Cross-sections for (n,2n), (n,α), (n,p),(n,d) and (n,t) reactions on molybdenum isotopes in the neutron energy range of 13 to 15 MeV

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Junhua Luo and Li Jiang. Cross-sections for (n,2n), (n,α), (n,p),(n,d) and (n,t) reactions on molybdenum isotopes in the neutron energy range of 13 to 15 MeV[J]. Chinese Physics C.
Junhua Luo and Li Jiang. Cross-sections for (n,2n), (n,α), (n,p),(n,d) and (n,t) reactions on molybdenum isotopes in the neutron energy range of 13 to 15 MeV[J]. Chinese Physics C. shu
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Cross-sections for (n,2n), (n,α), (n,p),(n,d) and (n,t) reactions on molybdenum isotopes in the neutron energy range of 13 to 15 MeV

    Corresponding author: Junhua Luo, luojh71@163.com
  • 1. Institute of New Energy, Hexi University, Zhangye 734000, China
  • 2. School of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000, China
  • 3. Institute of Nuclear Physics and Chemistry, Chinese Academy of Engineering Physics, Mianyang 621900, China

Abstract: Given the insufficient cross sectional data regarding the 14 MeV-neutron experiment of molybdenum, the vital fusion reactor structural material, as well as the significant heterogeneities among the reported values, this study examined the (n,2n), (n,α), (n,p), (n,d) and (n,t) reaction cross sections in the molybdenum isotopes based on those neutrons produced via T(d,n)4He reaction carried out in Pd-300 Neutron Generator at the China Academy of Engineering Physics (CAEP). The high-resolution gamma-ray spectrometer, which was equipped with the coaxial high-purity germanium detector, was used to measure the product nuclear gamma activities. Besides, 27Al(n,α)24Na along with 93Nb(n,2n)92mNb reaction was utilized as the neutron fluence standards. The experimental 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo, 98Mo(n,α)95Zr, 100Mo(n,α)97Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, 98Mo(n,p)98mNb, 92Mo(n,d)91mNb and 92Mo(n,t)90Nb reaction cross sections were acquired within the 13–15 MeV neuron energy range. Thereafter, we compared and analyzed those cross-sections obtained based on the existing IAEA-EXFOR database-derived experimental data, together with evaluation results in ENDF/B-VIII.0, JEFF-3.3, BROND-3.1, CENDL-3.1, and the theoretical outcomes acquired through TALYS-1.95 and EMPIRE-3.2.3 (the nuclear-reaction modeling tools).

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    1.   Introduction
    • Molybdenum (Mo) has been identified as one of the top five refractory metals with high resistance to intense pressure and heat. It is resistant to pressure, corrosion as well as high temperature, rendering it an ideal material for nuclear reactor, like the International Thermonuclear Experimental Reactor (ITER), together with the accelerator-driven subcritical systems (ADSs) [1]. Mo, a kind of plasma-facing material, has been utilized in fusion reactor. The 3H(d,n)4He reaction can be employed to obtain an output as high as 14 MeV, and the flux rate was approximately 3×1014n/s [2]. Natural molybdenum occurs as seven isotopes, which were 92Mo, 94Mo, 95Mo, 96Mo, 97Mo, 98Mo and 100Mo, accounting for 14.53%, 9.15%, 15.84%, 16.67%, 9.60%, 24.39% and 9.82%, respectively [3]. Therefore, structural material activation within the fusion reactor should be taken into consideration. Various nuclear reactions can be induced through neutrons at the incident neutron energy of 14 MeV, such as (n,2n), (n,α), (n,p), (n,d), as well as (n,t) [4]. Consequently, for Mo isotopes, the cross section data induced by neutrons can be used to be the vital approach to estimate the radiation damage, integral calculations and nuclear heating on the shield, blanket and first wall, respectively, for the conceptual fusion power reaction [5, 6] together with more associated nuclear engineering calculations. Nonetheless, for Mo isotopes, the reaction cross sections of 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo, 98Mo(n,α)95Zr, 100Mo(n,α)97Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, and 98Mo(n,p)98mNb at about 14 MeV are determined by some studies [7-68], yet great differences are found among results obtained from the Exchange Format (EXFOR) experimental nuclear reaction database [69]. The probable cause is attributable to the dissimilarities of nuclear parameters, data processing approaches, experimental methodology, and devices. For instance, for the 92Mo(n,2n)91Mo reaction, we found twenty-seven laboratories [733] reporting those neutrons-induced cross section profiles obtained experimentally based on the D–T reaction. Typically, only one study used characteristic gamma-ray method to determine the daughter nucleus activity [22], and all of the rest used the annihilation radiation or beta counting method. For the 94Mo(n,2n)93mMo reaction, we found that just ten laboratories [5, 6, 21, 31, 3439] provided neutrons-induced cross section profiles obtained experimentally based on D–T reaction; meanwhile, four studies reported a single cross section datum based on a singular neutron energy. The energy region at about 14 MeV has been extensively investigated, and 100Mo(n,2n)99Mo data are classified to three bands differing by approximately 30% and 20%, separately. These include those experimental values from refs. [21, 24, 30, 33, 41, 44] clustered at the 1800 mb cross-section value, as well as values reported in the refs. [1, 6, 8, 15, 34, 35, 39-40, 42, 43, 46-49] concentrated at about 1400 mb. However, those values in ref. [45] focuses at about 1130 mb, while those in ref. [9] varies widely in the range of 3790±1895 mb at 14.5 MeV energy point. Furthermore, there are also significant differences in the nuclear model calculations at about 14 MeV neutron energy, and they are discovered based on results obtained from the software packages EMPIRE-3.2.3 [70] and TALYS-1.95 [71]. To take an example, in 98Mo(n,α)95Zr reaction, EMPIRE-3.2.3 calculations produce results that are about thrice of those produced by TALYS-1.95 calculations at about 14 MeV neutron energy. Similarly, in the 100Mo(n,α)97Zr reaction too, EMPIRE-3.2.3 calculation results are about thrice of those obtained from the TALYS-1.95 calculations at about 14 MeV neutron energy. In 92Mo(n,p)92mNb and 96Mo(n,p)96Nb reactions, such divergence between the early experimental data is also very large. For the 14 MeV energy region, those experimental data are distributed in the intervals of 40~85 mb [6, 7, 12, 14, 21, 22, 34-40, 43, 45, 49, 50, 52, 53, 56] and 10~35 mb [5, 6, 12, 19, 21, 22, 24, 31, 34, 35, 37, 40, 43, 45, 47, 50-54, 62], respectively. With regard to cross-section data obtained from nuclear reaction 98Mo(n,p)98mNb, such divergence among the early literature results is more prominent as seen from the distribution of values in a wide range of 2 to 20 mb [5, 6, 12, 19, 21, 22, 31, 34, 35, 38-40, 43, 45, 50, 53, 56, 63, 66-68], the maximum value being nearly 10 times of the minimum value. For the 97Mo(n,p)97Nb reaction, we found just fifteen laboratories [5, 6, 21, 22, 35, 37, 40, 43, 45, 50, 51, 54, 63-65] stating neutron-induced cross-section values obtained experimentally based on D–T reaction, among which, two were abnormal data. One gave significantly larger results at the 14.7 MeV energy point (72.7±4.3 mb) [63] than the others reported, and the other used inappropriate decay data (Eγ=743.32 keV, Iγ=97.95%, obviously, this ray comes from the excited state of product 97Nb, and not the ground state) [64]. For 92Mo(n,d)91mNb [51, 72, 73] and 92Mo(n,t)90Nb [74-76] reactions only three laboratories examine neutron-induced cross-section values obtained at about 14 MeV neutron energy, with a majority at one singular neutron energy. Moreover, no consensus is reached among such values.

