Energy calibration of HPGe detector using the high-energy characteristic γ rays in ¹³C formed in ⁶Li + ¹²C reaction

Energy calibration of HPGe detector using the high-energy characteristic γ rays in 13 C formed in 6 Li + 12 C reaction 1 2 first-author 1 1 3 corresp zgl@buaa.edu.cn. zgl@buaa.edu.cn. zgl@buaa.edu.cn. https://orcid.org/0000-0003-4615-3187 4 5 corresp Guangxin.Zhang@pd.infn.it Guangxin.Zhang@pd.infn.it Guangxin.Zhang@pd.infn.it https://orcid.org/0000-0003-4615-3187 6 7 7 6 8 4 5 4 5 9 4 5 9 10 9 4 5 4 5 4 5 School of Physics, Beihang University, Beijing 100191, China School of Physics, Beihang University, Beijing 100191, China Shenyuan Honors College, Beihang University, Beijing 100191, China Shenyuan Honors College, Beihang University, Beijing 100191, China Beijing Advanced Innovation Center for Big Data-based Precision Medicine, Beihang University, Beijing 100083, China Beijing Advanced Innovation Center for Big Data-based Precision Medicine, Beihang University, Beijing 100083, China Dipartimento di Fisica Astronomia dell’Universit'a di Padova, Padova, Italy Dipartimento di Fisica Astronomia dell’Universit'a di Padova, Padova, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italy College of Physics Science and Technology, Shenzhen University, Shenzhen 518060, China College of Physics Science and Technology, Shenzhen University, Shenzhen 518060, China College of physics, Jilin University, ChangChun 130012, China College of physics, Jilin University, ChangChun 130012, China China Institute of Atomic Energy, Beijing 102413, China China Institute of Atomic Energy, Beijing 102413, China INFN, Laboratori Nazionali di Legnaro, Legnaro (Padova), Italy INFN, Laboratori Nazionali di Legnaro, Legnaro (Padova), Italy Irfu/CEA, Universit de Paris-Saclay, Gif-sur-Yvette, France Irfu/CEA, Universit de Paris-Saclay, Gif-sur-Yvette, France A 6 Li + 89 Y experiment was conducted at the Laboratori Nazinali di Legnaro, INFN, Italy. The 550 μ g/cm 2 -thick 89 Y target was backed on a 340 μ g/cm 2 thick 12 C foil. The several γ rays in the experiment with energies higher than 3000 keV can most likely be ascribed to the transitions in the 13 C nuclei, which can be formed through various interactions between the 6 Li beam and the 12 C foil. The high-energy properties of γ rays in 13 C are employed for energy calibrating HPGe detectors, especially for the > 3000 keV region, which is impossible to reach by common standard sources ( 152 Eu, 133 Ba etc.). Furthermore, γ - γ and particle- γ coincidence measurements were performed to investigate the formation of 13 C. Energy calibration Coincidence measurement 1 Introduction 1 Owing to their excellent energy resolution, high-purity Germanium (HPGe) detectors are widely employed in the detection of γ transitions. In γ -ray spectroscopy experiments, the energy calibration of HPGe detectors is critical. To perform a reliable energy calibration for HPGe detectors, a set of standard radioactive sources that can emit many γ rays with precisely known energies are used, such as 152 Eu, 133 Ba, 60 Co, and 137 Cs. However, when the high-energy γ rays (for instance, E γ > 3500 keV) require analysis, such energy regions cannot be calibrated by the aforementioned sources since none of them can produce the required intense γ rays with energies higher than 3500 keV [ 1 1 , 2 2 ]. Moreover, the few standard radioactive sources that can emit γ rays with energies higher than 1500 keV have short lifetimes [ 3 3 ]: 66 Ga (833.5-4806 keV, 13 γ rays in total, T 1/2 = 9.49 h), 10 γ rays have energies higher than 1500 keV; 24 Na (1368.6 and 2754 keV, T 1/2 = 14.997 h); 56 Co (846.8-3548.1 keV, 14 γ rays in total, T 1/2 = 77.236 d), 9 γ rays have energies higher than 1500 keV [ 2 2 , 3 3 ]. Assuming that one HPGe detector is calibrated by the 152 Eu source, this detector could exclusively measure γ rays with energies up to approximately 1500 keV since the measured energy is only valid in that calibration region. In the extrapolation region, the measured energy derived from the calibration coefficient might deviate significantly from the real value. The situation would be improved if any known high-energy γ rays, produced either by the radioactive source [ 3 3 ] or the in-beam experiment, could be employed in the energy-calibration