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

NUCLEAR PHYSICS AND INTERDISCIPLINARY RESEARCH

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

Jia-Tai Li，

Xue-Dou Su，

Gao-Long Zhang ，

Guang-Xin Zhang ，

Shi-Peng Hu，

Jing-Bin Lu，

Yi-Feng Lv，

Hui-Bin Sun，

Huan-Qiao Zhang，

D. Testov，

P. R. John，

J. J. Valiente-Dobón，

A. Goasduff，

M. Siciliano，

F. Galtarossa，

F. Recchia，

D. Mengoni，

D. Bazzacco

Nuclear Science and Techniques

Vol.31, No.5

Article number 49

Published in print 01 May 2020

Available online 04 May 2020

DOI：10.1007/s41365-020-00758-x

45200

A ⁶Li + ⁸⁹Y experiment was conducted at the Laboratori Nazinali di Legnaro, INFN, Italy. The 550 μg/cm²-thick ⁸⁹Y target was backed on a 340 μg/cm ² thick ¹²C foil. The several γ rays in the experiment with energies higher than 3000 keV can most likely be ascribed to the transitions in the ¹³C nuclei, which can be formed through various interactions between the ⁶Li beam and the ¹²C foil. The high-energy properties of γ rays in¹³C are employed for energy calibrating HPGe detectors, especially for the >3000 keV region, which is impossible to reach by common standard sources (¹⁵²Eu, ¹³³Ba etc.). Furthermore, γ-γ and particle-γ coincidence measurements were performed to investigate the formation of ¹³C.

Energy calibrationCoincidence measurement

1 Introduction

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 ¹⁵²Eu, ¹³³Ba, ⁶⁰Co, and ¹³⁷Cs. 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, 2]. Moreover, the few standard radioactive sources that can emit γ rays with energies higher than 1500 keV have short lifetimes [3]: ⁶⁶Ga (833.5-4806 keV, 13 γ rays in total, T_1/2 = 9.49 h), 10 γ rays have energies higher than 1500 keV; ²⁴Na (1368.6 and 2754 keV, T_1/2 = 14.997 h); ⁵⁶Co (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, 3].

Assuming that one HPGe detector is calibrated by the ¹⁵²Eu 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] 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 ^6,7Li) have drawn considerable attention during the last few decades [4-18]. Owing to the low breakup threshold and the strong cluster structure of the weakly bound nuclei (e.g., ⁷Li 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, 10, 19-35].

In a fusion reaction study [10, 30, 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 ⁶Li + ⁸⁹Y experiment was performed in the Laboratori Nazinali di Legnaro (LNL), INFN, Italy. In this experiment, the ⁸⁹Y’s target back material was ¹²C foil. Details of the experimental procedure are recorded in Sect. 2. Several possible reaction processes between the ⁶Li beam and the ¹²C foil produce ¹³C nuclei as a by-product. Nevertheless, as discussed in Sect. 3, the characteristic γ rays (3684.5 and 3853.8 keV) in ¹³C were applied to calibrate the HPGe detector. Furthermore, in the same section, the presence of ¹³C was confirmed by γ-γ analysis and the possible reaction mechanisms that may be responsible for the production of ¹³C 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

This ⁶Li + ⁸⁹Y experiment was conducted using the INFN-LNL Tandem-XTU accelerator in Italy. A ⁶Li³⁺ beam with E_Lab = 34 MeV and an average beam intensity of 1.0 enA was impinged on a 550-μg/cm²-thick ⁸⁹Y target, which was backed by 340-μg/cm²-thick ¹²C foil. A schematic view of the detector arrays obtained from [36] is shown in Fig. 1. Around the target position, 40 ΔE-E silicon detectors (a silicon-ball named EUCLIDES [37]) and 25 HPGe detectors (GALILEO array [37]) were used to measure the light-charged particles and γ rays, respectively. Each ΔE detector had a thickness of 130 μm 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° [38-40]. Along the beam direction, an Al cylindrical absorber with a thickness of 200 μm was inserted inside EUCLIDES to protect the silicon detectors from elastically scattered beams. Additional experimental details can be found in the previous publication [36].

Fig. 1.

(Color online) Schematic view of detector array around the target position, which is obtained from [36]; 40 ΔE-E silicon telescopes and 25 HPGe detectors are used to measure the light-charged particles and γ rays, respectively.

3 Data analysis

3.1 Calibration of γ-ray energy spectrum

In the current experiment, the HPGe detectors were initially calibrated by the standard radioactive sources including ⁶⁰Co,⁸⁸Y, ¹³³Ba and ¹⁵²Eu, and the function of

E_{standard} = \sum_{j = 0}^{5} b_{j} \times C h a n n e l^{j}

(1)

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 bj relates to the calibration coefficients. It is noted here that in the current stage, the highest E_standard = 2734 keV (⁸⁸Y 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 ¹³C are displayed in Table 1 and Fig. 2, respectively [2, 41]. After the first-step calibration, Fig. 3(a) shows the γ-ray energy spectrum measured by different HPGe detectors at 90° during the ⁶Li+⁸⁹Y experiment. It was observed that the peak positions varied among different detectors.

