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

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Evaluation of actinide nuclear data

Evaluation of actinide nuclear dataOsamu IwamotoJapan Atomic Energy Agency2010 Symposium on Nuclear Data

Applications of nuclear data

nucleosynthesisJRR-3J-PARCADSsoft error

()medical applicationnuclear dataAcceleratorReactorcrab nebulaTc-99m2recent actinide data in JENDLReleaseNo. of actinidesCovarianceJENDL-3.21994560 +6 (JENDL-3.2 Cov. File, Major)JENDL-3.32002626 + 7 (after release of JENDL-3.3, MA)JENDL/AC-20082008790JENDL-4.020107979 (all actinides, all cross sections)3Neutron induced reactions

U-235U-236U-235U-235Pa-235Nucleus(A~90)Nucleus(A~140)FissionSpallationCaptureElastic scatteringInelastic scattering4

neutron induced reaction cross sections5resolved resonanceunresolved resonancethermal235U5

Nuclear data evaluation6EXFORKALMAN, GMACRECTJNJOYCCONE6Physical quantities of actinide data in JENDL-4MFPhysical quantitiesreaction1number of neutrons per fission, Components of energy release due to fissionfission2Resonance parametersResolved RP, unresolved RP3Neutron cross sections(n,n), (n,n), (n,f),(n,g), (n,2n) ...4Angular distributions of secondary neutrons(n,n), fission5Energy Distributions of Secondary Neutrons fission 6Energy-angle distributions(n,n), (n,2n), (n,3n), (n,g)12Photon Production MultiplicitiesFission14Photon Angular DistributionsFission15Continuous Photon Energy SpectraFission31Covariances of average number of neutrons per fissionFission32Covariances of resonance parametersResolved RP33Covariances of neutron cross sections(n,n), (n,n), (n,f),(n,g), (n,2n) ...34Covariances for Angular Distributions(n,n)35Covariances for Energy DistributionsFission neutron7MF=1number of neutrons per fissionPrompt neutron (np )Delayed neutron (nd )Components of energy release due to fission

8

Prompt neutronExperimental dataSystematicsHowerton Nucl. Sci. Eng. 62, 348 (1997)Ohsawa J. Nucl. Radiochem. Sci. Eng. 9, 19 (2008)

Ohsawa(2008)9np for U isotopesNuclidesJENDL-3.3JENDL-4U-2322.453.12U-2332.482.48U-2342.35= JENDL-3.3U-2352.422.42U-2362.36= JENDL-3.3U-2372.42= JENDL-3.3U-2382.442.28

np for thermal neutron10

Experimental dataSystematicsR.J.TuttleINDC(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)

-(Ac-3Z)Ac/Z

Waldo (1981)Tuttle (1979)16.698-1.144Zc+0.377AcDelayed neutron11MF=2Resolved resonanceSAMMY code (N. Larson, ORNL/TM-9179/R8, ENDF-364/R2, 2008)Unresolved resonanceASREP code (Y. Kikuchi et al., JAERI-Data/Code 99-025)12Resonance TheoryUseful in the low energy regionBreit-Wigner formulaG. 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 formulaC.W. Reich and M.S. Moore Phys. Rev., 111, 929 (1958)

13 Resonance Cross Sections

235U(n,f)14 Compilation of Resonance ParametersS.F. MughabghabAtlas of neutron resonances: resonance parameters and thermal cross sections Z=1-100, Elsevier (2006)

E , n , , f for each L and JThermal cross sections Resonance integrals

Scattering radiusNeutron separation energy

15Np-237 capture cross section for thermal neutron

16Am-241 thermal capture cross section

( ) sg.s. = 620 25 IR=0.896 assumed 17total cross section18thermal capture cross section(b)Kalebin (1976)624 20Shinohara+ (1997)854 58Fioni+ (2001)696 48Bringer+ (2006)714 23Present697.1JENDL-3.3639.5

241Am thermal neutron capturesg = 620 25 S. Nakamura+ (2007) sg+m= 692 28 (IR=0.896) U fission cross sections at RRR

19Cm-243, 244(n,f)

Low resolution measurement using lead slowing-down spectrometer2020Unresolved resonance

distribution (Porter-Thomas)Width-fluctuation correction factor

:Breit-Wigner formulaAverage cross sectionASREP: Y. Kikuchi et al., JAERI-Data/Code 99-02521Result of fitting with ASREP

R =D =Gg =Gf =22MF=3, 4, 5, 6Least-squares fitting to experimental dataFission cross section (Simultaneous evaluation on KALMAN)Major actinide (U-233, 235, 238, Pu-239, 241, 242)GMAMATheoretical model calculationAll reaction cross sections, angular distribution, secondary particle spectrum model parameter adjustmentCCONESOK23

total(n,n)(n,g)(n,f)(n,2n)(n,3n)elasticMF=3Neutron induced reaction on U-23824MF=4U-238(n,n) angular distribution25

neutron spectrum

En=5.5 MeVJENDL-3.3CCONE

En=550 keVqdeg.JENDL-3.3CCONEdW/dq (b/sr)qdeg.En(MeV)25

MF=5, 6QCM(deg)ds/dW (b/sr)Direct process901800QCM(deg)ds/dW (b/sr)Pre-equilibrium process901800Compound processQCM(deg)ds/dW (b/sr)901800