procedure. The investigation of reaction mechanisms induced by stable weakly bound nuclei (such as 6,7 Li) have drawn considerable attention during the last few decades [ 4 4 - 18 18 4-18 ]. Owing to the low breakup threshold and the strong cluster structure of the weakly bound nuclei (e.g., 7 Li has an α +t cluster structure and a small separation energy of 2.47 MeV. Also the breakup, as well as the transfer channels, may couple to the fusion reaction especially when the beam energies approach the Coulomb barrier, leading to a series of complicated and interesting processes [ 5 5 , 10 10 , 19 19 - 35 35 19-35 ]. In a fusion reaction study [ 10 10 , 30 30 , 33 33 ], γ -ray spectroscopy has already proven to be powerful since, in principle, the yields of each residual nucleus (excited states) can be obtained by counting their characteristic γ transitions. For this study, a 6 Li + 89 Y experiment was performed in the Laboratori Nazinali di Legnaro (LNL), INFN, Italy. In this experiment, the 89 Y’s target back material was 12 C foil. Details of the experimental procedure are recorded in Sect. 2. Several possible reaction processes between the 6 Li beam and the 12 C foil produce 13 C nuclei as a by-product. Nevertheless, as discussed in Sect. 3, the characteristic γ rays (3684.5 and 3853.8 keV) in 13 C were applied to calibrate the HPGe detector. Furthermore, in the same section, the presence of 13 C was confirmed by γ - γ analysis and the possible reaction mechanisms that may be responsible for the production of 13 C were investigated by particle- γ coincidence analysis. It should be noted that such energy calibration methods might be appropriate for other experiments when the targets are backed with a carbon foil. 2 Experimental procedure 1 This 6 Li + 89 Y experiment was conducted using the INFN-LNL Tandem-XTU accelerator in Italy. A 6 Li 3+ beam with E Lab = 34 MeV and an average beam intensity of 1.0 enA was impinged on a 550- μ g/cm 2 -thick 89 Y target, which was backed by 340- μ g/cm 2 -thick 12 C foil. A schematic view of the detector arrays obtained from [ 36 36 ] is shown in Fig. 1 Fig. 1 . Around the target position, 40 Δ E-E silicon detectors (a silicon-ball named EUCLIDES [ 37 37 ]) and 25 HPGe detectors (GALILEO array [ 37 37 ]) were used to measure the light-charged particles and γ rays, respectively. Each Δ E detector had a thickness of 130 μ m and the E detector had a thickness of 1 mm. The GALILEO array had 10 HPGe detectors at 90° relative to the beam direction, and another 15 detectors were equally spaced at 119°, 129°, 152° [ 38 38 - 40 40 38-40 ]. Along the beam direction, an Al cylindrical absorber with a thickness of 200 μ m was inserted inside EUCLIDES to protect the silicon detectors from elastically scattered beams. Additional experimental details can be found in the previous publication [ 36 36 ]. 3 Data analysis 1 3.1 Calibration of γ -ray energy spectrum 2 In the current experiment, the HPGe detectors were initially calibrated by the standard radioactive sources including 60 Co, 88 Y, 133 Ba and 152 Eu, and the function of <math display="block" id="M1"><mrow><msub><mi>E</mi><mrow><mtext>standard</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mn>5</mn></munderover></mstyle><msub><mi>b</mi><mi>j</mi></msub><mo>×</mo><mi>C</mi><mi>h</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>e</mi><msup><mi>l</mi><mi>j</mi></msup></mrow></math> were used to perform the first energy calibration step. Here, E standard represents the energy of known γ rays emitted from the aforementioned sources, Channel is the channel position of each γ ray in the raw ADC (specific name of ADC in front and ADC in the bracket) spectrum, and b j relates to the calibration coefficients. It is noted here that in the current stage, the highest E standard = 2734 keV ( 88 Y source). Thus, in the experiment, a measured γ ray with energy higher than 2800 keV may be observed in a position different from its actual energy, and such deviations can vary between different detectors. The partial level scheme and several known γ rays in 13 C are displayed in Table 1 Table 1 and Fig. 2 Fig. 2 , respectively [ 2 2 , 41 41 ]. After the first-step calibration, Fig. 3(a) Fig. 3(a) shows the γ -ray energy spectrum measured by different HPGe detectors at 90° during the 6 Li+ 89 Y experiment. It was observed that the peak positions varied among different detectors. 