Evaluation of actinide nuclear data

Osamu IwamotoJapan Atomic Energy Agency

2010 Symposium on Nuclear Data

Applications of nuclear data

nucleosynthesis

JRR-3

J-PARCADS

soft error

( 株 ) 化研提供medical application

nuclear data

Accelerator

Reactor

crab nebula

Tc-99m

2

recent actinide data in JENDL

Release No. of actinides

Covariance

JENDL-3.2 1994 56 0 +6 (JENDL-3.2 Cov. File, Major)

JENDL-3.3 2002 62 6 + 7 (after release of JENDL-3.3, MA)

JENDL/AC-2008 2008 79 0JENDL-4.0 2010 79 79 (all actinides, all cross sections)

3

Neutron induced reactions

U-235

U-236

U-235

U-235

Pa-235

Nucleus(A~90)

Nucleus(A~140)

Fission

SpallationCapture

Elastic scattering

Inelastic scattering

4

neutron induced reaction cross sections

5

resolved resonance unresolved resonancethermal235U

Nuclear data evaluation

6

EXFOR

KALMAN, GMA

CRECTJ

NJOY

CCONE

Physical quantities of actinide data in JENDL-4MF Physical quantities reaction

1 number of neutrons per fission, Components of energy release due to fission

fission

2 Resonance parameters Resolved RP, unresolved RP

3 Neutron cross sections (n,n), (n,n’), (n,f),(n,g), (n,2n) ...

4 Angular distributions of secondary neutrons (n,n), fission

5 Energy Distributions of Secondary Neutrons fission

6 Energy-angle distributions (n,n’), (n,2n), (n,3n), (n,g)

12 Photon Production Multiplicities Fission

14 Photon Angular Distributions Fission

15 Continuous Photon Energy Spectra Fission

31 Covariances of average number of neutrons per fission Fission

32 Covariances of resonance parameters Resolved RP

33 Covariances of neutron cross sections (n,n), (n,n’), (n,f),(n,g), (n,2n) ...

34 Covariances for Angular Distributions (n,n)

35 Covariances for Energy Distributions Fission neutron7

MF=1

• number of neutrons per fission– Prompt neutron (np )

– Delayed neutron (nd )

• 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

np for U isotopes

Nuclides JENDL-3.3 JENDL-4

U-232 2.45 3.12

U-233 2.48 2.48

U-234 2.35 = JENDL-3.3

U-235 2.42 2.42

U-236 2.36 = JENDL-3.3

U-237 2.42 = JENDL-3.3

U-238 2.44 2.28

np for thermal neutron

10

• Experimental data• Systematics

– R.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+0.377Ac

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 99-

025)

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)

l J rrr

xrnrJxn

EEg

kE

222,

41

)'()(

13

Resonance Cross Sections

55 60 65 70 75

100

101

102

103

Neutron Energy (eV)

Cro

ss S

ecti

on (

b)

84 Weston+88 Schrack

JENDL-3.2 (R-M)JENDL-3.1 (B-W)

235U(n,f)235U(n,f)

14

Compilation of Resonance ParametersS.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

eV E

dEEI

5.0)(

15

Np-237 capture cross section for thermal neutron

16

Am-241 thermal capture cross section

( )

（ sg.s. = 620 25 、 IR=0.896 assumed ） 17

total cross section

18

thermal capture cross section(b)Kalebin (1976) 624 20Shinohara+ (1997)854 58Fioni+ (2001) 696 48Bringer+ (2006) 714 23

Present 697.1

JENDL-3.3 639.5 10-2 10-1 100102

103

104

Neutron Energy (eV)

Cro

ss S

ecti

on (

b)

Ju.V.Adamchuk+ ('55) Ju.V.Adamchuk+ ('55) Ju.V.Adamchuk+ ('55) G.G.Slaughter+ ('61) H.Derrien+ ('75) S.M.Kalebin+ ('76)

241Am total

Present JENDL-3.3

241Am thermal neutron capture

sg = 620 25 S. Nakamura+ (2007)

sg+m= 692 28 (IR=0.896)

U fission cross sections at RRR

10-2 10-1 100 101 10210-5

10-4

10-3

10-2

10-1

100

101

Neutron Energy (eV)

Cro

ss S

ecti

on (

b)

R.H.Odegaarden ('60) G.D.James+ ('68) G.D.James+ ('77) C.Wagemans+ ('02)

234U fission

present JENDL-3.3

19

Cm-243, 244(n,f)

40 50 60100

101

102

103

Neutron Energy (eV)

Cro

ss S

ecti

on (

b)

M.G.Silbert ('76)

