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: [email protected]
68