1 1 E γ (keV) 1 1 Transitions 1 1 169.3 1 1 <math id="M2"><mrow><msup><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mo>+</mo></msup><mover><mo>→</mo><mrow><mi>E</mi><mn>1</mn></mrow></mover><msup><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></mrow></math> 1 1 595.1 1 1 <math id="M3"><mrow><msup><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup><mover><mo>→</mo><mrow><mi>E</mi><mn>1</mn></mrow></mover><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>+</mo></msup></mrow></math> 1 1 764.4 1 1 <math id="M4"><mrow><msup><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mo>+</mo></msup><mover><mo>→</mo><mrow><mi>E</mi><mn>2</mn></mrow></mover><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>+</mo></msup></mrow></math> 1 1 3089.4 1 1 <math id="M5"><mrow><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>+</mo></msup><mover><mo>→</mo><mrow><mi>E</mi><mn>1</mn></mrow></mover><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></mrow></math> 1 1 3684.5 1 1 <math id="M6"><mrow><msup><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup><mover><mo>→</mo><mrow><mi>M</mi><mn>1</mn><mo>+</mo><mi>E</mi><mn>2</mn></mrow></mover><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></mrow></math> 1 1 3853.8 1 1 <math id="M7"><mrow><msup><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mo>+</mo></msup><mover><mo>→</mo><mrow><mi>M</mi><mn>2</mn><mo>+</mo><mi>E</mi><mn>3</mn></mrow></mover><msup><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mo>−</mo></msup></mrow></math> Since the first-step energy calibration included the E standard up to 2734 keV, the γ -ray energies measured in the region shown in Fig. 3(a) Fig. 3(a) could be inaccurate. Conversely, detectors at 90° in Fig. 3(a) Fig. 3(a) were selected to avoid a possible Doppler shift effect on the γ -ray measurement. In conclusion, the incorrect calibration in this energy region becomes the only possible explanation for the phenomenon shown in Fig. 3(a) Fig. 3(a) . The two γ rays observed in each detector in Fig. 3(a) Fig. 3(a) are probably attributed to the 3684.5 and 3853.8 keV transitions de-exciting the 3853.8 keV state in 13 C as shown in Fig. 2 Fig. 2 . Further confirmation of this assumption can be found in the following two subsections. A second-step calibration of the HPGe detector could then be performed. The γ rays which were used in the previous calibration, as well as 3684.5- and 3853.8-keV γ rays in 13 C were employed in the new energy calibration for the same functions Eq. 1 as shown before. The newly calibrated γ -ray energy spectra of each HPGe detector at 90° are shown in Fig. 3(b) Fig. 3(b) which are shown in the same energy region by Fig. 3(a) Fig. 3(a) . It can be concluded that the second-step energy-calibration solves the energy discrepancy for the γ rays with E γ > 3500 keV in Fig. 3(b) Fig. 3(b) . The newly calibrated γ -ray energy spectra having different energy regions are also shown in Fig. 4 Fig. 4 . It can be seen in Fig. 4 Fig. 4 that besides the γ transitions in 13 C, other peaks corresponding to fusion-evaporation residues, such as 92 Mo, produced from the 6 Li + 89 Y system were identified. 3.2 γ - γ coincidence analysis 2 In this section, γ - γ coincidence analysis, which is based on the result of the aforementioned second-calibration, is applied to confirm the partial level scheme of 13 C as shown in Fig. 2 Fig. 2 . Figs. 5(a)–(c) Figs. 5(a)–(c) show the γ -ray spectra which were gated by the 169.3-, 764.4- and 3089.4-keV transitions, respectively. From Figs. 5(a) and (b) Figs. 5(a) and (b) , it can be concluded that the 169.3- and 3684.5- keV γ rays were in coincidence with each other, the 764.4- and 3089.4-keV γ rays were also in conincidence with each other. Figure 5(c) Figure 5(c) not only re-confirms the coincidence between the 764.4- and 3089.4-keV transitions but also establishes the cascade order by identifying the 595.1-keV γ rays which were mutually in coincidence with the 169.3- and 3089.4-keV transitions. Consequently, this experiment confirmed the partial level scheme as shown in Fig. 2 Fig. 2 . Because the γ transitions with energies higher than 3000-keV are frequently referenced in previous