Transmutation by neutrons, produced by high flux accelerated protons bombarding a heavy metal target, is the primary method to deal with long-lived fission products (LLFPs) with large neutron capture cross-sections. However, for nuclides, whose neutron capture cross sections are small, this method is not very efficient. In addition, (n, γ) reactions may transmute stable nuclides into long-lived radiotoxic nuclides. For example, ¹³³Cs is stable, of which the (n, γ) transmutation product will be ¹³⁴Cs followed by ¹³⁵Cs. They are unstable and radiotoxic with long half-lives of 2.06 years and 2.3 million years, respectively.

Photo-transmutation can be a good supplement to neutron transmutation.^[1] There are several methods to obtain γ rays: positron annihilation in flight, bremsstrahlung, laser-Compton scattering (LCS), and nuclear resonance reactions. γ-ray beams obtained by positron annihilation in flight is of low intensity, thus it is not appropriate for transmutations. Transmutations of ¹²⁹I based on a laser-induced bremsstrahlung (LIB) source have been already performed experimentally in Germany,^[2–4] UK,^[5] and Japan.^[6] Theoretical investigations have been done on LLFPs such as ¹²⁶Sn,^{[7,8] 107}Pd,^{[9] 93}Zr,^{[10] 90}Sr,^{[11] 135}Cs,^[12–14] and ¹³⁷Ca.^[15] An LCS γ-ray source can produce γ-rays in a wide energy range, which can be utilized to transmute LLFPs. The Upgraded HIγS, operating since 2009, can produce up to 3×10⁹ photons/s. The energy of photons can be adjusted in 1 MeV–100 MeV. The energy of electron beam is 0.24 GeV–1.2 GeV and the laser wavelength is . The rate of transmutation reaction of ¹³⁵Cs by the Upgraded HIγS is evaluated in Ref. [16] to reach 10¹¹ per hour. Studies^[17,18] show that the LCS-based photo-transmutation is more efficient than LIB. Many experimental^[19,20] and theoretical^{[14,16–18,21]} studies have been done using LCS γ-ray source to transmute LLFPs.

In the present paper, γ rays emitted from resonance reactions induced by proton is utilized to transmute LLFPs. Nuclear resonance reaction can produce mono-energetic γ rays, which can be used to transmute LLFPs. To do so, the energy of incident protons is supposed to be hundreds of keV to several MeV. Figure 1 shows high power proton beams worldwide (non exhaustive) crossing this region.^[22–30] The mean beam current of high power proton beams that have already been constructed can reach 100 mA.

Fig. 1

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	Fig. 1 High current proton beams worldwide (non exhaustive) in MeV region.

The excited levels of the compound nucleus are discrete and widely spaced when the bombarding proton energies are low. The so-called Breit–Wigner formula, as shown below, gives a good description for the cross section of a single resonance level,

Table 1.

Table 1.

Table 1. γ yields of some narrow resonance reactions. . Reactions Resonance γ-ray Thick target Width energy/keV energy/MeV yield/proton Γ/keV 7Li(p, γ) 441.4 ± 0.5 14.8(33%) 1.9×10−8 12 17.6(67%) 9Be 998.0±4 7.4 1.78×10−8 94 1087.0±2 6.7, 0.72 1.01×10−9 4 19F 340.0±2 6.1(96%) 1.74×10−8 3.2 7.0(4%) 873.5±1 6.1(72%) 3.6×10−7 5.2 7.0(28%) 935.3±1 6.1(77%) 2.0×10−7 8.0 7.0(23%) 6.1(72%) 6.9×10−7 – 7.0(28%) 13C 1747 9.17 4.7×10−9 –

Table 1. γ yields of some narrow resonance reactions. .

The GDR peak energy of most LLFPs is about 15 MeV, therefore it would be better to use the reaction ⁷Li ⁸Be to obtain higher transmutation rates. According to the data listed in Table 1, the yield of 14.8 MeV (33%) and 17.6 MeV (67%) γ rays emitted from ⁷Li when the energy of incident protons is 441.4 keV is 1.90×10⁻⁸ per proton in total.^[31,32] The yield of 9.17-MeV γ-ray emitted from ¹³C ¹⁴N is 4.7×10⁻⁹.^[33]

Different compound nuclides have different energy levels ranging from several hundreds of keV to tens of MeV, which cover most Giant Dipole Resonance (GDR) regions. The yields of γ-radiation produced by proton beams in narrow resonance region follow the equation:

Next, using the γ-radiation produced above, we obtain the transmutation rate without considering secondary process:

From Eqs. (2) and (3), we can increase the transmutation rate n_t in the following ways: 1) higher proton beam intensity I_p; 2) reactions with higher cross-section of proton induced γ-rays; 3) larger solid angle of the transmutation target.

3. ¹⁹⁷Au ¹⁹⁶Au experiment

First, to ensure the accuracy of the calculation, the experiment of ¹⁹⁷Au ¹⁹⁶Au was carried out in the 2×1.7-MV tandem accelerator of China Institute of Atomic Energy (CIAE).^[33] Two gold targets of the same size are irradiated. Figure 2 shows the transmutation process. The γ photons are produced by ¹³C ¹⁴N reaction when the resonant energy of incident protons is 1.747 MeV. ¹³C is evaporated onto a ϕ10×2 mm gold target up to a mass thickness of . Bombarded by the 9.17-MeV γ photons, ¹⁹⁷Au can be transmuted into ¹⁹⁶Au through reaction. However, ¹⁹⁶Au is unstable, it decays to ¹⁹⁶Pt through electron capture process and to ¹⁹⁶Hg through β decay.

Fig. 2

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	Fig. 2 197Au transmutation process.