      Consequently, precisely measuring those reaction cross-sections on Mo isotopes at 14 MeV neutron energy is necessary. In this study, we measured the 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo, 98Mo(n,α)95Zr, 100Mo(n,α)97Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, 98Mo(n,p)98mNb, 92Mo(n,d)91m1Nb and 92Mo(n,t)90Nb reaction cross sections at three neutron energies in the 13–15 MeV region. Specifically, we used a data acquisition system and gamma-ray counting from the high-resolution gamma-ray spectrometer. Besides, the coaxial high-purity germanium (HPGe) detector was utilized to absolutely measure the gamma activities of the product nuclei, so as to obtain reaction yields. In the process of irradiation, we wrapped each sample within the pure cadmium foils, for the sake of avoiding those effects of reactions 98Mo(n,γ)99mMo and 92Mo(n,γ)93mMo induced by thermal neutron to reactions 100Mo(n,2n)99Mo and 94Mo(n,2n)93mMo, separately. All results obtained were analyzed and compared with those previously reported, those evaluated from ENDF/B-VIII.0 [77], JEFF-3.3 [78], BROND-3.1 [79], CENDL-3.1 [80], and those theoretical values acquired through the EMPIRE-3.2.3 [70] and TALYS-1.95 [71] nuclear-reaction modeling tools.

    2.   Experimental
    • The radioactive products were identified to measure the cross sections of nuclear reactions. The detailed procedure is available from published works [8185]. Only a few salient characteristics associated with our measurements are shown in this study.

    • 2.1.   Samples and irradiation

    • Natural molybdenum foils (purity, 99.99%; thickness, 0.5 mm) were prepared as the circular samples (diameter, 20 mm). Then, they were sandwiched by two niobium foils (thickness, 0.5 mm; purity, 99.99%) or aluminium foils (thickness, 0.3 mm; purity, 99.999%) as neutron flux monitor with the same diameter as the circular molybdenum foil. Afterwards, the cadmium foil (thickness, 1 mm; purity, 99.95%) was used for wrapping to decrease the impacts of reactions 98Mo(n,γ)99mMo and 92Mo(n,γ)93mMo induced by thermal neutrons on reactions 100Mo(n,2n)99Mo and 94Mo(n,2n)93mMo, separately.

      The Pd-300 Neutron Generator was used for sample irradiation for 2 h at the Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, and the yield was around (3~4)×1010 n/s. Then, the 3H(d,n)4He reaction was utilized to generate neutrons at 14 MeV energy by means of the 200 μA beam current and the 135 keV deuteron beam energy. For this neutron generator, it adopts solid tritium–titanium (T–Ti) target with the thickness of approximately 2.4 mg cm−2. At the time of irradiation, those accompanying α-particles were utilized to monitor neutron flux, and an Au–Si surface barrier detector that was placed at 135° was used to detect them. In this way, those small changes in neutron flux were corrected. We put all samples at 0°, 90°, and 135°, separately, compared with deuteron beam direction. All samples were approximately 5 cm away from the T–Ti target center.

    • 2.2.   Incident neutron energy measurement

    • For the present experiment, the average neutron energy values adopted for sample irradiation at the emergent angles of 0°, 90° as well as 135° were measured according to the following formulae: [86]

      $ \overline E ({0^ \circ }) = \frac{{2{L^2}}}{{{R^2}}}\int_0^{{\rm{arctan}}\left( {R/L} \right)} {{E_{\rm{n}}}(\theta )\frac{{{\rm{tan}}\theta }}{{{{\cos }^2}\theta }}} {\rm{ d}}\theta $

      (1)

      $ \begin{split} \overline E ({90^ \circ }) = & \frac{{2L}}{{\pi {R^2}}}\int_{\frac{\pi }{2} - \arctan (R/L)}^{\frac{\pi }{2} + \arctan (R/L)} {{E_n}(\theta )}\\ &\sqrt {{R^2} - {L^2}{{\tan }^2}\left(\frac{\pi }{2} - \theta \right)} \frac{1}{{{{\cos }^2}\left(\dfrac{\pi }{2} - \theta \right)}}d\theta \end{split} $

      (2)