explications, it may be concluded that without the second-calibration, the level scheme confirmation of 13 C cannot be performed. The success in reconstructing the 13 C level scheme proves reasonable the assumption that the γ rays observed in Fig. 3 Fig. 3 belong to 13 C. Moreover, 511 and 3172.1 keV γ rays can be identified in the newly calibrated γ -ray energy spectra and γ -ray energy spectrum which is gated by the 169.3-keV γ ray (see Fig. 5(a) Fig. 5(a) ). Since 3172.1-keV is approximately 511 keV smaller than 3684.5-keV, it is concluded that the 3172.1-keV peak is the single escape peak of the 3684.5-keV γ ray. 3.3 Particle- γ coincidence analysis 2 Figures 6 (a) and (b) Figures 6 (a) and (b) display the γ -ray energy spectra which are measured in coincidence with protons and α particles, respectively. The characteristic γ rays of 13 C at 168.8-, 598.6-, 762.5-, 3684.6- and 3853.8-keV (see Table 1) are clearly visible in Fig. 6(a) Fig. 6(a) . The characteristic γ rays of 13 C at 168.6- and 597.1-keV can also be observed in Fig. 6(b) Fig. 6(b) with low statistics. The other characteristic γ rays of 13 C as listed in Table 1 cannot be seen in Fig. 6(b) Fig. 6(b) owing to their low relative intensities [ 2 2 ]. Thus, it can be concluded that (at least part of) the 13 C nuclei are created in coincidence with α and protons. Considering the possible reaction channels, there are several possible causal processes, such as (1) one-neutron stripping process, denoted as 6 Li + 12 C ⟶ 5 Li + 13 C * (there is no bound state for 5 Li thus it will disassociate into a proton and α immediately), (2) complete fusion of 6 Li + 12 C followed by the 1 α 1p evaporation channel, and (3) an incomplete fusion channel. This means that the 6 Li breaks up to α and deuteron, and the deuteron is then captured by the 12 C followed by one proton evaporation. All the aforementioned processes might account for the production of the 13 C nuclei, since such (1)-(3) channels can populate 13 C with excited states, as well as α and proton particles, being consistent with the experimental observations. A more detailed, or quantitative investigation of the causal processes requires additional measurement of the charged particles ( α and protons) with considerably higher energy resolution. 4 Summary 1 A 6 Li + 89 Y experiment to study fusion reactions induced by weakly bound nuclei was performed at INFN-LNL in Italy. 13 C can be formed by the one-neutron stripping process, complete fusion channel and incomplete fusion channel between the 6 Li beam, and the 12 C back material. The characteristic γ rays of 13 C can be used for energy calibrating HPGe detectors in the high-energy region. It is concluded that this method is appropriate for other experiments with carbon foil and can contribute to the investigation of high-energy γ rays. The partial level scheme of 13 C is confirmed by γ - γ coincidence analysis and the formation of 13 C in the 6 Li + 12 C system was investigated by particle- γ coincidence analysis. References E. K. Warburton , D. E. Alburger and D. J. Millener . 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INFN-LNL Annual Report No. 105 , 2015 . The first physical campaign of the EUCLIDES Si-ball detector coupled to GALILEO gamma-ray spectrometer. INFN-LNL Annual Report No. 105 A. Gadea , E. Farnea , G. de Angelis , et al ., A new Charged particle Si detector for EUROBALL. INFN-LNL Annual Report No. 225 , 1996 . A new Charged particle Si detector for EUROBALL. INFN-LNL Annual Report No. 225 F. Ajzenberg-Selove . Energy levels of light nuclei A = 13-15 . Nuclear Physics A 268 ( 1 ): 1 - 204 ( 1976 ). https://doi.org/10.1016/0375-9474(76)90563-7 https://doi.org/10.1016/0375-9474(76)90563-7 Energy levels of light nuclei A = 13-15 We are grateful to the INFN-LNL staff for providing a stable 6 Li beam throughout the experiment. 10.1007/s41365-020-00758-x This work was supported by the National Natural Science Foundation of China (Nos. 11975040, U1832130 and 11475013) and the HIRFL User Project, CAS. 2019-10-11 2020-02-23 2020-02-25 2020-05-04 2020-05-01 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. 2020 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/s41365-020-00758-x http://dx.doi.org/10.1007/s41365-020-00758-x . 2020 Nuclear Science and Techniques 5 31