New measurements of 92Mo(γ, n) and (γ, 3n) reactions using laser-driven bremsstrahlung γ-ray

The flux-weighted average cross sections and isomeric ratios of ⁹²Mo(γ, n)^91m,gMo and ⁹²Mo(γ, 3n)⁸⁹Mo reactions were measured through activation methods. Laser-driven bremsstrahlung γ-ray were generated by the laser wakefield accelerated quasi-monoenergetic electrons using the 200 TW laser in the Compact Laser Plasma Accelerator laboratory, Peking University. The results showed good agreements with previous works using traditional γ-ray sources, and were compared with TALYS 1.9 calculations. We extended the experimental results of ⁹²Mo photonuclear reactions to higher energies, the experimental discrepancies of ⁹²Mo(γ, n)^91m,gMo isomeric ratios at high energy region were clarified, and the cross sections of ⁹²Mo(γ, 3n)⁸⁹Mo reaction were first obtained.

1 Introduction

With the rapid developments of laser electron accelerations, especially laser wakefield accelerations (LWFA) [1–7], laser-driven γ-ray can reach an extremely high intensities of 10^22–24 s⁻¹ [8–12], which are several orders of magnitude stronger than other γ-ray sources such as laser Compton scattering (LCS) [13, 14] or electron linac bremsstrahlung [15]. Researchers have shown considerable interests in laser-induced nuclear reactions in nuclear physics such as photonuclear studies [16, 17], photon fission [16, 18] and photon activation analysis [19].

Photonuclear reaction cross sections and their isomeric ratios (IR) play a significant role in nuclear structure, nuclear reaction mechanism, and nuclear astrophysics [20–22]. The IRs of a nuclear reaction were a powerful tool for testing nuclear structure theories and nuclear reaction models [20, 21, 23, 24]. In nuclear astrophysics, there are 30–35 proton-rich nuclei (p-nuclei) that can only be produced by p-processes [25–28]. The production mechanisms of p-nuclei contain a series of photonuclear reactions [29]. The experimental measurements of those reactions are vital for nuclear synthesis and stellar models [29]. Recently, Wu et al. successfully measured the flux-weighted average cross sections (FACS) and IRs of ¹⁹⁷Au(γ, xn; x = 1∼7) reactions using a 200TW laser facility [30]. Their results demonstrated that the accuracy of laser-driven γ-rays is sufficient for photonuclear reaction cross section and IR measurements.

⁹²Mo, one of the light p-nucleus pair ^92,94Mo [29], is a well known even-even nuclei with a spin of 0 and a neutron number of 50. For ⁹²Mo(γ, n)⁹¹Mo reaction, ⁹¹Mo can be formed with the isomeric state with a spin of 1/2⁻ or the ground state with a spin of 9/2⁺. A lot of works had reported the cross sections [31–33] and IRs [31, 34–39] of ⁹²Mo(γ, n)^91m,gMo reaction, but the experimental IRs did not match each other very well, especially at high energy region. In the giant dipole resonance (GDR) region, Thiep et al. [39] and Davidov et al. [37] had a maximum difference of 26%. In high energy region, Bartsch et al. [38] reported an IR of 0.97 at end-point energy of 55 MeV while Haustein et al. [35] measured an IR of 0.52 at end-point energy of 70 MeV, the huge difference is quite doubtful for high-energy IRs. For ⁹²Mo(γ, 3n)⁸⁹Mo reaction, no experimental cross section data are available for now.

In this study, we used laser-driven bremsstrahlung γ-rays to measure the FACSs and IRs of ⁹²Mo(γ, n)^91m,gMo reaction. The discrepancies of ⁹²Mo(γ, n)^91m,gMo IRs at high energy region were clarified. Meanwhile, the ⁹²Mo(γ, 3n)⁸⁹Mo reaction cross sections were first achieved.

2 Experiment

2.1 Accelerator

The experiments were performed at the 200 TW laser facility in the Compact Laser Plasma Accelerator (CLAPA) Laboratory, Peking University. The facility delivers 4 J, 30 fs, 5 Hz laser pulses in the center wavelength of 800 nm. 60∼250 MeV monoenergetic electrons were generated in LWFA by focusing the laser with a focal length of 100 cm on a supersonic nozzle. A 2 mm Ta (99.9%) disk was used as a bremsstrahlung converter. More details can be found in our previous work [30]. In this experiment, the averaged center energies of electrons were 135 ± 20, 103 ± 14, and 78 ± 10 MeV at gas pressures of 33, 36, and 39 bar, respectively, with a charge of 300∼600 pC per laser shoot. Typical electron spectra are shown in Figure 1. The bremsstrahlung γ-ray spectra were obtained by the average electron spectra of 100 continuous shots and GEANT4 simulations, which are also shown in Figure 1. The γ-ray intensities ($\ge$8 MeV) were (1.60$\pm 0.14)\left.\right)\times {10}^8$, (1.76$\pm 0.13)\left.\right)\times {10}^8$, and (1.84$\pm 0.11)\left.\right)\times {10}^8$ per shoot at gas pressures of 33, 36, and 39 bar, respectively, the duration times were about 6.7 ps, which made the instantaneous intensities higher than 10¹⁹ S⁻¹.