      $ \begin{split} \overline E ({135^ \circ }) = & \frac{{2L}}{{\pi {R^2}}}\int_{\frac{{3\pi }}{4} - \arctan (R/L)}^{\frac{{3\pi }}{4} + \arctan (R/L)} {{E_n}(\theta )}\\ & \sqrt {{R^2} - {L^2}{{\tan }^2}\left(\frac{{3\pi }}{4} - \theta \right)} \frac{1}{{{{\cos }^2}\left(\dfrac{{3\pi }}{4} - \theta \right)}}d\theta \end{split} $

      (3)

      in the formulae, R stands for target sample radius, L suggests the distance from T-Ti target to target sample. Theoretically, neutron energy was determined according to the formula below [87]:

      ${E_n}(\theta ) = {\left[ {\frac{{{{({M_d}{M_n}{E_d})}^{\tfrac{1}{2}}}\cos \theta \pm {{({M_d}{M_n}{E_d}{{\cos }^2}\theta + ({M_\alpha } + {M_n})[{M_\alpha }Q + {E_d}({M_\alpha } - {M_n})])}^{\tfrac{1}{2}}}}}{{{M_\alpha } + {M_n}}}} \right]^2}$

      (4)

      Where En(θ) and Ed represent the neutron kinetic energy and deuteron beam energy emitted at θ angle, separately. Additionally, Md indicates the deuteron mass, Mn stands for neutron mass, while Mα represents the mass of α-particle. In d-T reaction, Q-value was 17.6 MeV, as a result, the “±” signs in Eq. (4) was appropriately changed into “+” sign. In addition, we measured the neutron energies based on cross-section ratios of reactions 90Zr(n,2n)89m+gZr and 93Nb(n,2n)92mNb ahead of time [88]. Consequently, at 135°, 90° and 0° irradiation positions with respect to beam direction, those neutron energy values were measured to be 13.5, 14.1, and 14.8 MeV, separately. With regard to the neutron energy uncertainty at a distance of approximately 5 cm, it was predicted as 0.2 MeV after taking sample size and d+ ~4 mm beam diameter into consideration [88].

    • 2.3.   Radioactivity measurement

    • The samples were cooled for 5–1800 min after irradiation, as required in each case, and we measured the gamma-ray activities of 91Mo, 93mMo, 99Mo, 95Zr, 97Zr, 92mNb, 96Nb, 97Nb, 98mNb, 91mNb, 90Nb, and 24Na nuclei through the well-calibrated GEM-60P coaxial HPGe detector (crystal length, 72.3 mm; crystal diameter, 70.1mmand) at the 1.69 keV energy resolution at 1.332 MeV and about 68% relative efficiency. Individual molybdenum samples were measured thrice at a distance of less than 80 mm away from the cap of the detector, every measuring step was approximately 28 to 32248 s. The detector efficiency was subject to pre-calibration by means of different normalized γ-ray sources. Partial γ-ray spectra acquired based on molybdenum samples at around 30 hours, 1 hour, and 21 min following irradiation completion are shown in Figures 1, 2, and 3, separately. The ORTEC® GammaVision® Gamma Spectrum Analysis Software was used to analyzed peak area [89] (with the ORTEC® MAESTRO® MCA emulation software package being adopted to obtain and analyze data [89]).

      Figure 1.  γ-ray spectrum of molybdenum obtained after 30 hours of cooling following the end of irradiation; acquisition time: about 8.96 hours.

      Figure 2.  γ-ray spectrum of molybdenum obtained after 1 hour of cooling following the end of irradiation; acquisition time: about 9 minutes.

      Figure 3.  γ-ray spectrum of molybdenum obtained after 21 minutes of cooling following the end of irradiation; acquisition time: about 15 minutes.

      Table 1 presents the above-mentioned reactions, together with corresponding reaction product radioactive decay characteristics in addition to those target isotope natural abundances covered in this study.

      Abundance of target isotope (%)ReactionE-threshold (MeV)Mode of decay (%)Half-life of product (keV) (%)
      14.533092Mo(n,2n)91Mo12.810EC(100)15.49 m11637.30.32921
      9.15994Mo(n,2n)93mMo12.233IT(99.88)6.85 h7684.69399.98
      9.8231100Mo(n,2n)99Mo8.378β-(100)65.796 h24739.512.2016
      24.393798Mo(n,α)95Zr0.000β-(100)64.032 d6756.72554.3822
      9.8231100Mo(n,α)97Zr0.000β-(100)16.749 h8743.3693.0916
      14.533092Mo(n,p)92mNb0.000EC(100)10.15 d2934.4499.154
      16.671596Mo(n,p)96Nb2.435β-(100)23.35 h5778.22496.4522
      9.601497Mo(n,p)97Nb1.169β-(100)72.1 m7657.9498.238
      24.393798Mo(n,p)98mNb3.933β-(99.90)51.3 m4787.36393.4020
      14.533092Mo(n,d)91mNb5.398IT(96.6)60.86 d221204.672.03
      14.533092Mo(n,t)90Nb11.147EC(100)14.60 h51129.22492.75
      10027Al(n,α)24Na3.249β-(100)14.997 h121368.6100
      10093Nb(n,2n)92mNb8.972EC (100)10.15 d2934.4499.154
      The lower index and italic numbers represent the uncertainties, for example, 14.5330% means 14.53±0.30%, 15.49 m1 means 15.49±0.01 m.s

      Table 1.  Neutron-induced nuclear reactions on molybdenum and decay data of the associated activation products (taken from ENSDF (2020) [3])

    3.   Cross-section calculation together with corresponding uncertainties

      3.1.   Experimental values for cross sections

    • Those cross-sections for interested reactions were determined according to the formula below [82-84]:

      ${\sigma _x} = \frac{{{{[S\varepsilon {I_\gamma }\eta KMD]}_0}}}{{{{[S\varepsilon {I_\gamma }\eta KMD]}_x}}}\frac{{{{[\lambda AFC]}_x}}}{{{{[\lambda AFC]}_0}}}{\sigma _0}$

      (5)

      in the formula, subscript 0 stands for standard monitor reaction-related terms, whereas subscript x were measured reaction-related terms, and F represents the overall activity correction factor:

      $F = {f_c} \times {f_s} \times {f_g}$

      (6)

      In the formula, fc, fs and fg, stand for correction factors for coincidence sum effect of cascade γ-rays generated from the investigated nuclide, sample self-absorption for the specific gamma-ray energy, and sample counting geometry, separately. In sequence, the approach reported in refs. [90, 91] was used to calculate the coincidence summing correction factor. In Mo foils, the gamma-ray attenuation correction factor fs as well as geometry correction factor fg were determined based on the equations below, respectively.

