iaea-nd cm on “prompt fission neutron spectra of major actinides”, 24-27. nov. 2008
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IAEA-ND CM on “Prompt fission neutron spectra of major actinides”, 24-27. Nov. 2008. Application of Multimodal Madland-Nix Model ・ Evaluation of PFNS in JENDL-series ・ Multimodal Random Neck-rupture Model : An Outline ・ Refinements in the Madland-Nix Model 1) Multimodal fission, - PowerPoint PPT PresentationTRANSCRIPT
IAEA-ND CM on “Prompt fission neutron spectra of major actinides”, 24-27. Nov. 2008
Application of Multimodal Madland-Nix Model
・ Evaluation of PFNS in JENDL-series ・ Multimodal Random Neck-rupture Model : An Outline ・ Refinements in the Madland-Nix Model 1) Multimodal fission, 2) Level density parameter considering the shell effect, 3) Asymmetry in ν for LF and HF, 4) Asymmetry in T for LF and HF ・ Possible early neutrons : Neutron emission during acceleration ( NEDA) Takaaki Ohsawa ( 大澤孝明 )
Dept. of Electric & Electronic EngineeringSchool of Science and EngineeringKinki University, Osaka, Japan
Prompt fission neuron spectra in JENDL-3.3 and JENDL/AC2008
JENDL-3.3 JENDL/AC2008Th-232 Maxwellian [TM=Howerton-Doyas’ syst.] CCONE (O.Iwamoto)Pa-231 Maxwellian (taken from ENDF/B-V) CCONE U-233 Multimodal M-N (T.Ohsawa) Multimodal M-N [E≤5MeV], CCONE [E>5MeV] U-235 Multimodal M-N [E≤5MeV], Multimodal M-N [E≤5MeV], Preeq. spectrum by FKK model CCONE [E>5MeV]U-238 Multimodal M-N Multimodal M-N [E≤5MeV], CCONE [E>5MeV] Np-237 Maxwellian [TM: Baba(2000),Boikov(1994)] CCONEPu-239 Multimodal M-N Multimodal M-N [E≤5MeV] CCONE [E>5MeV] Pu-241 Maxwellian [TM=Smith’s systematics] CCONE [E>5MeV] Am-241 Maslov’s evaluation (1996) Multimodal M-N [E≤6MeV], CCONE [E>6MeV]Am-242m Maslov’s evaluation (1997) Multimodal M-N [E≤6MeV], CCONE [E>6MeV]Cm-243 Maslov’s evaluation (1995) Multimodal M-N [E≤6MeV], CCONE[E>6MeV]Cm-245 Maslov’s evaluation (1996) Multimodal M-N [E≤6MeV], CCONE[E>6MeV]
JENDL-3.3JENDL-3.3 JENDL/AC2008JENDL/AC2008 JENDL-4 JENDL-4
・ Released March 2008・ Ac –Fm (Z=89-100)・ 79 nuclides
・ Released May 2002・ 62 nuclides
Evaluated Nuclear Data for Actinides in the JENDL-series
・ Will be released in 2010・ Slight revision(?)
New 17 nuclides (T1/2 >1d) added
Program CCONE (by O. Iwamoto, JAEA)
Main features・” All-in-one” code for evaluation of nuclear data・ Witten in C++ for ease of extension & modification ・ Architecture based on object oriented programming・ Coupled-channel theory・ Hauser-Feshbach theory including Moldauer effect・ DWBA for direct excitation of vibrational states・ Two-component exciton model (Kalbach)・ Multi-particle emission from the CN with spin- and parity-conservation・ Double-humped fission barriers with consideration of collective enhancement of the level density・ Madland-Nix model (original implementation)
cf. Osamu Iwamoto, J. Nucl. Sci. Technol. 44, 687 (2007)
Multimodal Random Neck-rupture Model [U.Brosa, S.Grossmann, A.Müller]
Random Neck- Rupture Model Random Neck- Rupture Model
Multichannel Fission Model Multichannel Fission Model
Multimodal Random Neck-Rupture Model (BGM model)Multimodal Random Neck-Rupture Model (BGM model)
[S.L.Whetstone,1959] [e.g. E.K.Hulet et al. 1989]
“hybrid”
Multimodal Random Neck-rupture Model
Several distinct deformation paths ⇒ several pre-scission shapes
Neck-rupture occursrandomly according tothe Gaussian function
S1
S2SL
[U. Brosa et al.1990]
2 2Rupture probability ( ) exp{ 2 [ ( ) ( )] / }rW A z z T
Standard-1
Standard-2
Superlong
Example: 235U(n,f)
3 modes overlapping → largest σ
Standard-1
Standard-2
Superlong
[H.-H. Knitter et al. Z. Naturforsch,42a,760(1987)]
Mas
s Y
ield
TK
Eσ
(TK
E)
2 modes overlapping → larger σ
single mode prevails → smaller σ
Justification of the MM-RNR model on the basis of deformation energy surface calc.