FIGURE 1

FIGURE 1. (A–C) are the typical LWFA electron spectra obtained by the magnetic spectrometer at gas pressure of 33, 36, 39 bar, respectively. (D) is the bremsstrahlung γ-ray energy spectra obtained from GEANT4 simulations using the averaged electron spectra of 100 continuous shots.

2.2 Target

A laminated target made of 0.1mm ^natMo (99.99%), 0.1 mm ^natCu (99.99%), and 1 mm ²⁷Al (99.99%) was used for activation analysis in this experiment, all targets had a size of 2 × 2 cm. Some relative nuclear spectroscopic data of the radioactive nuclei from the Mo photonuclear reaction are shown in Table 1 [40]. The ⁶⁵Cu(γ, n)⁶⁴Cu reaction (threshold energy at 9.91 MeV) and the ²⁷Al(γ, 2pn)²⁴Na reaction (threshold energy at 31.45 MeV) were used as γ-ray flux monitors [15, 41]. The measurements of the FACSs of ⁶⁵Cu(γ, n)⁶⁴Cu reaction and ²⁷Al(γ, 2pn)²⁴Na reaction directly reflected the accuracy of γ-ray spectrum. The repetition frequency was set at 0.2 Hz to keep the vacuum at acceptable levels. The irradiation time of each laminated target was 20 min for each electron energy.

TABLE 1

TABLE 1. Relative nuclear spectroscopic data of the radioactive nuclei from the Mo photonuclear reactions.

2.3 Detector

Two HPGe detectors with a relative efficiency of 40% and a 3 × 3 inch LaBr₃ detector were used to measure activation signals after irradiation, all detectors were shielded in Pb brick. The detector efficiencies were calibrated using a standard ¹⁵²Eu source and a standard ⁶⁰Co source with an energy range of 121.8–1,408.0 keV, and were finally determined by GEANT4 simulations [42, 43]. The measuring of the Mo target started 1.5 min after the irradiation using a HPGe detector, the spectrum was saved every minute to analyze the decay characteristics and the total measuring time of each Mo target was 20 min. A typical activation spectrum of the Mo target with a measuring time of the first 3 min is shown in Figure 2.

FIGURE 2

FIGURE 2. A typical spectrum of Mo target at gas pressure of 33 bar. The background spectrum measured for 5 h with a blank Mo target was also shown in the figure, the spectrum counts were normalized due to the living times.

3 Data analysis

As shown in Table 1 and Figure 2, the 652.9 and 1,508.0 keV γ-ray from ^91mMo decay were clearly distinguished, but the 511 keV annihilation γ-ray of β + decay can be produced in a variety of ways. The ⁹⁰Mo and ⁹⁰Nb have relatively long half-life times compared with ^91m,gMo and ^89gMo. Their contributions are relatively small due to the short irradiation time and can be regarded as a constant value during the short measuring time. The 511 keV signal of the background spectrum, as shown in Figure 2, is the combination of the β+ decay and the 510 keV γ-ray decay of ²²²Rn in the environment, it was taken out as a constant value in our calculations. For the 568.6 keV γ-ray from ^89gMo decay, it could not be distinguished from the 657.9 keV γ-ray from ⁹⁷Nb decay because of the similar energy. Meanwhile, the ^89mMo could not be measured in this experiment due to its short half-life time of 190 ms. Therefore, the yields of ^91mMo were determined by the 652.9 keV γ-ray and the yields of ^91gMo and ⁸⁹Mo were determined by the 511 keV γ-ray.

The FACS σ_FA(E) is defined as

${\sigma }_{FA}\left(E\right)=\frac{{\int }_{E_{\mathit{thr}}}^{E_{\mathit{max}}}\sigma \left(E\right)\phi \left(E\right)dE}{{\int }_{E_{\mathit{thr}}}^{E_{\mathit{max}}}\phi \left(E\right)dE}(1)$

where E_thr is the reaction threshold, E_max is the maximum energy of the γ-ray, σ(E) is the energy-dependent reaction cross section, φ(E) is the bremsstrahlung γ-ray flux. The reaction thresholds for the productions of ^91gMo, ^91mMo, and ⁸⁹Mo are 12.67, 13.32, and 36.01 MeV, respectively. Then the FACS can be given by

${\sigma }_{FA}\left(E\right)=\frac{Y\left(E\right)}{N_0{\int }_{E_{\mathit{thr}}}^{E_{\mathit{max}}}\phi \left(E\right)dE}(2)$

where Y(E) is the total yield, N₀ is the target nuclear number. The IR can be determined by

$IR=\frac{{\sigma }_{FA}^m\left(E\right)}{{\sigma }_{FA}^g\left(E\right)}(3)$

where m and g stand for the parameters of isomeric state and ground state, respectively.