      ${f_s} = \frac{{\mu h}}{{1 - \exp ( - \mu h)}}$

      (7)

      $ {f_g} = \frac{{{{(L + h/2)}^2}}}{{{L^2}}} $

      (8)

      in the formula, μ stands for linear attenuation coefficient within Mo of gamma-rays at every photon energy E (shown in Table 1), h represents thickness of sample, while L indicates the distance from the investigated sample to germanium crystal surface. The mass attenuation coefficient (μ/ρ) was calculated based on gamma-ray energies originated from Ref. [92]. For Mo, its linear attenuation coefficient were determined based on the formula $\mu = 10.23(\mu /\rho )$, where 10.23 (in g/cm3) is the density of the Mo sample [93]. With regard to correction factors for sample self-absorption under the specific gamma-ray energy, the h value in Eqs. (7,8) was deemed to be the sample thickness.

      In the process of calculating the cross sections of the 96Mo(n,p)96Nb and 97Mo(n,p)97Nb reactions, the contribution of the interfering reactions 97Mo(n,d)96Nb and 98Mo(n,d)97Nb were subtracted using Eqs. (9,10) [85], respectively.

      $ \begin{split} \sigma {(^{{\rm{nat}}}}{\rm{Mo(n,x}}{{\rm{)}}^{{\rm{96}}}}{\rm{Nb}}) = & 0.1667\sigma {(^{{\rm{96}}}}{\rm{Mo(n,p}}{{\rm{)}}^{{\rm{96}}}}{\rm{Nb}}) \\ &+ 0.0960\sigma {(^{{\rm{97}}}}{\rm{Mo(n,d}}{{\rm{)}}^{{\rm{96}}}}{\rm{Nb}})\\ = & \frac{{{{[S\varepsilon {I_\gamma }\eta KMD]}_0}}}{{{{[S\varepsilon {I_\gamma }KMD]}_x}}}\frac{{{{[\lambda AFC]}_x}}}{{{{[\lambda AFC]}_0}}}{\sigma _0} \end{split} $

      (9)

      $ \begin{split} \sigma {(^{{\rm{nat}}}}{\rm{Mo(n,x}}{{\rm{)}}^{{\rm{97}}}}{\rm{Nb}}) = & 0.0960\sigma {(^{{\rm{97}}}}{\rm{Mo(n,p}}{{\rm{)}}^{{\rm{97}}}}{\rm{Nb}}) \\ & + 0.2439\sigma {(^{{\rm{98}}}}{\rm{Mo(n,d}}{{\rm{)}}^{{\rm{97}}}}{\rm{Nb}})\\ = & \frac{{{{[S\varepsilon {I_\gamma }\eta KMD]}_0}}}{{{{[S\varepsilon {I_\gamma }KMD]}_x}}}\frac{{{{[\lambda AFC]}_x}}}{{{{[\lambda AFC]}_0}}}{\sigma _0} \end{split} $

      (10)

      The cross sections of the interfering reactions 97Mo(n,d)96Nb and 98Mo(n,d)97Nb, which are 1.10, 1.96 and 3.29 mb, 0.40, 0.84 and 1.63 mb at 13.5, 14.1 and 14.8 MeV neutron energies respectively, were obtained by interpolating the evaluated values of the CENDL-3.1 [80]. The small contribution to the activities of the product nuclei 96Nb and 92mNb from interfering reactions 98Mo(n,t)96Nb and 94Mo(n,t)92mNb could be safely ignored because of small cross section (<0.2 mb in the neutron energy 13-15 MeV region [80]).

    • 3.2.   Experimental uncertainties

    • In this study, the major sources of uncertainties were due to the detector efficiency (2-4%), counting statistics (0.1-15%), sample weight (0.1%), standard uncertainty of cross sections (0.5-1.5%), measuring and cooling times (0.1-1%), and γ−ray self-absorption (1%). In addition, other sources include investigated and standard nuclear parameters, like characteristic γ−ray branching ratio (0.01-15%), nuclear half-lives of radioactive products (0.01-1%), as well as abundance of target isotopes (0.7-3.2%). In this study, quadratic sum rule was applied to analyze uncertainties [94].

    4.   Calculation for cross sections of nuclear reactions by the use of TALYS and EMPIRE codes
    • The 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo, 98Mo(n,α)95Zr, 100Mo(n,α)97Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, 98Mo(n,p)98mNb, 92Mo(n,d)91mNb and 92Mo(n,t)90Nb reaction cross sections were estimated using TALYS-1.95 code [71] at diverse neutron energies (range, threshold of reaction to 20 MeV). TALYS-1.95 has been developed as the nuclear model code utilized for replicating diverse nuclear reactions involving proton, photon, neutron, triton, deuteron, 3He, as well as α-particles to be the projectiles for the target nuclei in order to cover incident energies as high as 200 MeV. Koning and Delaroche had put forward candidate parameters for use in the local optical model, which were adopted to simulate proton and neutron emissions adopted in the ECIS06 code to directly calculate reaction and transmission coefficient [95]. Accordingly, Hauser-Feshbach model was used to calculate total nuclear contribution [96]. For α-particles, we used that folding method shown in Ref. [97]. Kalbach [98] established a two-component exciton model, which was utilized to calculate nuclear contribution before equilibrium. Using the TALYS-1.95 code, the calculation has been done by means of the default parameterization available in the code for the prediction of reaction cross-section [99].

