Evaluation of actinide nuclear data

Report
2010 Symposium on Nuclear Data
Evaluation of actinide nuclear
data
Osamu Iwamoto
Japan Atomic Energy Agency
Applications of nuclear data
Reactor
Accelerator
JRR-3
ADS
J-PARC
nuclear
data
Tc-99m
medical application
soft error
(株)化研提供
crab nebula
nucleosynthesis
2
recent actinide data in JENDL
Release No. of
Covariance
actinides
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
0
JENDL-4.0
2010
79
79 (all actinides, all cross sections)
3
Neutron induced reactions
Pa-235
U-235
Nucleus(A~140)
Nucleus(A~90)
U-235
Elastic scattering
Fission
U-235
U-236
Inelastic scattering
Capture
Spallation
4
neutron induced reaction cross sections
235U
thermal
resolved resonance
unresolved resonance
5
Nuclear data evaluation
CCONE
EXFOR
KALMAN, GMA
CRECTJ
NJOY
6
Physical quantities of actinide data in JENDL-4
MF
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 neutron
7
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
np for thermal neutron
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
10
Delayed neutron
• 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)
Waldo (1981)
Tuttle (1979)
-(Ac-3Z)Ac/Z
16.698-1.144Zc+0.377Ac
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 99025)
12
Resonance Theory
• Useful in the low energy region
• Breit-Wigner formula
– G. Breit and E.P. Wigner
Phys. Rev., 49, 519 (1936).
 n, x ( E ) 

k
2
 g 
J
l
J
r
nr xr
1
( E  Er ' ) 2  r2
4
– 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
3
Cross Section (b)
10
102
235
235
U(n,f)
U(n,f)
JENDL-3.2 (R-M)
JENDL-3.1 (B-W)
84 Weston+
88 Schrack
101
100
55
60
65
70
Neutron Energy (eV)
75
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