4 Results and discussion

The present FACSs and IRs are listed in Table 2 and shown in Figures 3, 4, 5 with comparisons of the previous works [31–39]. The statistical errors in this experiment range from 4.4% to 11.3% for different decay γ-ray, and the systematic errors include the instabilities of each electron pulse, the γ-ray spectrum calculation, the calibration of detection efficiency, and the correction of the activation target.

TABLE 2

TABLE 2. Experimental flux-weighted average cross sections of⁹²Mo(γ, n) and (γ, 3n) reactions determined by present work and theoretical values of TALYS 1.9 calculated using a monoenergetic electron beam with the energies of 78, 103 and 135 MeV.

FIGURE 3

FIGURE 3. Experimental results of ⁹²Mo(γ, n)^91m,gMo reaction FACSs, comparing with previous works [31–33] and TALYS 1.9 calculations.

FIGURE 4

FIGURE 4. Experimental results of ⁹²Mo(γ, n)^91m,gMo reaction IRs, comparing with previous works [31, 34–39] and TALYS 1.9 calculations.

FIGURE 5

FIGURE 5. Experimental results of ⁹²Mo(γ, 3n)⁸⁹Mo reaction FACSs, comparing with TALYS 1.9 calculations.

Theoretical values of the FACSs and IRs were calculated by GEANT4 simulation using the data from TENDL-2019 library [44] based on TALYS 1.9 code [45, 46], which were also shown in Tab. 2, Figure 3, Figure 4, and Figure 5.

For ⁹²Mo(γ, n)^91m,gMo reaction, the total FACSs matched well with previous works. As shown in Figures 3, 4, the TALYS 1.9 calculation could not describe the reaction to the isomeric state or the ground state well, even though it gave a well-matched value of total cross sections. The TALYS 1.9 calculation underestimated the ⁹²Mo(γ, n)^91gMo reaction cross sections by 38% at maximum while overestimated the ⁹²Mo(γ, n)^91mMo reaction cross sections by 27% at maximum. The deviations between theory calculations and experiments might be caused by the inappropriate parameters of nuclear reaction model, nuclear level density, or optical potential, more theory calculations are stilled needed for this reaction. The IRs measured in this work matched well with the value of Bartsch et al. [38] within the uncertainties, the experimental discrepancies of ⁹²Mo(γ, n)^91m,gMo IRs were clarified. For ⁹²Mo(γ, 3n)⁸⁹Mo reaction, which is first achieved in this experiment, the TALYS 1.9 calculation described the FACSs very well.

5 Conclusion

The FACSs and IRs of ⁹²Mo(γ, n)^91m,gMo reaction and ⁹²Mo(γ, 3n)⁸⁹Mo reaction were determined using laser-driven γ-ray by activation measurements. The experimental discrepancies of ⁹²Mo(γ, n)^91m,gMo IRs at high energy region were clarified. However, we found thar the TALYS 1.9 code was not suitable for the production calculations of ⁹²Mo(γ, n) reaction, highlighting the need for more theoretical calculations. Additionally, the ⁹²Mo(γ, 3n)⁸⁹Mo reaction FACSs were achieved for the first time, filling in the gap of relevant experimental data.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

DW designed and preformed the experiment. DW, HL, and JZ analyzed the experimental data and performed TALYS and GEANT4 calculations. JL, JL, and HL performed the laser electron acceleration. XX and YG provided guidance on laser electron acceleration. HZ and YZ operated and optimized the laser machine. DW, HW, FL, and CH were involved in the activation measurement. JY, BG, NW, and XY provided investigations and resources for the experiment. XY was the supervisor of this work. DW wrote the first draft of the manuscript and HL and JL edited and contributed to sections of the manuscript. All authors contributed to the final editing and revision of the manuscript and approved it for submission.

Funding

This work was supported by the National Natural Science Foundation of China (Grants No. 11921006, 12125509), Beijing Outstanding Young Scientists Program, the National Grand Instrument Project (No. 2019YFF01014400), and the Open Foundation of Key Laboratory of High Power Laser and Physics, Chinese Academy of Sciences (No. SGKF202104).

Acknowledgments

The authors thank the staff of the 200 TW laser of CLAPA laboratory for the smooth operation of the machine.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer YS declared a shared affiliation with the authors HW, FL, BG, NW, and CH to the editor at the time of review.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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