      EMPIRE-3.2.3 serves as another nuclear reaction code modular system. It was developed by the ENEA/IAEA/BNL joint venture in the year 1980. Using the EMPIRE-3.2.3 reaction code, the calculations can house each pre-equilibrium (PE), direct nuclear (DI) and potential compound nuclear (CN) reactions. Feshbach et al. (1980) obtained the model for treating the neutron emission data before equilibrium based on multistep direct (MSD) and multistep compound (MSC) theories [100], whereas the DEGAS exciton model code was used to treat proton PE (Herman et al., 2013 [101]). The PCROSS exciton model code was utilized to obtain γ−ray emission data before equilibrium [96]. Coupled-channels calculation was obtained by the suitable optical potential (OP), which was then used to describe deformed nuclear direct reactions at low-lying collective state (ECIS code was utilized for such a purpose). We depicted γ−ray CN emission and α-particle in statistical theory parameters put forward by Feshbach and Hauser (1952) [96] by the use of appropriate OP, γ−ray strength functions (γSF) and nuclear level densities (NLD) based on RIPL-2 database [102]. This work completed EMPIRE-3.2.3 calculations by the use of default parameters.

    5.   Results and discussions
    • We used the offline γ-ray spectroscopic measuring technique to measure the cross sections of 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo, 98Mo(n,α)95Zr, 100Mo(n,α)97Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, 98Mo(n,p)98mNb, 92Mo(n,d)91mNb and 92Mo(n,t)90Nb reactions. In addition, neutron flux for lower threshold reactions like 100Mo(n,α)97Zr, 98Mo(n,α)95Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, 98Mo(n,p)98mNb and 92Mo(n,d)91mNb was monitored by reaction 27Al(n,α)24Na (Eth=3.249 MeV). For reaction 27Al(n,α)24Na, its cross sections were 125.7±0.8, 121.6±0.6, and 111.9±0.5 mb at 13.5, 14.1, and 14.8 MeV neutron energies, respectively [103]. Moreover, neutron flux for higher threshold reactions such as 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo and 92Mo(n,t)90Nb was monitored using reaction 93Nb(n,2n)92mNb (Eth=8.792 MeV). For reaction 93Nb(n,2n)92mNb, its cross sections were 457.9±6.8, 459.8±6.8, as well as 459.7±5.0 mb at 13.5, 14.1, along with 14.8 MeV neutron energies, separately [103]. We then compared these experimental data with those evaluated data from the ENDF/B-VIII.0 [77], JEFF-3.3 [78], BROND-3.1 [79] together with CENDL-3.1 [80] data libraries. In addition, we also compared such results with those obtained by employing the theoretical model codes EMPIRE-3.2.3 [70] and TALYS-1.95 [71]. The present experimental results are given in Table 2. The various reactions are discussed below.

      ReactionCross-sections (in mb) at various
      neutron energies (in MeV)
      En=13.5±0.2En=14.1±0.2En=14.8±0.2
      92Mo(n,2n)91Mo94±10112±12141±15
      94Mo(n,2n)93mMo1.1±0.12.1±0.23.7±0.3
      100Mo(n,2n)99Mo1466±881400±981436±101
      98Mo(n,α)95Zr5.5±0.55.6±0.45.8±0.4
      100Mo(n,α)97Zr1.8±0.22.1±0.22.3±0.2
      92Mo(n,p)92mNb85±673±567±5
      96Mo(n,p)96Nb23±225±229±2
      97Mo(n,p)97Nb15.7±1.118.6±1.219.5±1.2
      98Mo(n,p)98mNb2.9±0.23.2±0.23.5±0.3
      92Mo(n,d)91mNb128±23135±24171±29
      92Mo(n,t)90Nb29±5 (μb)32±6 (μb)41±6 (μb)

      Table 2.  Measurements of cross-sections

    • 5.1.   Reaction 92Mo(n,2n)91Mo

    • As shown in Table 2 and Figure 4, such evaluation excitation curves obtained via ENDF/B-VIII.0 [77], JEFF-3.3 [78], BROND-3.1 [79] as well as CENDL-3.1 [80] are nearly identical to the theoretical excitation curves obtained by the use of the EMPIRE-3.2.3 [70] and TALYS-1.95 [71] nuclear-reaction modeling tools. The results obtained from our experiment at about the 14 MeV neutron energy increases as neutron energy increases at about 14 MeV, which is also similar to the theoretical data and the data obtained from the databases but there are slight differences between these. The result obtained in the present experiment mildly increased compared with the EMPIRE-3.2.3-obtained theoretical excitation curve and those four evaluation excitation curves obtained at 13.5 MeV neutron energy. However, at 14.1/14.8 MeV neutron energies, the values obtained in this experiment slightly decreased compared with those obtained from TALYS-1.95-derived theoretical excitation curve and four evaluation excitation curves. With regard to reaction 92Mo(n,2n)91Mo, twenty-seven laboratories [7-33] reporting those neutron-induced experimental cross-section data based on D–T reaction were found. Twenty-six among these used annihilation radiation (511 keV) or beta counting method, while only one of those used the characteristic gamma-ray method to determine the daughter nucleus activity. Our report within the limits of experimental error is consistent with those obtained from the TALYS-1.95 and value reported by Abboud et al. [26] at the energy point of 13.5 MeV. At 14.1 as well as 14.8 MeV neutron energies, those experimentally established cross-section values conformed to the limits of experimental error and were consistent with those reported by Yasumi [13], Kanda [14] and Karolyi et al. [29] at related energy values. Additionally, Brollry et al [10], Strohal et al. [24] and Araminowicz and Dresler [30] had reported apparently higher cross-section values compared with those from ENDF/B-VIII.0 [77], JEFF-3.3 [78] and BROND-3.1 [79] evaluations, as well as those from theoretical calculations with EMPIRE-3.2.3 [70] and TALYS-1.95 [71] codes.