243Cm fission

modified JENDL-3.3

10-2 10-1 100 101 102 103 104 10510-2

10-1

100

101

Neutron Energy (eV)

Cro

ss S

ecti

on (

b)

244Cm fission

Maguire et al. Modified JENDL-3.3

Modified (+Cm243) JENDL-3.3 (+Cm243)

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 99-025

21

Result of fitting with ASREP

R =D =

Gg =Gf =

22

MF=3, 4, 5, 6

• Least-squares fitting to experimental dataFission cross section– (Simultaneous evaluation on KALMAN)

• Major actinide (U-233, 235, 238, Pu-239, 241, 242)

– GMA• MA

• Theoretical model calculationAll reaction cross sections, angular distribution, secondary

particle spectrum–

• model parameter adjustment

CCONE

SOK

23

total

(n,n’)

(n,g)

(n,f)

(n,2n) (n,3n)

elastic

MF=3Neutron induced reaction on U-238

24

MF=4U-238(n,n) angular distribution

25

neutron spectrum

En=5.5 MeV

JENDL-3.3

CCONE

実験En=550 keV

q （ deg. ）

JENDL-3.3

CCONE

dW/d

q (b

/sr)

q （ deg. ）

En(MeV)

MF=5, 6

QCM(deg)

ds/

dW

(b

/sr)

Direct process

90 1800

QCM(deg)

ds/

dW

(b

/sr)

Pre-equilibrium process

90 1800

Compound process

QCM(deg)

ds/

dW

(b

/sr)

90 1800

U-239

neutron

26

Simultaneous evaluation of fission cross section

• Least-squares fitting– SOK code (Kawano)– First order spline

• Experimental dataReaction sets Reaction sets

233U 13 233U/235U 9235U 17 238U/233U 1238U 9 238U/235U 18239Pu 16 239Pu/235U 14240Pu 4 240Pu/235U 12241Pu 6 240Pu/239Pu 1

241Pu/235U 4

SOK

27

SOK

28

evaluated data

1st order spline

cross section ratio

linearize

experimental data

posterior covariance

prior cov.

experimental data cov.

posterior

design matrix

SOK

1st order splineCorrelation matrix

SOK

29

235 Ｕ fission cross section (SOK)

30

SOK

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

CCONE

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

CCONE

Incident channel

34

incident nucleon

1p state 2p-1h state 3p-2h state compound state

direct process

pre-equilibrium process

CCONE

Optical model

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

Optical model potential (OMP)

scattering matrix(strength of scattering waves ）

Schrödinger equation

35

CCONE

incident nucleon

OMP and wave function

Wave function

Potential

Fe-56 + n (En=10 MeV) OMP=koning-n

Imaginary

real

36

CCONE

Cross section variation with OMPs

total

shape elastic

reaction

37

CCONE

Direct process

38

incident nucleon

1p state 2p-1h state 3p-2h state compound state

direct process

pre-equilibrium process

CCONE

Coupled-channels optical model

U-238

deformation on ground state

incident wavescattered wave

ground state rotational band

strong couplings between levels

39

CCONE

Coupled-channel optical modelrotational band

Deformed nucleus

40

Nuclear radius

Nuclear wave function

Coupled-channels equationIntrinsic wave function

Rotational wave function

CCONE

deformed OMPneutron radial wave function

Neutron Strength Function @10 keV

Exp.Spherical OM calc.RRM-CC calc.

s-wave (l=0)

s-wave neutron strength functionglobal CC OMP S. Kunieda et al., J. Nucl. Sci. Technol. 44, 838 (2007)

actinide

CCONE

41

U-238 scattering cross section (0++2+

+4++6+)

CCONE

42

pre-equilibrium process

43

incident nucleon

1p state 2p-1h state 3p-2h state compound state

direct process

pre-equilibrium process

CCONE

pp,hp,pn,hn 1,0,0,0

2,1,0,0 1,0,1,1

3,2,0,0 2,1,1,1 1,0,2,2

p,n,g emission

Pre-equilibrium processExciton model (2 components)

44

particle hole

p: protonn: neutron

CCONE

Parameters in exciton modelpp,hp,pn,hn 1,0,0,0

2,1,0,0 1,0,1,1

3,2,0,0 2,1,1,1 1,0,2,2

p,n emission

transition rate

emission rate of particle

p-h creation by proton

p-h creation by neutron

45inverse reaction cross section (OM calculation)

CCONE

Exciton model parameterstransition matrix element

state density

C

C

single particle state density

Koning et al., Nucl. Phys. A744, 15 (2004)