Fig. 2.

Partial level scheme of ¹³C below the excitation energy of 4000 keV. The unit of energy for each state and the γ transition is keV [2, 41].

Fig. 3.

γ-ray energy spectrum of 10 HPGe detectors at 90° (3500 keV < Eγ < 4000 keV). (a) The first-step calibration. (b) The second-step calibration.

Partial characteristic γ transitions in ¹³C with Eγ < 4000 keV [2, 41].

Eγ(keV)	Transitions
169.3	${5 / 2}^{+} \overset{E 1}{\to} {3 / 2}^{-}$
595.1	${3 / 2}^{-} \overset{E 1}{\to} {1 / 2}^{+}$
764.4	${5 / 2}^{+} \overset{E 2}{\to} {1 / 2}^{+}$
3089.4	${1 / 2}^{+} \overset{E 1}{\to} {1 / 2}^{-}$
3684.5	${3 / 2}^{-} \overset{M 1 + E 2}{\to} {1 / 2}^{-}$
3853.8	${5 / 2}^{+} \overset{M 2 + E 3}{\to} {1 / 2}^{-}$

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) could be inaccurate. Conversely, detectors at 90° in 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). The two γ rays observed in each detector in Fig. 3(a) are probably attributed to the 3684.5 and 3853.8 keV transitions de-exciting the 3853.8 keV state in ¹³C as shown in 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 ¹³C 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) which are shown in the same energy region by Fig. 3(a). It can be concluded that the second-step energy-calibration solves the energy discrepancy for the γ rays with Eγ > 3500 keV in Fig. 3(b). The newly calibrated γ-ray energy spectra having different energy regions are also shown in Fig. 4. It can be seen in Fig. 4 that besides the γ transitions in ¹³C, other peaks corresponding to fusion-evaporation residues, such as ⁹²Mo, produced from the ⁶Li + ⁸⁹Y system were identified.

Fig. 4.

Newly calibrated γ-ray energy spectra. (a) Eγ < 1000 keV; (b) 1000 keV < Eγ < 2000 keV;(c) 3000 keV < Eγ < 4000 keV.

3.2 γ-γ coincidence analysis

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 ¹³C as shown in Fig. 2.

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), 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) 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. 5.

γ-ray energy spectra gated by the 169.3-keV γ ray (a), the 764.4-keV γ ray (b) and the 3089.4-keV γ ray (c).

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 ¹³C cannot be performed. The success in reconstructing the ¹³C level scheme proves reasonable the assumption that the γ rays observed in Fig. 3 belong to ¹³C.

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)). 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

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 ¹³C at 168.8-, 598.6-, 762.5-, 3684.6- and 3853.8-keV (see Table 1) are clearly visible in Fig. 6(a). The characteristic γ rays of ¹³C at 168.6- and 597.1-keV can also be observed in Fig. 6(b) with low statistics. The other characteristic γ rays of ¹³C as listed in Table 1 cannot be seen in Fig. 6(b) owing to their low relative intensities [2]. Thus, it can be concluded that (at least part of) the ¹³C nuclei are created in coincidence with α and protons.

Fig. 6.

The γ-ray energy spectra, which are measured in coincidence with (a) protons and (b) α particles, respectively.

Considering the possible reaction channels, there are several possible causal processes, such as (1) one-neutron stripping process, denoted as ⁶Li + ¹²C ⟶ ⁵Li + ¹³C^* (there is no bound state for ⁵Li thus it will disassociate into a proton and α immediately), (2) complete fusion of ⁶Li + ¹²C followed by the 1α1p evaporation channel, and (3) an incomplete fusion channel. This means that the ⁶Li breaks up to α and deuteron, and the deuteron is then captured by the ¹²C followed by one proton evaporation. All the aforementioned processes might account for the production of the ¹³C nuclei, since such (1)-(3) channels can populate ¹³C 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

A ⁶Li + ⁸⁹Y experiment to study fusion reactions induced by weakly bound nuclei was performed at INFN-LNL in Italy. ¹³C can be formed by the one-neutron stripping process, complete fusion channel and incomplete fusion channel between the ⁶Li beam, and the ¹²C back material. The characteristic γ rays of ¹³C 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 ¹³C is confirmed by γ-γ coincidence analysis and the formation of ¹³C in the ⁶Li + ¹²C system was investigated by particle-γ coincidence analysis.

References

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Energies and branching ratios of transitions in 13C

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