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