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Neutron Cross Section Evaluation of U-238

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Neutron Cross Section Evaluation of U-238 FIESTA2017 FIssion ExperimentS and Theoretical Advances Neutron Cross Section Evaluation of U-238 Hyeong Il Kim Nuclear Data Center Korea Atomic Energy Research Institute 2017. 9. 18 Table of Contents 1 Introduction 2 Nuclear Data Evaluation 3 Results 4 Summary Introduction Overview Introduction Nuclear Data Evaluation Analyzing the measured physical quanties + Combing them with theoretical predictions => Extract the true values of such quanties DataBase ENDF Library (Compact format) Processed to Pointwised or Groupwised Libraries Application Inputs for various simulation codes (MCNP, Geant4, PHITS, DRAGON, DANTSYS, DORT ··· ) FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 1 Introduction Overview Nuclear data activities An example of nuclear data eval. for 235U Applications FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 2 Introduction Overview Uranium Abundances of natural uranium 234U: 0.0054 % 235U: 0.7204 % 238U: 99.2742 % U-238 Fuel of nuclear reactor LWR: 95 ∼ 97 %, HWR: 98 ∼ 99 % Well evaluated but Continuoulsy updated Current version: ENDF/B-VII.1, JENDL-4.0, JEFF-3.2,CENDL-3.1,RUSFOND-2010,... Preliminary: ENDF/B-VIII-b4, JEFF33T4 FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 3 Nuclear Data Evaluation Cross section Cross sections for U-238 FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 4 Nuclear Data Evaluation Cross section Cross Sections Cross Sections Cross Section: function of the kinetic energy of the particle a ZZ 2 d σ(Ea; Eb; Ω) σ(Ea) = dEbdΩ dEbdΩ Differential Cross Section: Distributions of an emitted particle for anlge or energy dσ(Ea; Eb) dσ(Ea; Ω) dEb dΩ Double-Differential Cross Section (DDX): Distributions of an emitted particle for anlge and energy 2 d σ(Ea; Eb; Ω) dEbdΩ FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 5 Nuclear Data Evaluation Nuclear Reaction Interactions between particle and nucleus Schrodinger¨ equation 2 ~ 2 − O + U(r) Ψ = EΨ; 2µ m where Ψ(r; θ; φ) = R(r)Yl (θ; φ): Scattering matrix I (kr) Scattering l region i S O (kr) Ψ(r) = I (kr) − S O (kr) l l 2 l l l r Scattering Matrix FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 6 Nuclear Data Evaluation Nuclear Reaction Phenomenological Optical Model Potential (OMP) U(r, E) = Vc(r, E) Coulomb (VV(E) + iWV(E)) fV(r) Volume − +(VD(E) iWD(E))gD(r) Surface − 2l ~s(V (E) + iW (E))h (r), Spin-Orbit − · SO SO SO where VV,SO and WV,D,SO are the real and imaginary components of the volume central (V), surface-central (D) and spin-orbit (SO) potentials, respectively. 1 d 1 d f (r) = , g (r) = 4a f (r), h (r) = f (r), i (1 exp[(r R )/a ]) i − D dr i i r dr i − − i i 1/3 where the geometry parameters are the radius Ri = riA , whith A begins atomic mass number, and the diffuseness parameters ai. FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 7 Nuclear Data Evaluation Nuclear Reaction K-D form 2 3 VV(E) = v [1 v2(E E ) + v3(E E ) v (E E ) ], 1 − − f − f − 4 − f 2 (E E f ) WV(E) = w1 − , (E E )2 + w2 − f 2 (E E )2 W (E) = f D d1 − exp[ d2(E E f )], (E E )2 + d2 − − − f 3 VSO(E) = v exp[ v 2(E E )], so1 − so − f 2 (E E f ) WD(E) = − wso1 2 2 , (E E ) + (w 2) − f so where E f , N, Z and A are the Fermi energy, number of neutrons, number of protons, and mass number, respectively. In all cases, the geometry (ri, ai) of the potential is assumed to be independent of the energy. FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 8 Nuclear Data Evaluation Reaction Model Model calculation Model OMP, Level density, Model Calculations preequilibrium, fission Adjustments model, γ-ray strength of parameters function, ··· no χ2 & Eyeguide? (Exp. of Isotope) Parameterization Adjustments yes Default parameters: of parameters Taken from the recommended data in χ2 & Eyeguide? no RIPL-3 (Reference Input (Exp. of Element) Parameter Library) Parameterizing to yes reproduce the measured Evaluated files data Code: Empire-3.2 FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 9 Nuclear Data Evaluation Reaction Model Total cross section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 10 Nuclear Data Evaluation Reaction Model Elastic cross section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 11 Nuclear Data Evaluation Reaction Model Elastic Angular Distribution 1010 Angular Distribution 1.500 x106 12.000 x102 2.500 x105 14.100 x101 109 4.000 x104 15.000 x100 7.000 x103 108 107 106 105 104 Cross Section (mb) 103 102 101 100 10-1 Discrepancies0 20 40 with60 80 total100 120 and140 elastic160 180 XS Energy (MeV) Do not consider too much in this work FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 12 Nuclear Data Evaluation Reaction Model FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 13 Nuclear Data Evaluation Reaction Model Particle Spectra FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 14 Nuclear Data Evaluation Reaction Model Neutron proudctions induced by neutron with 14.1 MeV energy FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 15 Nuclear Data Evaluation Reaction Model Neutron proudctions induced by neutron around 14 MeV FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 16 Nuclear Data Evaluation Recursive Evaluation KAERI/NDC evaluation Modern Computing Power ∼ hrs Initial Models Parameterizations EMPIRE/TALYS Reaction Models ENDF-6 format Parameters NJOY Correction Criticality ACE file MCNP FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 17 Results Cross Section Results FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 18 Results Cross Section Prompt ν Linear fit in energy bin FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 19 Results Cross Section Total ν prompt ν + delayed ν from (ENDF/B-VII.1) FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 20 Results Cross Section Inelastic cross section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 21 Results Cross Section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 22 Results Cross Section Capture cross section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 23 Results Cross Section Fission cross section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 24 Results Cross Section Fission spectra FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 25 Results Cross Section (n,2n) cross section FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 26 Results ICSBEP Criticality (Fast Spectra) FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 27 Results ICSBEP Criticality (Fast Spectra) FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 28 Results ICSBEP Cross Sections of U-235 FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 29 Summary Summary The U238 evaluation in fast neutron region was introduced. The fast check from evaluation to validation is possible by the up-to-date nuclear reaction model code and modern computing power. Our U-238 evaluation will be finalized soon together with the U-235 one. FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 30 Thank you for your attention! FIESTA2017, Eldorado Hotel, Santa Fe, NM H. I. Kim 30.
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