1 INTRODUCTION

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^[1-6]. 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 below). The second is that an interlaced overlap exists (as shown in 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 below), the effect of other γ rays can be ignored. If significant interlaced overlap occurs (as shown in 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.

Fig.1Full-screen View

Small interlaced overlap between the characteristic γ-ray FEP and another γ-ray FEP.

Fig.2Full-screen View

Significant interlaced overlap between characteristic γ-ray FEP and another γ-ray FEP.

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); 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 or Fig. 2 above).

Fig.3Full-screen View

Characteristic γ-ray FEP in the nonoverlapping case.

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

3 EXPERIMENT RESULTS AND DISCUSSION

In fact, two cases of interlaced overlap peak exist (as shown in Figs. 1 and 2) in our experiments with regard to the cross-section measurement of the ¹⁸⁶W (n,p)¹⁸⁶Ta reaction. The related experimental conditions and cross section obtained using the processing method of interlaced overlap peak mentioned above concerning the ¹⁸⁶W (n,p)¹⁸⁶Ta 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 5×10¹⁰ n/s, were produced by the T(d,n)⁴He 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/cm² 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 ⁹⁰Zr(n,2n)^89m+gZr and ⁹³Nb(n,2n)^92mNb reactions^[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^[9]. The abundance of ⁹³Nb are from Ref. [10] because no ⁹³Nb abundance is given in Ref. [9]. For the product radionuclide ¹⁸⁶Ta, the four γ rays with relatively large intensities and their intensities are all summarized in 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 ¹⁸²W (n,p)^182(m+g)Ta+¹⁸³W (n,d) ^182(m+g)Ta+¹⁸⁴W (n,t) ^182(m+g)Ta reactions. The characteristic γ ray of 615.3 keV (from the ¹⁸⁶W (n,p)¹⁸⁶Ta reaction) affected by the γ ray of 615.17 keV with intensity 0.23345% are from the ¹⁸⁴W (n,α)¹⁸¹Hf 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 ¹⁸⁶W (n,γ)¹⁸⁷W reaction) and 618.3 keV (with 28% of the intensity from the ¹⁸⁶W (n,p)¹⁸⁶Ta reaction)(as shown in Fig.1), and significant interlaced overlap occurred between the FEPs of 737.5 keV and 739.2 keV (as shown in Fig. 2).

The cross sections were calculated using the equation proposed by Xiangzhong Kong et al.(1999) ^[11]. The cross-section values of the ¹⁸⁶W(n,p)¹⁸⁶Ta reaction were obtained relative to those of the ⁹³Nb(n,2n)^92mNb reaction.

The cross-section values of the ¹⁸⁶W (n,p)¹⁸⁶Ta reaction were obtained using the equation^[11] and net count of the FEP of 197.9 keV (using multichannel γ spectrum processing software). In this process, the effects from the ¹⁸²W(n,p)^182(m+g)Ta+¹⁸³W(n,d) ^182(m+g)Ta+¹⁸⁴W(n,t) ^182(m+g)Ta reactions have been deducted using the method in literature [12]. The obtained result with the superscript b is shown in Table 2 and plotted in Fig.4.

Fig.4Full-screen View

(Color online) Cross section of the ¹⁸⁶W (n, p)¹⁸⁶Ta reaction.

The cross-section values of the ¹⁸⁶W(n,p)¹⁸⁶Ta reaction were obtained using the equation in literature [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 ¹⁸⁴W (n,α)¹⁸¹Hf reaction was deducted using the method in literature [12]. The obtained results that are marked with the superscripts c and d are shown in Table 2 and plotted in Fig. 4.

The cross-section values of the ¹⁸⁶W(n,p)¹⁸⁶Ta reaction were obtained using the equation^[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 and plotted in Fig. 4.

The cross-section values of the ¹⁸⁶W(n,p)¹⁸⁶Ta reaction were also obtained using the equation ^[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 and plotted in Fig. 4.

The values given in the literatures [13-20] and the evaluated data from JEFF-3.3 and JENDL-4.0^[21] are shown in Table 2 and plotted in Fig. 4 for comparison. However, when Fig. 4 is plotted, the result from Ref. [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 ⁹³Nb(n,2n)^92mNb are obtained from Ref. [22] and listed in Table 2 as well.

As shown in Table 2 and 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. [13,18], 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] and [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

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. It is noteworthy that for the small interlaced overlap between the characteristic γ-ray FEP and other γ-ray FEPs, the symmetric conversion method based on Gaussian distribution is more suitable, while the energy average value of two close γ-rays (from radioactive nuclei generated by the same reaction) is more suitable for more interlaced overlap between the characteristic γ-ray FEP and other γ-ray FEPs.