Be
ta-
def
orm
atio
n
N Z
Spherical nucleus
N=86 (Meta-stable deformation; S2)
N=82 (S1) Z=50 (S1)
[B. D. Wilkins et al., Phys. Rev. C14,1832 (1976)]
The nascent HF is likely to be formed close to these hollows
Application of the Multimodal RNR Model
Multi-channelFissionModel
Random Neck-Rupture Model
Multimodal RNR Model
Madland-Nix (LA) Model
SummationCalculation
MultimodalMadland-Nix Model
Multimodal Analysis of DNY
T.Ohsawa et al., Nucl. Phys. A653, 17 (1999).
T. Ohsawa & F.-J. Hambsch, Nucl. Sci. Eng. 148, 50 (2004)
Fluctuations Observed in the Fission Yield in the Resonance Region for U-235 [F.-J. Hambsch]
Precursors are localized, because they have a structure of closed shell + loosely bound neutrons outside of the core.
Fluctuation in the Precursor Yields in the Resonance Region of U-235
The precursor yields in the LF-S2-region are considerably decreased.This brings about decrease in the delayed neutron yield at the resonance.
Fluctuation in the Delayed Neutron Yields for U-235
-3.5%
cf. T. Ohsawa and F.-J. Hambsch, Nucl. Sci. Eng. 148, 50 (2004)
271
n1
d i ii
Y P
Sudden decrease in the 4 - 7MeV region
Slight decrease in thermal & resonance
regions
CM-spectrum:
)exp(2
)(3/2 T
EE
TE
M
]/)(2sinh[)/exp()(
)/exp()( 2/1
WfWWf
Wf TEETETE
TEE
1. Maxwellian
2. Watt
3. Madland-Nix (LA) model
mT
m
C dTTTTkT 0
2)/exp()(
)(2)(
2
2
*
0
/2)(
m
totfnnr
m
mm
aT
EEBEE
TT
TTTTTP
Models of PFNS
S.S.Kapoor et al., Phys. Rev. 131, 283 (1963)
2
2
( )
20( )
( , , )
1( ) ( ) exp( / )
2
f m
f
f
E E T
C
f m E E
N E E
d k T T T dTE T
LS-spectrum:
Märten & Seeliger Hu Jimin
4. Cascade Evaporation Model
5. Hauser-Feshbach ModelBrowne & DietrichGerasimenko
6. Monte Carlo Simulation
Lemaire, Talou, Kawano, Chadwick, MadlandDostrovsky, Fraenkel (1959)
Criteria for choosing a model for evaluation: 1. Accuracy 2. Simplicity 3. Predictive power
Improvements in the Method
Original Madland-Nix Model χtot= ½{ χL+ χH }
Multimodal Madland-Nix Model
(2) LDP : Shell effects on the LDP (Ignatyuk’s model)
(1) Multimodal Fission: Energy partition in the fission process is very different for different fission modes
( ) [ ( )] /[ ]tot n i i i n i ii i
E w E w
(3) Asymmetry inν: νL≠νH
/( )i iL iL iH iH iL iH
(4) Asymmetry in T : T L ≠ TH
because of the difference in deformation
(1) Multimodal Fission Model
Each different deformation path leads to different scission configuration, therefore to different energy partition.
