Evaluation of actinide nuclear data Osamu Iwamoto Japan Atomic Energy Agency 2010 Symposium on Nuclear Data

Applications of nuclear data nucleosynthesis JRR-3 J-PARC ADS soft error ( 株 ) 化研提供 medical application nuclear data Accelerator Reactor crab nebula Tc-99m 2

recent actinide data in JENDL ReleaseNo. of actinides Covariance JENDL (JENDL-3.2 Cov. File, Major) JENDL (after release of JENDL-3.3, MA) JENDL/AC JENDL (all actinides, all cross sections) 3

Neutron induced reactions U-235 U-236 U-235 Pa-235 Nucleus (A~90) Nucleus (A~140) Fission Spallation Capture Elastic scattering Inelastic scattering 4

neutron induced reaction cross sections 5 resolved resonanceunresolved resonance thermal 235 U

Nuclear data evaluation 6 EXFOR KALMAN, GMA CRECTJ NJOY CCONE

Physical quantities of actinide data in JENDL-4 MFPhysical quantitiesreaction 1number of neutrons per fission, Components of energy release due to fission fission 2Resonance parametersResolved RP, unresolved RP 3Neutron cross sections(n,n), (n,n’), (n,f),(n,g), (n,2n)... 4Angular distributions of secondary neutrons(n,n), fission 5Energy Distributions of Secondary Neutronsfission 6Energy-angle distributions(n,n’), (n,2n), (n,3n), (n,g) 12Photon Production MultiplicitiesFission 14Photon Angular DistributionsFission 15Continuous Photon Energy SpectraFission 31Covariances of average number of neutrons per fissionFission 32Covariances of resonance parametersResolved RP 33Covariances of neutron cross sections(n,n), (n,n’), (n,f),(n,g), (n,2n)... 34Covariances for Angular Distributions(n,n) 35Covariances for Energy DistributionsFission neutron 7

MF=1 number of neutrons per fission – Prompt neutron ( p ) – Delayed neutron ( d ) Components of energy release due to fission 8

Prompt neutron Experimental data Systematics – Howerton Nucl. Sci. Eng. 62, 348 (1997) – Ohsawa J. Nucl. Radiochem. Sci. Eng. 9, 19 (2008) Ohsawa(2008) 9

p for U isotopes NuclidesJENDL-3.3JENDL-4 U U U = JENDL-3.3 U U = JENDL-3.3 U = JENDL-3.3 U p for thermal neutron 10

Experimental data Systematics – R.J.Tuttle INDC(NDS)-107/G+Special, p.29 (1979) – G.Benedetti et al. Nucl. Sci. Eng., 80, 379 (1982) – R.Waldo et al. Phys. Rev., C23, 1113 (1981) -(A c -3Z)A c /Z Waldo (1981) Tuttle (1979) Z c A c Delayed neutron 11

MF=2 Resolved resonance – SAMMY code (N. Larson, ORNL/TM-9179/R8, ENDF-364/R2, 2008) Unresolved resonance – ASREP code (Y. Kikuchi et al., JAERI-Data/Code ) 12

Resonance Theory Useful in the low energy region Breit-Wigner formula – G. Breit and E.P. Wigner Phys. Rev., 49, 519 (1936). – Resonance parameters E ’,  n,  x should be evaluated for each J and L. Reich-Moore formula – C.W. Reich and M.S. Moore Phys. Rev., 111, 929 (1958) 13

Resonance Cross Sections 235 U(n,f) 14

Compilation of Resonance Parameters S.F. Mughabghab “ Atlas of neutron resonances: resonance parameters and thermal cross sections Z=1-100 ”, Elsevier (2006) E,  n,  ,  f for each L and J Thermal cross sections Resonance integrals Scattering radius Neutron separation energy 15

Np-237 capture cross section for thermal neutron 16

Am-241 thermal capture cross section ( ) （  g.s. = 620  25 、 IR=0.896 assumed ） 17 total cross section

18 thermal capture cross section(b) Kalebin (1976)624  20 Shinohara+ (1997)854  58 Fioni+ (2001)696  48 Bringer+ (2006)714  23 Present697.1 JENDL Am thermal neutron capture  g = 620  25 S. Nakamura+ (2007)  g+m = 692  28 (IR=0.896)

U fission cross sections at RRR 19

Cm-243, 244(n,f) Low resolution measurement using lead slowing-down spectrometer 20

Unresolved resonance distribution (Porter-Thomas) Width-fluctuation correction factor : Breit-Wigner formula Average cross section ASREP: Y. Kikuchi et al., JAERI-Data/Code

Result of fitting with ASREP R = D =  g =  f = 22

MF=3, 4, 5, 6 Least-squares fitting to experimental data Fission cross section – (Simultaneous evaluation on KALMAN) Major actinide (U-233, 235, 238, Pu-239, 241, 242) – GMA MA Theoretical model calculation All reaction cross sections, angular distribution, secondary particle spectrum – model parameter adjustment 23

total (n,n’) (n,  ) (n,f) (n,2n)(n,3n) elastic MF=3 Neutron induced reaction on U

MF=4 U-238(n,n) angular distribution 25 neutron spectrum En=5.5 MeV JENDL-3.3 CCONE 実験 En=550 keV  （ deg. ） JENDL-3.3 CCONE d  /d  (b/sr)  （ deg. ） En(MeV)

MF=5, 6  CM (deg) d  /d  (b/sr) Direct process  CM (deg ) d  /d  (b/sr) Pre-equilibrium process Compound process  CM (deg) d  /d  (b/sr) U-239 neutron 26