      Figure 4.  (Color online) Plot of 92Mo(n,2n)91Mo reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0, BROND-3.1, JEFF-3.3, and CENDL-3.1 libraries as well as with the values calculated using theTALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

    • 5.2.   Reaction 94Mo(n,2n)93mMo

    • In reaction 94Mo(n,2n)93mMo, only ten measurements have so far been proposed in the related field [5, 6, 21, 31, 34-39]. In reaction 94Mo(n,2n)93mMo, we determined its cross-section by the 93Nb(n,2n)92mNb monitor reaction with high threshold, and each sample was packaged within the pure cadmium foils, for avoiding the impact of deuterium accumulation-derived low-energy neutron within tritium target over a period of time, as well as background neutrons. Figure 5 shows those cross-sections in reaction 94Mo(n,2n)93mMo and calculations obtained from TALYS-1.95 code in the manner of continuous lines. As observed from Figure 5, within the 13-15 MeV energy region, except for value reported by Ikeda et al. [35] at 13.52 MeV, all other previous experimental data as well as the results obtained in the present work are lower than those acquired based on TALYS-1.95. Within the energy range of 13-14.5 MeV, we obtained consistent outcomes relative to those reported from refs. [6, 38] in the limit of experimental uncertainty, yet our results are lower than those obtained from refs. [35, 37]. Clearly, at the neutron energy point of 14.8 MeV, the value obtained by Amemiya et al. [14] conformed to ours. However, such experimental data nonetheless are lower than those acquired based on TALYS-1.95 and those reported in refs. [35, 37-39]. Regarding the experimental results reported by the authors Ikeda et al. [35] at 13.52 MeV, we highly suspect that there was an error in the data entry.

      Figure 5.  (Color online) Plot of 94Mo(n,2n)93mMo reaction cross-section values obtained in the present work along with the literature data and the values calculated from TALYS-1.95 as a function of neutron energy.

    • 5.3.   Reaction 100Mo(n,2n)99Mo

    • So far twenty-three laboratories have reported their cross-section values from experiments, which can be found in the nuclear reaction database regarding molybdenum isotopes at about 14 MeV neutron energy. As a result, it lays solid foundation to verify experimental result reliability as well as theoretical calculation model correctness adopted herein. As shown in Figure 6, the trends and shapes of excitation curves taken from the ENDF/B-VIII.0 [77] (as same as CENDL-3.1 [80]), JEFF-3.3 [78] and BROND-3.1 [79] databases are almost identical to those obtained from theoretical excitation curves through EMPIRE-3.2.3 [70] together with TALYS-1.95 [71] nuclear-reaction modeling tools within the range of neutron energy of threshold-20 MeV, and there was only minor heterogeneities among them. The cross-section data of 100Mo(n,2n)99Mo reaction obtained from experiment are classified as three bands with the differences of approximately 30% and 20%, separately. In addition, those experimental data reported by refs. [21, 24, 30, 33, 41, 44] can be classified at about 1800 mb cross section values. Those data reported by refs. [1, 6, 8, 15, 34, 35, 39-40, 42, 43, 46-49] are centered around 1400 mb, whereas those reported by ref. [45] is concentrated at about 1130 mb. The data reported by ref. [9] however, is varies over a large region of 3790±1895 mb at the energy point of 14.5 MeV.

      Figure 6.  (Color online) Plot of 100Mo(n,2n)99Mo reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0, BROND-3.1, JEFF-3.3 and CENDL-3.1 libraries as well as the calculated values from TALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

      The experimental data found from this work, within the limits of experimental error, conform to results obtained from three ENDF/B-VIII.0 [77], CENDL-3.1 [80] and BROND-3.1 [79] databases-obtained evaluation excitation curves. Two theoretical excitation curves at 13.5 MeV neutron energy are somewhat bigger than those obtained by JEFF-3.3 [78] at this neutron energy point. Yet, at the 14.1 and 14.8 MeV neutron energies the experimental data conform to the data of two evaluation excitation curves taken from JEFF-3.3 [78] and BROND-3.1 [79], but are somewhat lower than the value obtained via ENDF/B-VIII.0 [77] and CENDL-3.1 [80], together with two theoretical excitation curves at the corresponding energies. Within the 13-15 MeV energy region, Parashari et al. [1], Marcinkowski et al. [6], Lu et al [8], Qaim [15], Cuzzocrea et al. [19], Fujino et al. [34], Ikeda et al. [35], Filatenkov [39], Kong et al. [47] and Filatenkov et al. [49], reported the same results as our values obtained based on the fitting line at identical neutron energy points. As for cross-section data obtained from Amemiya et al. [21], Strohal et al. [24], Araminowicz and Dresler [30], Maslov et al. [33], Khurana and Hans [44], they are significantly larger than those from four evaluation excitation curves as well as two theoretical excitation curves and the present results in addition to the values reported in refs. [1, 6, 8, 15, 19, 34, 35, 39, 47, 49] at the corresponding energies. The result of Paul and Clarke [9], 3790±1895 mb at the neutron energy of 14.5 MeV, is not included because it is too high to be clearly displayed compared to the other data near 14 MeV.

    • 5.4.   Reaction 98Mo(n,α)95Zr

    • Fig.7 presents the experimental cross-section values for reaction 98Mo(n,α)95Zr. Those values obtained based on TALYS-1.95 and EMPIRE-3.2.3 calculation and those evaluation values acquired based on ENDF/B-VIII.0 [77], JEFF-3.3 [78], BROND-3.1 [79] and CENDL-3.1 [80] libraries are shown in Figure7 in the manner of continuous lines. Clearly, within the energy range of 13-15 MeV, our values conform to those reported from refs. [21, 35, 37, 39, 40, 49, 51-55] in the limit of experimental uncertainties, but lower than values obtained from Ref. [50], and data obtained from EMPIRE-3.2.3 calculation. However, the values are higher than those obtained from TALYS-1.95 calculation. Consistent with the trends for reactions 92Mo(n,2n)91Mo together with 94Mo(n,2n)93mMo, the cross-section for reaction 98Mo(n,α)95Zr in the 13-15 MeV energy range increases as the neutron energy increases.