S1
S2SL
Asymmetric fission
(standard mode)
Symmetric fis
sion
(superlong mode)
Hartree-Fock-Bogoliubov calc.by H.Goutte et al., Phys. Rev. C71, 024316(2005)
134
236
102
118
14195
118
Standard-1
Standard-2
Superlong
81.6%
18.3
%
0.007%
ER=194.5MeVTKE=187MeV
ER=184.9MeVTKE=167MeV
ER=190.9MeVTKE=157MeV
Multimodal Fission Process 235U(n,f), Ein=thermal
Average fragment mass
ER : calc. with TUYY mass formula (Tachibana et al., Atomic & Nucl. Data Tables, 39, 251 (1988) )TKE : Knitter et al., Naturforsch, 42a, 786 (1987)
Decomposition of Primary FF Mass Distribution
<TXE>= 14.0 MeV24.4 MeV
40.5 MeV24.4 MeV
14.0 MeV
S1-spectrum – softestS2-spectrum – harderSL-spectrum - hardest
Comparison with experimentfor U-235(nth,f)
( )
iL iL iH iHi
iL iH
●Modal spectrum :
●Total spectrum :
wi : mode branching ratio
1, 2,
1, 2,
i i ii S S SL
toti i
i S S SL
w
w
This evaluation is contained in JENDL-3.3 & JENDL/AC2008 and will also be in JENDL-4.
0 5 10 15 201E-7
1E-6
1E-5
1E-4
1E-3
0.01
0.1
1
U-235(n,f)
En=0 MeV
En=2 MeV
En=5 MeV
No.of Neutrons (1/MeV)
Neutron Energy (MeV)
Spectra for Different Incident Energies
0 5 10 15 200.5
1.0
1.5
2.0
2.5
3.0
En=0 MeV
En=2 MeV
En=5 MeV
U-235(n,f)
Ratio to Thermal Fission
Neutron Energy (MeV)
At higher incident energiesthe spectrum becomesharder due to1. Higher excitation energies of the FFs.2. Increase in the S2- component.
(2) Shell Effects on LDP for FF
( ) ( )[1 ( ) / ]U a A f U Wa U
exp LD( , ) ( , )W M Z A M Z A
)exp(1)( UUf
2a A A
●Shell effects on the LDP vary according to the mass and excitation energy of the FFs.
Ignatyuk’s LDP
-10.054 MeV
Excitation-energy dependence :
0.154 5103.6 Asymptotic value :
Shell correction :
2condU E E ta Effective excitation energy :
20 03 , 12 /cond critE a A
Eq.(1) is a transcendental eq.→Solve it numerically! ( IGNA3 code )
(1)
Effect of the Level Density Parameter on the Spectrum
LDP has a great effecton the spectrum, esp. inthe higher energy region.
(3) Asymmetry in ν for LF and HF: νL(A) ≠ νH(A)
Saw-tooth structure
)]()([1
)(
)]()()[2/1()(
niHiHniLiLiHiL
ni
niHniLni
EEE
EEE
Madland- Nix:
New modalspectra:
This is important because the neutron spectra from the LF and HF are very different!
HF LF
mHvH = mLvL
1. The LF travels faster than the HF.
Two effects2. Low energy neutrons are more easily emitted from HFs than from LFs.
CM LS
HF
LF
S.S.Kapoor et al.,Phys.Rev. 131,283 (1963)
Consideration of non-equality νL(A) ≠ νH(A) brings about a difference of ~10% at maximum in the spectrum
(4) Asymmetry in the Nuclear Temperatures ・ T. Ohsawa, INDC(NDS)-251 (1991), IAEA/CM on Nuclear Data for Neutron Emission in the Fission Process, Vienna, 1990. p.71.・ T. Ohsawa and T. Shibata, Proc. Int. Conf. on Nucl. Data for Science and Technology, Juelich, 1991, p.965 (1992), Springer-Verlag.・ P. Talou, ND2007, Nice (2008)
●Total excitation energy of the FF:
TXE = Eint (L) + Edef (L) + Eint (H) + Edef (H)
at the scission-point
= E*(L) + E*(H)
at the moment of neutron emission
The nuclear temperatures of the two FFs at the moment of neutron emission are generally not equal, if the deformation is different at scission.