Simultaneous evaluation of fission cross section Least-squares fitting – SOK code (Kawano) – First order spline Experimental data ReactionsetsReactionsets 233 U U/ 235 U9 235 U U/ 233 U1 238 U9 238 U/ 235 U Pu Pu/ 235 U Pu4 240 Pu/ 235 U Pu6 240 Pu/ 239 Pu1 241 Pu/ 235 U4 27

SOK 28 evaluated data 1 st order spline cross section ratio linearize experimental data posterior covariance prior cov. experimental data cov. posterior design matrix

1 st order spline Correlation matrix 29

235 Ｕ fission cross section (SOK) 30

U-233(n,f)/U-235(n,f) (SOK) 31

Time evolution of nucleon induced reaction 32 incident nucleon 1p state 2p-1h state 3p-2h state compound state direct process pre-equilibrium process

Reaction models in CCONE code Direct prosess – Optical model – Coupled-channel method – Distorted wave Born approximation Pre-equilibrium process – Exciton model (2 components) Compound process – Hauser-Feshbach 33

Incident channel 34 incident nucleon 1p state 2p-1h state 3p-2h state compound state direct process pre-equilibrium process

Optical model  Total cross section  Shape elastic scattering cross section  Transmission coefficient (used in statistical model) Optical model potential (OMP) scattering matrix (strength of scattering waves ） Schrödinger equation 35 incident nucleon

OMP and wave function Wave function Potential Fe-56 + n (En=10 MeV) OMP=koning-n Imaginary real 36

Cross section variation with OMPs total shape elastic reaction 37

Direct process 38 incident nucleon 1p state 2p-1h state 3p-2h state compound state direct process pre-equilibrium process

Coupled-channels optical model U-238 deformation on ground state incident wave scattered wave ground state rotational band strong couplings between levels 39

Coupled-channel optical model rotational band Deformed nucleus 40 Nuclear radius Nuclear wave function Coupled-channels equation Intrinsic wave function Rotational wave function deformed OMP neutron radial wave function

Neutron Strength keV Exp. Spherical OM calc. RRM-CC calc. s-wave (l=0) s-wave neutron strength function global CC OMP S. Kunieda et al., J. Nucl. Sci. Technol. 44, 838 (2007) actinide 41

U-238 scattering cross section ( ) 42

pre-equilibrium process 43 incident nucleon 1p state 2p-1h state 3p-2h state compound state direct process pre-equilibrium process

p ,h ,p,h 1,0,0,0 2,1,0,01,0,1,1 3,2,0,0 2,1,1,11,0,2,2 p,n,  emission Pre-equilibrium process Exciton model (2 components) 44 particlehole  : proton : neutron

Parameters in exciton model p ,h ,p,h 1,0,0,0 2,1,0,01,0,1,1 3,2,0,0 2,1,1,11,0,2,2 p,n emission transition rate emission rate of particle p-h creation by proton p-h creation by neutron 45 inverse reaction cross section (OM calculation)

Exciton model parameters transition matrix element state density C C single particle state density Koning et al., Nucl. Phys. A744, 15 (2004) 46 1/g EfEf Pauli correction

Dependences of spectrum and cross sections on exciton model parameters Neutron En=14 MeV 47

compound process 48 incident nucleon 1p state 2p-1h state 3p-2h state compound state direct process pre-equilibrium process

Decay chain on statistical model Target discrete Continuum 49 Ex

Hauser-Feshbach Width fluctuation correction Normalization coefficient Transmission coefficient (OM calculation ） Level density of daughter nucleus Excitation energy of target Energy conservation Parity conservation Total spin, parity 50

Cumulative number of levels for U isotopes Level density discrete level continuum level 51

Level density (Fermi gas model) average resonance spacing spin excitation energy dependence parity 52

Level density Saddle point （ inner γ-deformation ） （ outer mass asymmetry ） Collective enhancement (rotational level) Shell structure washout Ground state Fermi gas constant temperature 53

 -ray strength function 54 Standard Lorentzian Enhanced Generalized Lorentzian Kopecky et al. PRC47,312 (1993), PRC41,1941(1990)  -ray transmission coefficient

Giant dipole resonance parameter 55 Systematics

Fission Transition state Penetrability of a parabolic barrier double barriers Transmission coefficient 56 barrier curvature barrier height transition state energy

Fission cross sections for U isotopes 57

U capture cross section 58

U-238(n,2n) Frehaut data without correction 59

Capture cross sections for Pu and N ｐ 60 Pu-237 Pu-239 Pu-241 Pu-244 Pu-246 Np-235 Np-236 Np-237 Np-239 Np-238 JENDL-3.3 JENDL-4.0

Np fission cross sections GMA CCONE 61

Neutron spectrum 62

WPEC Subgroup 29 U-235 Capture Cross Section in the keV to MeV Energy Region 63

Problem of integral experiment sodium voided reactivity in BFS MOX Sensitivity to 235 U capture cross section sodium voided reactivity 64

Possible overestimation of capture cross section of U-235 U-235 capture cross section capture cross section/ fission cross section Resonance region 65

U-235 capture cross section 66 Upper boundary of RRR: 2.25  0.5 keV

C/E value of BFS criticalities 67

Resources for nuclear data evaluation EXFOR – – – RIPL – JAEA Nuclear data center – – SPES (Search and Plot Executive System) – mailto: 68