPs of 737.5 keV and 739.2 keV. The obtained result with the superscript f is shown in Table 2 Table 2 and plotted in Fig. 4 Fig. 4 . The values given in the literatures [ 13 13 - 20 20 13-20 ] and the evaluated data from JEFF-3.3 and JENDL-4.0 [ 21 21 ] are shown in Table 2 Table 2 and plotted in Fig. 4 Fig. 4 for comparison. However, when Fig. 4 Fig. 4 is plotted, the result from Ref. [ 17 17 ] (that is, 11±4 mb at 14.8 MeV) is not adopted because the value was too large to demonstrate clearly the relations to the other data near 14 MeV. The cross-section values of the monitor reaction 93 Nb(n,2n) 92m Nb are obtained from Ref. [ 22 22 ] and listed in Table 2 Table 2 as well. As shown in Table 2 Table 2 and Fig. 4 Fig. 4 , the obtained results marked with the superscripts d,e,f are consistent and in agreement with the corresponding point values on the excitation curves in Refs. [ 13 13 , 18 18 ], as well as the evaluated data from JEFF-3.3 and JENDL-4.0 within the experimental uncertainty at the neutron energy of 13.5 MeV. The obtained values marked with the superscripts b,d,e,f are consistent and in agreement with the corresponding point values on the excitation curves in Refs. [ 13 13 ] and [ 18 18 ], as well as the evaluated data from JEFF-3.3 and JENDL-4.0 within the experimental uncertainty at the neutron energy of 14.4 MeV. However, the obtained values marked with the superscript c are lower than those marked with the superscripts b,d,e,f, those in Refs., as well as the evaluated data from JEFF-3.3 and JENDL-4.0 at the neutron energy of 13.5 and 14.4 MeV. The reason is that the net count of the FEP of 615.3 keV was obtained using multichannel gamma spectrum processing software, and the count missed the count of overlapped part with the FEP of 618.3 keV. The cross-section values obtained using the net count of the FEP, which was obtained through the symmetric conversion method based on Gaussian distribution and the energy average value of two close γ-rays, are in agreement with those in the literatures mentioned above and the evaluated data from JEFF-3.3 and JENDL-4.0 on the condition that an interlaced overlap peak exists between the characteristic γ-ray FEP and another γ-ray FEP. This demonstrates that the two methods mentioned above are reliable and credible. 4 CONCLUSION 1 In this work, two new methods were proposed to obtain the characteristic γ-ray net peak count from the interlaced overlap peak in the HPGe γ-ray spectrometer system. The problem in which the reliable and credible net count of the characteristic γ-ray with interlaced overlap peak could not be obtained using the current HPGe multichannel γ-ray spectrum software was solved effectively. Further, the validity and reliability of the two methods were verified through our experimental results. This study is of great significance for the development of better γ-ray spectrum processing software, for measuring complex γ-ray spectra regarding the nuclear reaction cross section, neutron activation analysis, and analysis of transuranium elements using the HPGe detector. 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Evaluation of cross sections for 14 important neutron-dosimetry reactions We thank the crew of the K-400 Neutron Generator at Institute of Nuclear Physics and Chemistry China Academy of Engineering Physics for performing irradiation work. 10.1007/s41365-018-0525-7 This work was supported by the National Natural Science Foundation of China (Nos. 11575090 and 11605099) and the Young Key Teachers Training Porgram of He’nan Higher Education in China (No. 2015GGJS-258). 2018-06-22 2018-09-16 2018-09-19 2019-01-02 2019-01-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2019 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0525-7 http://dx.doi.org/10.1007/s41365-018-0525-7 . 2019 Nuclear Science and Techniques 01 30