46

CCONE

1/g

Ef

Pauli correction

Dependences of spectrum and cross sections on exciton model parameters

Neutron spectrum @ En=14 MeV

47

CCONE

compound process

48

incident nucleon

1p state 2p-1h state 3p-2h state compound state

direct process

pre-equilibrium process

CCONE

Decay chain on statistical model Target

discrete

Continuum

49

CCONE

Ex

Hauser-FeshbachWidth fluctuation correction

Normalization coefficient

Transmission coefficient(OM calculation ）

Level density of daughter nucleusExcitation energy of target

Energy conservation

Parity conservation

Total spin, parity

50

CCONE

Cumulative number of levels for U isotopes

Level density

discrete level

continuum level51

CCONE

Level density (Fermi gas model)

average resonance spacing

spinexcitation energy dependenceparity

52

CCONE

Level density

Saddle point

（ inner 　 γ-deformation ）

（ outer mass asymmetry ）

Collective enhancement (rotational level)

Shell structure washout

Ground state

Fermi gas

constanttemperature

53

CCONE

g-ray strength function

54

Standard Lorentzian

Enhanced Generalized Lorentzian

Kopecky et al. PRC47,312 (1993), PRC41,1941(1990)

g-ray transmission coefficient

CCONE

Giant dipole resonance parameter

55

Systematics

CCONE

FissionTransition state

Penetrability of a parabolic barrier

double barriers

Transmission coefficient

56

barrier curvature

barrier height

transition state energy

CCONE

Fission cross sections for U isotopesCCONE

57

U capture cross sectionCCONE

58

U-238(n,2n)

10 15 200

0.5

1.0

1.5

Neutron Energy (MeV)

Cro

ss S

ecti

on (

b)

L.R.Veeser+ ('78) H.Karius+ ('79) J.Frehaut+ ('80) J.Frehaut+ ('80) N.V.Kornilov+ ('80) P.Raics+ ('80) T.B.Ryves+ ('80) R.Pepelnik+ ('85) V.Ya.Golovnya+ ('87) V.Ya.Golovnya+ ('87) C.Konno+ ('93) A.A.Filatenkov+ ('99) A.A.Filatenkov+ ('99)

238U (n,2n)

CCONE (= present) JENDL-3.3 ENDF/B-VII .0

修正前のFrehaut+のデータ

Frehaut data without correction

CCONE

59

Capture cross sections for Pu and N ｐ

60

Pu-237

Pu-239

Pu-241

Pu-244

Pu-246

Np-235Np-236

Np-237

Np-239

Np-238

JENDL-3.3JENDL-4.0

CCONE

Np fission cross sections

GMA

CCONE

CCONE

61

CCONE

Neutron spectrumCCONE

62

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

63

LEZ MEZ HEZ LEZ MEZ MOX HEZ MOX2 3A 5

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

JENDL-3.3

JEFF-3.1

ENDF/B-VII.0

C/E

Problem of integral experiment sodium voided reactivity in BFS

MOX

Sensitivity to 235U capture cross section

sodium voided reactivity

64

102 103 104 10510-1

100

101

Neutron Energy (eV)

Cro

ss S

ecti

on (

b)

235U capture

ENDF/B-VII.0 JENDL-3.2 statistical model

2.25 keV

500eV

25 keV

30 keV

Possible overestimation of capture cross section of U-235

U-235 capture cross section capture cross section/ fission cross section

102 103 1040.0

0.2

0.4

0.6

0.8

1.0

Neutron Energy (eV)

Cro

ss S

ecti

on R

atio

P.E.Vorotnikov+ ('71) P.E.Vorotnikov+ ('71) F.Corvi+ ('75) V.G.Dvukhsherstnov+ ('75) V.G.Dvukhsherstnov+ ('75)

235U

G.V.Muradyan+ ('80) F.Corvi+ ('82)

JENDL-3.2 ENDF/B-VII.0

500 eV 2.25 keV

Resonance region

65

U-235 capture cross section

66

Upper boundary of RRR: 2.25 0.5 keV

C/E value of BFS criticalities

0.985

0.990

0.995

1.000

1.005

62-1

62-2

62-3

A

62-4

62-5

66-1

C/E

J ENDL- 4.0J ENDL- 3.3

67

Resources for nuclear data evaluation

• EXFOR– http://www-nds.iaea.org/exfor/exfor.htm– http://www.nndc.bnl.gov/exfor/exfor00.htm– http://www.nea.fr/dbdata/x4/

• RIPL– http://www-nds.iaea.org/RIPL-3/

• JAEA Nuclear data center– http://wwwndc.jaea.go.jp/– SPES (Search and Plot Executive System)

http://spes.jaea.go.jp/cgi-bin/spes.cgi– mailto: jendl@jaea.go.jp

68