      Figure 7.  (Color online) Plot of 98Mo(n,α)95Zr reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0, BROND-3.1, JEFF-3.3 and CENDL-3.1 libraries as well as the calculated values obtained from TALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

    • 5.5.   Reaction 100Mo(n,α)97Zr

    • Figure 8 shows the cross sections of reaction 100Mo(n,α)97Zr based on results obtained in refs. [6, 19, 24, 35, 39, 40, 51-54]. In Figure 8, the values acquired based on EMPIRE-3.2.3 and TALYS-1.95 calculations and evaluated data obtained based on ENDF/B-VIII.0 [77], BROND-3.1 [78], JEFF-3.3 [79] along with CENDL-3.1 [80] libraries are expressed in the manner of continuous lines. As shown in Figure 8, there are great dissimilarities in the results obtained from the nuclear model calculations, namely EMPIRE-3.2.3 [70] and TALYS-1.95 [71], around the 14 MeV neutron energy. In reaction 100Mo(n,α)97Zr, those EMPIRE-3.2.3 calculation results are about thrice the TALYS-1.95 calculation results at about 14 MeV neutron energy. Meanwhile, the present result is consistent with results taken from refs. [35, 52] and the evaluation values acquired based on ENDF/B-VIII.0 [77], and JEFF-3.3 [79] at the 13.5 MeV neutron energy, within the limits of experimental error. At the neutron energy of 14.8 MeV, our results conform to those reported by the authors Artemev et al. [54] and results obtained based on TALYS-1.95 in scope of experimental error, but decrease compare with values obtained from refs. [6, 35, 51, 53], the EMPIRE-3.2.3 calculations, and the evaluated data obtained from JEFF-3.3 [78], BROND-3.1 [79] as well as CENDL-3.1 [80] libraries under this neutron energy point.

      Figure 8.  (Color online) Plot of 100Mo(n,α)97Zr reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0, BROND-3.1, JEFF-3.3, and CENDL-3.1 libraries as well as the calculated values obtained from TALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

    • 5.6.   Reaction 92Mo(n,p)92mNb

    • In reaction 92Mo(n,p)92mNb, the following conditions were adopted for measurements, including gamma-ray at 934.4 keV (Iγ=99.15%) emitted via 92mNb (half-life, T1/2=10.15 d). Almost all the measurements reported in the literature also use the same decay data as the present work. Figure 9 shows our obtained data and those provided by refs. [6, 7, 12, 14, 21, 22, 34-40, 43, 45, 49, 50, 52-54, 56-60] and the values obtained from TALYS-1.95 calculations. As can be seen from Figure 9, in the 13.5 to 14.8 MeV region, although tremendous experimental data are present in an early stage, the divergence is also very obvious. Within the 13.5-14.8 MeV neutron energy, our values conform to those experimental data obtained from the refs. [6, 12, 21, 22, 34-40, 43, 45, 49, 50, 56-60] within the limits of experimental uncertainty. As shown in Figure 8, all data in the present study are lower than values reported by Sigg and Kuroda [7] as well as Liskien et al. [52],. The values are however, somewhat higher than those published by Kanda [14], Grallert et al. [53] and Artemev et al. [54].

      Figure 9.  (Color online) Plot of 92Mo(n,p)92mNb reaction cross-section values from the present work along with the literature data and the calculated values obtained from TALYS-1.95 as a function of neutron energy.

    • 5.7.   Reaction 96Mo(n,p)96Nb

    • For reaction 96Mo(n,p)96Nb, twenty-one previous reports are available in refs. [5, 6, 12, 19, 21, 22, 24, 31, 34, 35, 37, 40, 43, 45, 47, 50-54, 62]. As clearly seen from Figure 10, in 13.5-14.8 MeV neutron energy, our cross-section data conform to those theoretical values obtained from EMPIRE-3.2.3 [70] and the values reported by Kong et al. [47] in the scope of experimental uncertainty. Nonetheless, these values are bigger than those obtained from ref. [15] and those obtained based on ENDF/B-VIII.0 [77], JEFF-3.3 [78], BROND-3.1 [79] and CENDL-3.1 [80], but smaller than those obtained from Bramlitt and Fink [12].

      Figure 10.  (Color online) Plot of 96Mo(n,p)96Nb reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0, BROND-3.1, JEFF-3.3, and CENDL-3.1 libraries as well as the calculated values obtained from TALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

    • 5.8.   Reaction 97Mo(n,p)97Nb

    • Likewise, Figure 11 presents cross-section of reaction 97Mo(n,p)97Nb. As observed, fifteen previous reports are available, including Reimer et al. (2005) [5], Marcinkowski et al. (1986) [6], Amemiya et al. (1982) [21], Pepelnik et al. (1986) [22], Ikeda et al. (1988) [35], Molla et al. (1997) [37], Semkova and Nolte (2014) [40], Molla et al. (1986) [43], Osman and Habbani (1996) [45], Lu et al. (1970) [50], Qaim and Stoecklin (1974) [51], Artemev et al. (1980) [54], Tikku et al. (1972) [63], Kong et al. (1992) [64] and Lalremruata et al. (2012) [65]). According to Figure 11, within the 13.3-15 MeV neutron energy, diverse experimental data are highly consistent within the experimental uncertainty limits, in addition to the shapes of the excitation curves obtained from TALYS-1.95 [71], ENDF/B-VIII.0 [77], JEFF-3.3 [78], BROND-3.1 [79] and CENDL-3.1 [80]. These also exhibit a trend similar to that reported by Reimer et al. (2005) [5], Marcinkowski et al. (1986) [6], Ikeda et al. (1988) [35], Molla et al. (1997) [37], Kong et al. (1992) [64] and the present data set. We do not consider the result reported by Tikku et al. (1972) [63], 72.7 ± 4.3 mb at 14.7 MeV, since it is over-great for displaying any clear relation with other values around 14 MeV.