The first sample is radiated for 6 hours and the second for 5.5 hours. Then, the radioactivity of the irradiated gold samples is measured in a low-background lead chamber with anti-Compton method used to reduce the background radioactivity. The detected counts obey the exponential law given by

Fig. 3

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	Fig. 3 γ spectrum of irradiated 197Au, peaks at 355.73 keV (Iγ=87%) and 333.03 keV (Iγ=22.9%) originates from 196Au.

Table 2.

Table 2.

Table 2. Transmutation numbers of different samples. . Sample Tirradiation/s NDet Ntr/106 1 21600 1566 ± 49 1.01 ± 0.03 2 19800 6610 ± 100 1.09 ± 0.02 Average 20700 – 1.05 ± 0.03

Table 2. Transmutation numbers of different samples. .

The thick target γ photon yield of ¹³C was measured with an HPGe detector (GXM35P4-70). The maximum yield of 9.17-MeV γ photons is (4.7±0.4)×10⁻⁹/proton.^[33] As the average current of the proton beam during the ¹⁹⁷Au transmutation experiment is , the number of incident protons during 20700-s irradiation time is 1.04×10¹⁸, producing (4.9±0.4)×10⁹ γ photons.

In the Geant4 simulation, 4.9×10⁹ γ photons are assumed to be emitted in 4π direction from a point source. The point source is on the center of the front surface of a ϕ10×2 mm gold target, with zero distance. The number of transmutation is (6.6±0.5)×10⁵, which is 37% less than the experimental results but with no deviation in magnitude.

In this section, we simulate photo-transmutation yields of nuclear waste like ¹²⁹I. The photonuclear cross sections of ¹²⁹I extracted from Geant4 packages are shown in Fig. 4.

Fig. 4

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	Fig. 4 Photonuclear cross section. The red circle, black square, and blue triangle present the cross section of 129I 128I, 129I 127I, and in total, respectively. The unit 1 b = 10−28 m2.

Photoelectric effect, Compton effect, pair production, and photo-nuclear reactions are the principal mechanisms by which γ rays interact with matter. Figure 5 shows cross section of each mechanism when γ rays interact with ¹²⁹I.

Fig. 5

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	Fig. 5 129I cross section of different mechanisms, the black square, red circle, blue triangle, and pink inverted triangle show a cross section of the photo-nuclear reaction, photoelectric effect (pho), pair production (conv), and Compton effect (Compt), respectively.

Assuming the intensity of the proton accelerator is 10 mA at 441 keV, according to the yields of 441-keV narrow resonance of reaction ⁷Li ⁸Be in Table 1, γ-ray yield of 14.8 MeV and 17.6 MeV can reach 1.2×10⁹ per second, and the γ-ray source, produced by the reaction ⁷Li ⁸Be, is assumed to be point shape and isotropic in 4π direction, of which 33% are 14.8 MeV and 67% are 17.6 MeV. Next, the ¹²⁹I target, with width and height are 2 cm, is placed 5 cm away from the point source. The ¹²⁹I ¹²⁸I yields against target depth are shown in Fig. 6, the maximum yield can reach 5.7×10⁻⁵ per γ. Taking the γ-ray yield into consideration, there are 6.8×10^{4 129}I ¹²⁸I reactions per second.

Fig. 6

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	Fig. 6 Yields of 129I 128I, the red circle, black square, and blue triangle show transmutations rates of 14.8-MeV γ photons, 17.6-MeV γ photons, and weighted average respectively.

Regarding transmutation of other LLFPs based on ⁷Li ⁸Be 441-keV resonance γ-radiation in the same condition as mentioned earlier but the point source with zero distance is on the front surface center of the targets and the targets are as thick as 10 cm. The rates of transmutation reactions are calculated and shown in Table 3.

Table 3.

Table 3.

Table 3. Transmutation rates of different LLFPs. . Reactions/hour 129I 135Cs 126Sn 93Zr 107Pd 137Ca 90Sr 4.7×109 2.1×109 2.8×109 8.6×1010 9.7×1010 1.8×109 2.8×109 4.7×109 2.2×109 7.9×109 7.9×1010 5.4×1010 2.5×109 6.1×109 Total 9.4×109 4.3×109 1.1×1010 1.7×1011 1.5×1011 4.3×109 8.9×109

Table 3. Transmutation rates of different LLFPs. .

The transmutation rate of ¹³⁵Cs is 10⁹ per hour is shown in this chart in total. According to Ref. [16], among LCS facilities constructed around the world, the best transmutation ability is of the Upgraded HIγS, which can reach 10¹¹ per hour, the HIγS is 10⁹ per hour, and the NewSUBARU is 10⁸ per hour.

Considering a 10-mA proton accelerator, nuclear waste transmutation driven by ⁷Li ⁸Be 441-keV narrow resonance γ-rays have been investigated through Geant4 simulation. The maximum transmutation yield of ¹²⁹I is 9.4×10⁹ per hour. The transmutation yield of ¹³⁵Cs is obtained to be the same order as HIγS of 10⁹, which is less than that of the upgraded HIγS by one order of magnitude but greater than that of the NewSUBARU by two orders of magnitude. In the future, we will improve the transmutation rates by improving the current of the proton accelerator, searching for higher yields of γ-radiation in GDR region, designing better target structure, and so on. Moreover, when compared with the good direction of LCS γ source, the γ-radiation emitted from narrow resonance is in directions, which is appropriate for large areas of LLFP radiation.

The authors would like to thank Prof. Bing Guo, Prof. Hong-Wei Wang, Prof. Wen Luo, and Prof. Shi-Lun Guo for valuable comments. We appreciate the help from Dr. Yang-Ping Shen on the simulation.