U-239neutron26Simultaneous evaluation of fission cross sectionLeast-squares fittingSOK code (Kawano)First order splineExperimental data

ReactionsetsReactionsets233U13233U/235U9235U17238U/233U1238U9238U/235U18239Pu16239Pu/235U14240Pu4240Pu/235U12241Pu6240Pu/239Pu1241Pu/235U4SOK27SOK28

evaluated data1st order splinecross section ratiolinearizeexperimental data

posterior covarianceprior cov.experimental data cov.

posterior

design matrixSOK

1st order spline

Correlation matrixSOK29235 fission cross section (SOK)30

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

SOK31Time evolution of nucleon induced reaction

32incident nucleon1p state2p-1h state3p-2h statecompound statedirect processpre-equilibrium processCCONE32Reaction models in CCONE codeDirect prosessOptical modelCoupled-channel methodDistorted wave Born approximationPre-equilibrium processExciton model (2 components)Compound processHauser-Feshbach

33CCONEIncident channel

34incident nucleon1p state2p-1h state3p-2h statecompound statedirect processpre-equilibrium processCCONE34Optical model

Total cross sectionShape elastic scattering cross sectionTransmission coefficient (used in statistical model)

Optical model potential (OMP)scattering matrix(strength of scattering wavesSchrdinger equation35CCONEincident nucleon35OMP and wave function

Wave functionPotentialFe-56 + n (En=10 MeV) OMP=koning-nImaginaryreal36CCONECross section variation with OMPs

totalshape elasticreaction37CCONEDirect process

38incident nucleon1p state2p-1h state3p-2h statecompound statedirect processpre-equilibrium processCCONE38Coupled-channels optical model

U-238deformation on ground stateincident wavescattered waveground state rotational bandstrong couplings between levels39CCONECoupled-channel optical modelrotational bandDeformed nucleus

40Nuclear radiusNuclear wave functionCoupled-channels equationIntrinsic wave functionRotational wave functionCCONE

deformed OMPneutron radial wave function40

Neutron Strength Function @10 keVExp.Spherical OM calc.RRM-CC calc.s-wave (l=0)s-wave neutron strength functionglobal CC OMPS. Kunieda et al., J. Nucl. Sci. Technol. 44, 838 (2007)actinideCCONE4141U-238 scattering cross section (0++2++4++6+)

CCONE42pre-equilibrium process

43incident nucleon1p state2p-1h state3p-2h statecompound statedirect processpre-equilibrium processCCONE43

pp,hp,pn,hn1,0,0,02,1,0,01,0,1,13,2,0,02,1,1,11,0,2,2p,n,g emissionPre-equilibrium processExciton model (2 components)44particleholep: protonn: neutronCCONE44Parameters in exciton modelpp,hp,pn,hn1,0,0,02,1,0,01,0,1,13,2,0,02,1,1,11,0,2,2p,n emission

transition rateemission rate of particle p-h creation by protonp-h creation by neutron45inverse reaction cross section (OM calculation)CCONEExciton model parameters

transition matrix elementstate density

CCsingle particle state densityKoning et al., Nucl. Phys. A744, 15 (2004)46CCONE1/gEfPauli correction

Dependences of spectrum and cross sections on exciton model parameters

Neutron spectrum @ En=14 MeV 47CCONEcompound process

48incident nucleon1p state2p-1h state3p-2h statecompound statedirect processpre-equilibrium processCCONE48

Decay chain on statistical model TargetdiscreteContinuum49CCONEEx49

Hauser-FeshbachWidth fluctuation correction

Normalization coefficientTransmission coefficient(OM calculation

Level density of daughter nucleusExcitation energy of targetEnergy conservationParity conservationTotal spin, parity50CCONE50Cumulative number of levels for U isotopes

Level density

discrete levelcontinuum level51CCONELevel density (Fermi gas model)

average resonance spacingspinexcitation energy dependenceparity52CCONE52Level density

Saddle point

inner-deformationouter mass asymmetryCollective enhancement (rotational level)Shell structure washoutGround stateFermi gasconstanttemperature53CCONE

g-ray strength function54

Standard LorentzianEnhanced Generalized LorentzianKopecky et al. PRC47,312 (1993), PRC41,1941(1990)

g-ray transmission coefficientCCONE54

Giant dipole resonance parameter55

SystematicsCCONEFission

Transition statePenetrability of a parabolic barrier double barriersTransmission coefficient56barrier curvaturebarrier heighttransition state energyCCONE56Fission cross sections for U isotopes

CCONE57U capture cross section

CCONE58U-238(n,2n)

Frehaut data without correctionCCONE59

Capture cross sections for Pu and N60

Pu-237Pu-239Pu-241Pu-244Pu-246Np-235Np-236Np-237Np-239Np-238JENDL-3.3JENDL-4.0CCONENp fission cross sections

GMACCONECCONE61CCONENeutron spectrum

CCONE62WPEC Subgroup 29 U-235 Capture Cross Section in the keV to MeV Energy Region63

Problem of integral experiment sodium voided reactivity in BFSMOXSensitivity to 235U capture cross sectionsodium voided reactivity

6464

Possible overestimation of capture cross section of U-235U-235 capture cross sectioncapture cross section/ fission cross sectio