      Figure 11.  (Color online) Plot of 97Mo(n,p)97Nb reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0, BROND-3.1, JEFF-3.3and CENDL-3.1 libraries as well as the values calculated using TALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

    • 5.9.   Reaction 98Mo(n,p)98mNb

    • Concerning the 98Mo(n,p)98mNb reaction, there are twenty-one earlier reports that can be found in the literature [5, 6, 12, 19, 21, 22, 31, 34, 35, 38-40, 43, 45, 50, 53, 56, 63, 66-68]. The measured cross-sections for the 98Mo(n,p)98mNb reaction are shown in Fig. 12. Regarding the nuclear model calculations in Figure12, the results obtained from TALYS-1.95 calculations with default parameters are represented as continuous lines. We can see from Figure 12 that in the neutron energy region of 14.8±0.2 MeV, the present result is in excellent agreement with the previously published results of Pepelnik et al. [22], Fujino et al. [34] and Molla et al. [43] within the limits of experimental uncertainties. Nonetheless, at this energy region, results previously published by Bramlitt and Fink [12], Srinivasa Rao et al. [31] and Gujrathi and Mukherjee [68] are 1.8 times, and the results published by Bramlitt and Fink [12], Prasad and Sarkar [66] are 4.4 times higher than the value we report herein. However, at the neutron energy points of 13.5 and 14.1 MeV, results from the present work are lower than the previously published results of Marcinkowski et al. [6], Ikeda et al. [35], Kong et al. [38] and Filatenkov [39] and the results obtained from TALYS-1.95 calculations.

      Figure 12.  (Color online) Plot of 98Mo(n,p)98mNb reaction cross-section values from the present work along with the literature data and the values calculated using TALYS-1.95 as a function of neutron energy.

    • 5.10.   Reaction 92Mo(n,d)91mNb

    • There are no evaluation cross-section values for the 92Mo(n,d)91mNb reaction in the evaluation database of IAEA, and only a few experimental cross-section values are available in the 13.5 to 14.8 MeV region (cf. refs. Qaim and Stoecklin (1974) [51], Haight et al. (1981) [72] and Konno et al. (1993) [73]). The cross-section data for this reaction are given in Fig.13. In the neutron energy range of 13.5 to 14.8 MeV, results obtained in the present experiment are in agreement with the experimental results reported in ref. [73] within experimental uncertainty limits. We can also see from Figure 13 that the data reported in the present work have lower values than those obtained from TALYS-1.95 code. At 14.8 MeV energy point, results from the present work and those reported by Konno et al. (1993) [73] are about seven times higher than the values reported by Qaim and Stoecklin (1974) [51] and Haight et al. (1981) [72], whereas at the neutron energy point 13.5 MeV, the result reported herein, is the first one.

      Figure 13.  (Color online) Plot of 92Mo(n,d)91mNb reaction cross-section values from the present work along with the literature data and the values calculated using TALYS-1.95 as a function of neutron energy.

    • 5.11.   Reaction 92Mo(n,t)90Nb

    • Figure 14 shows the cross sections for the 92Mo(n,t)90Nb reaction. The results obtained from TALYS-1.95 and EMPIRE-3.2.3 calculations with default parameters and the evaluated data obtained from ENDF/B-VIII.0 (as same as BROND-3.1), JEFF-3.3 and CENDL-3.1 libraries are represented as continuous lines. For this (n,t) reaction, only three laboratories [74-76] have reported the data at single energy point of 14.8 MeV. The results obtained in the present work is in agreement with experimental results reported in ref. [75] within experimental uncertainty limits, whereas at neutron energies 13.5 and 14.1 MeV, the results in the present work are the first of its kind.

      Figure 14.  (Color online) Plot of 92Mo(n,t)90Nb reaction cross-section values from the present work along with the literature data, evaluated data obtained from ENDF/B-VIII.0 (as same as BROND-3.1), JEFF-3.3 and CENDL-3.1 libraries as well as the values calculated using TALYS-1.95 and EMPIRE-3.2.3 as a function of neutron energy.

    6.   Conclusions
    • We measured reactions 92Mo(n,2n)91Mo, 94Mo(n,2n)93mMo, 100Mo(n,2n)99Mo, 98Mo(n,α)95Zr, 100Mo(n,α)97Zr, 92Mo(n,p)92mNb, 96Mo(n,p)96Nb, 97Mo(n,p)97Nb, 98Mo(n,p)98mNb, 92Mo(n,d)91mNb and 92Mo(n,t)90Nb for activation of molybdenum isotope cross-sections for the 13.5±0.2, 14.1±0.2 as well as 14.8±0.2 MeV neutron energies. Those uncertainties in the experimental results were calculated using quadratic sum rule, and they were found to be within the range of 6-18%. We then compared the measured data with those theoretical values acquired through the TALYS-1.95 and EMPIRE-3.2.3 nuclear-reaction modeling tools, together with evaluation data obtained based on ENDF/B-VIII.0, JEFF-3.3, BROND-3.1, CENDL-3.1 databases, and literature data. In general, our research has produced experimental data at about 14 MeV neutron energy and the results conform well to some previous experimental values reported in literature in the experimental error scope. Nonetheless, there are certain differences across those literature reported data, and this may be due to the variations in experimental methodology, equipment type, the adopted nuclear parameters and data processing techniques. According to theoretical calculations based on the TALYS-1.95 and EMPIRE-3.2.3 nuclear-reaction modeling approaches, for a specific channel considered, its cross-section of reaction can be well reproduced at around 14 MeV neutron energy through the use of default parameters. As a result, the theoretical calculation model can be suitably used to simulate the cross-section of a reaction for a specific channel at about 14 MeV neutron energy. Taken together, the experimental values presented herein can significantly enhance the neutron cross-section database quality, which can assist in evaluating the cross-sections of molybdenum isotopes at about 14 MeV neutron energy. Moreover, this study also sheds light on the TALYS-1.95 and EMPIRE-3.2.3 theoretical model codes. Besides, it is important to report these experimental values at moderate-fast neutron energy points for testing diverse nuclear model codes as well as advancing the modern nuclear reactor techniques. Noticeably, this study first reports the experimental cross-section values at 13.5 and 14.1 MeV neuron energies for the reaction 92Mo(n,t)90Nb, and at 13.5 MeV neutron energy for the reaction 92Mo(n,d)91mNb.

      We would like to thank the Intense Neutron Generator group at Chinese Academy of Engineering Physics for performing the irradiations.

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