dE
I    (E)
0.5 eV
E
• Scattering radius
• Neutron separation energy
15
Np-237 capture cross section for
thermal neutron
16
Am-241 thermal capture cross section
( )
total cross section
17
( g.s. = 620  25、 IR=0.896 assumed)
thermal neutron capture
thermal capture cross section(b)
Kalebin (1976)
624  20
Shinohara+ (1997) 854  58
Fioni+ (2001)
696  48
Bringer+ (2006)
714  23
Present
JENDL-3.3
697.1
639.5
g = 620  25 S. Nakamura+ (2007)
g+m= 692  28 (IR=0.896)
241
4
10
Cross Section (b)
241Am
Am total
Ju.V.Adamchuk+ ('55)
Ju.V.Adamchuk+ ('55)
Ju.V.Adamchuk+ ('55)
G.G.Slaughter+ ('61)
H.Derrien+ ('75)
S.M.Kalebin+ ('76)
103
Present
JENDL-3.3
102
10-2
10-1
Neutron Energy (eV)
100
18
U fission cross sections at RRR
234
U fission
Cross Section (b)
101
R.H.Odegaarden ('60)
G.D.James+ ('68)
G.D.James+ ('77)
C.Wagemans+ ('02)
100
10-1
10-2
10-3
present
JENDL-3.3
-4
10
10-5
10-2
10-1
100
101
Neutron Energy (eV)
102
19
Cm-243, 244(n,f)
244
243
10
Cm fission
3
1
10
102
101
100
Maguire et al.
Modified
JENDL-3.3
modified
JENDL-3.3
Cross Section (b)
Cross Section (b)
M.G.Silbert ('76)
40
50
Neutron Energy (eV)
Cm fission
60
Modified (+Cm243)
JENDL-3.3 (+Cm243)
0
10
10-1
10-2 -2
10
10-1
100 101 102 103
Neutron Energy (eV)
104
Low resolution measurement using
lead slowing-down spectrometer
20
105
Unresolved resonance
ASREP: Y. Kikuchi et al., JAERI-Data/Code 99-025
Breit-Wigner formula
Average cross section
:
distribution (Porter-Thomas)
Width-fluctuation
correction factor 21
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
MF=3
Neutron induced reaction on U-238
total
elastic
(n,n’)
(n,)
(n,f)
(n,2n) (n,3n)
24
neutron spectrum
MF=4
U-238(n,n) angular distribution
En(MeV)
dW/dq (b/sr)
En=550 keV
実験
JENDL-3.3
CCONE
En=5.5 MeV
JENDL-3.3
CCONE
q(deg.)
q(deg.)
25
MF=5, 6
Direct
process
d/dW (b/sr)
Compound
process
neutron
d/dW (b/sr)
U-239
0
0
90
QCM(deg)
90
QCM(deg)
180
180
d/dW (b/sr)
Pre-equilibrium
process
0
90
QCM(deg
)
180
26
Simultaneous evaluation of fission
cross section
• Least-squares fitting
– SOK code (Kawano)
– First order spline
• Experimental data
Reaction
233
U
235
U
238
U
239
Pu
240
Pu
241
Pu
sets
13
17
9
16
4
6
Reaction
233
U/235U
238
U/233U
238
U/235U
239
Pu/235U
240
Pu/235U
240
Pu/239Pu
241
Pu/235U
sets
9
1
18
14
12
1
4
27
experimental data
SOK
evaluated data
design matrix
1st order spline
cross section ratio
linearize
experimental data cov.
posterior
posterior covariance
prior cov.
28
1st order spline
Correlation matrix
29
235U
fission cross section (SOK)
30
U-233(n,f)/U-235(n,f) (SOK)
31
Time evolution of
nucleon induced reaction
pre-equilibrium process
incident nucleon
1p state
direct process
2p-1h state
3p-2h state
compound state
32
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
pre-equilibrium process
incident nucleon
1p state
direct process
2p-1h state
3p-2h state
compound state
34
Optical model
Schrödinger equation
Optical model potential (OMP)
incident nucleon
scattering matrix
(strength of scattering waves)
Total cross section
Shape elastic scattering cross section
Transmission coefficient
(used in statistical model)
35
OMP and wave function
Fe-56 + n (En=10 MeV) OMP=koning-n
Wave function
Imaginary
Potential
real
36
Cross section variation with OMPs
reaction
total
shape elastic
37
Direct process
pre-equilibrium process
incident nucleon
1p state
direct process
2p-1h state
3p-2h state
compound state
38
Coupled-channels optical model
deformation on ground state
ground state rotational band
strong couplings between levels
scattered wave
incident wave
U-238
39
Coupled-channel optical model
rotational band
Deformed nucleus
Nuclear radius
Nuclear wave function
Coupled-channels equation
neutron radial
wave function
Rotational wave function
Intrinsic wave function
deformed OMP
40
s-wave neutron strength function
global CC OMP
S. Kunieda et al., J. Nucl. Sci. Technol. 44, 838 (2007)
Neutron Strength Function @10 keV
s-wave (l=0)
Exp.
Spherical OM calc.
RRM-CC calc.
actinide
41
U-238 scattering cross section
(0++2++4++6+)
42
pre-equilibrium process
pre-equilibrium process
incident nucleon
1p state
direct process
2p-1h state
3p-2h state
compound state
43
Pre-equilibrium process
Exciton model (2 components)
p,h,pn,hn
1,0,0,0
: proton
n: neutron
p,n, emission
particle hole
2,1,0,0
3,2,0,0
1,0,1,1
2,1,1,1
1,0,2,2
44
Parameters in exciton model
p,h,pn,hn
1,0,0,0
p,n emission
2,1,0,0
3,2,0,0
1,0,1,1
2,1,1,1
1,0,2,2
p-h creation by proton
transition rate
emission rate of particle
p-h creation by neutron
inverse reaction cross section (OM calculation)
45
Exciton model parameters
transition matrix element
Koning et al., Nucl. Phys. A744, 15 (2004)
state density
Pauli correction
1/g
single particle state density
Ef
C
C
46
Dependences of spectrum and cross
sections on exciton model parameters
Neutron spectrum @ En=14 MeV
47
compound process
pre-equilibrium process
incident nucleon
1p state
direct process
2p-1h state
3p-2h state
compound state
48
Decay chain on statistical model
Target
Ex
Continuum
discrete
49
Hauser-Feshbach
Width fluctuation correction
Total spin, parity
Normalization coefficient
Energy conservation
Level density of daughter nucleus
Excitation energy of target
Parity conservation
Transmission coefficient
(OM calculation) 50
Cumulative number of levels for U isotopes
Level density
discrete level
continuum level
51
Level density (Fermi gas model)
parity
spin
excitation energy
dependence
average resonance spacing
52
Level density
Fermi gas
constant
temperature
Shell structure washout
Collective enhancement (rotational level)
Ground state
Saddle point
(inner γ-deformation)
(outer mass asymmetry)
53
-ray strength function
-ray transmission coefficient
Standard Lorentzian
Enhanced Generalized Lorentzian
Kopecky et al. PRC47,312 (1993), PRC41,1941(1990)
54
Giant dipole resonance parameter
Systematics
55
Fission
Transition state
Penetrability of a parabolic barrier
barrier height
double barriers
barrier curvature
transition state energy
Transmission coefficient
56
Fission cross sections for U isotopes
57
U capture cross section
58
U-238(n,2n)
238
U (n,2n)
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)
Cross Section (b)
1.5
1.0
修正前のFrehaut+
Frehaut data のデータ
0.5
without correction
CCONE (= present)
JENDL-3.3
ENDF/B-VII .0
0
10
15
Neutron Energy (MeV)
20
59
Capture cross sections for Pu and Np
JENDL-3.3
JENDL-4.0
Pu-237
Pu-239
Pu-241
Pu-244
Pu-246
Np-236
Np-235
Np-237
Np-238
Np-239
60
Np fission cross sections
CCONE
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
1.2
1.1
1
C/E
0.9
0.8
JENDL-3.3
JEFF-3.1
ENDF/B-VII.0
JENDL-3.2
0.7
0.6
0.5
0.4
LEZ
MEZ
2
HEZ
LEZ
MEZ
MOX
3A
HEZ
MOX
5
sodium voided reactivity
Sensitivity to 235U capture cross section 64
Possible overestimation of
capture cross section of U-235
capture cross section/ fission
cross section
U-235 capture cross section
U capture
ENDF/B-VII.0
JENDL-3.2
statistical model
Cross Section (b)
10
30 keV
500eV
2.25 keV
-1
10
25 keV
Cross Section Ratio
1.0
1
100
0.8
103
104
Neutron Energy (eV)
P.E.Vorotnikov+ ('71)
P.E.Vorotnikov+ ('71)
F.Corvi+ ('75)
V.G.Dvukhsherstnov+ ('75)
V.G.Dvukhsherstnov+ ('75)
G.V.Muradyan+ ('80)
F.Corvi+ ('82)
JENDL-3.2
ENDF/B-VII.0
0.6
0.4
0.2
Resonance region
102
U
235
235
500 eV
105
0.0 2
10
2.25 keV
103
Neutron Energy (eV)
104
65
U-235 capture cross section
Upper boundary of RRR: 2.25  0.5 keV
66
C/E value of BFS criticalities
1.005
0.995
0.990
JENDL-4.0
JENDL-3.3
66-1
62-5
62-4
62-3A
62-2
0.985
62-1
C/E
1.000
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

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