E*CN=Bn+En E*
L=aLT2L E*
H=aHT2H
E*L= Eint L +Edef L
E*H= Eint H +Edef H
TXE =<ER> + Bn + En ー TKE = aCNT2m
= aLT2L + aHT2
H
=(aLRT2 + aH)T2
H
where RT=TL/TH : temperature ratio
CN CNL H2 2
T L H
T
H LT
2
,m m
a aT T T T
a
R
R a a R a
Mode Standard-1 Standard-2 Superlong
Nuclides Zr-102 Te-134 Sr-95 Xe-141 Pd-118 Pd-118
ER 194.49 184.86 190.95
TKE 187 167 157
E* 8.39 10.51 11.74 9.11 22.89 22.89
LDP 11.43 8.89 10.31 13.25 11.79 11.79
1.05 1.31 1.47 1.14 2.86 2.86
TL,i, TH,i 0.86 1.09 1.06 0.83 1.39 1.39
L,i H,iν , ν
Basic Fission Data for U-235(nth,f)
Multimodal mass distribution model
TUYYMass Formula Ignatyuk’s Level
Density ModelOptical Model(ELIESEⅢ )
Modified UnchangedCharge Distribution Model
Charge distribution
Total energyrelease LDP for
LF & HF
Inverse reactioncross sections
for LF & HF
TKE for Each Mode
ν L, ν H
Prompt Neutron Spectrum Calculation Code (FISPEK-O)
Total & Modal Neutron Spectra
Systematicsin Modal TKE
Mass distribution &mode branching ratios
Typical LF/ HF & their yields for each mode
TOTAL CODESYSTEM
Possible Early Neutrons
Neutron Emission During Acceleration (NEDA)
x
x
x
x
v
st
k 1
1ln
2
1
10
t = time after scissionx = E/Ek : ratio of the FF-KE relative to its final value Ek
s0 = charge-center distancevk = final velocity=[2{(M-m)Mm} ・ 1.44(Z-z)z/s0]1/2
s0
t
・ Certain fraction of prompt neutrons may be emitted before full acceleration of FF [V.P. Eismont,1965]
Z, Mz,m
Time Scale of Neutron Emission
)(10)/exp(2 21
3/1
sTBBU
An
n
Neutron emission time from an excited nucleus of excitation energy U and binding energy Bn [T. Ericson, Advances in Nuclear Physics 6, 425 (1960)]
If n-emission time > acceleration time t → NE after full acceleration < t → NE during acceleration
NEDA is possible, at least in the Standard-2 fission
● Define two parameters:
・ NEDA factor : fraction of neutrons emitted during acceleration ・ Timing factor TF : the ratio E/Ek at which neutrons are emitted
● Then find the best set of parameters that reproduce the experimental data.
Empirical Examination Parametric survey
0 1 2 30.1
0.2
0.3
0.4
Cm-245(n,f), En=thermal
Drapchinsky's Measurement Full acceleration 0.9N(TF=1)+0.1N(TF=0.7) 0.8N(TF=1)+0.2N(TF=0.7) 0.7N(TF=1)+0.3N(TF=0.7) 0.6N(TF=1)+0.4N(TF=0.7) Maslov's calc.
No.
of
Neu
tron
s (1
/MeV
)
Neutron Energy (MeV)
Results of parameter search : Best fit set of values that reproduce the experimental data for Cm-245(nth,f) is NEDA=0.3, TF=0.7
NEDA factor increases with excitation energy
Concluding Remarks1. Madland-Nix model, refined by considering 1) multimodal nature of the fission process 2) appropriate LDP with inclusion of the shell effect 3) asymmetry in ν for LF & HF 4) asymmetry in T for LF & HF provides a good representation of the spectra for major actinides in the first chance fission region where multimodal analyses have been done.
2. In order to further improve the accuracy and extend the predictive power of the method, it is necessary to have a better knowledge on the systematics of the multimodal parameters for more fissioning systems.
3. Mode detailed study should be undertaken in order to solve the pre-scission/scission neutrons or neutron emission during acceleration.
Justification of the Triangular Temperature Distribution with Sharp Cutoff
2* * 2
( ) ( *) *
( *) 2
( )
when ( *) constant
E aT dE aTdT
P T dT P E dE
P E aTdT
P T T
P E
・
The approximate validity ofthis model is based on aspecific relationship between the FF neutron separation energyand the width of the initial distribution of FF excitation energy. [Terrell; Kapoor et al.]
Mis-alined Valleys [W.J.S. Swiatecki & S. Bjornholm, Phys. Rep.4C, 325 (1972) ]
Hartree-Fock-Bogoliubov calc. [J.F. Bernard, M. Girod, D. Gogny, Comp. Phys. Comm. 63, 365 (1991)]
Mis-alined Fission and Fusion Valleys
Scission occurs some-where around here.
・ Fission and fusion valleys are separated by a ridge.・ The nucleus gets over the ridge somewhere from the fission to fusion valley.
T.-S.Fan et al., Nucl. Phys. A591,161 (1995)
Pre-scission shapes
S1
SL
S2
Average number of neutrons emitted from a fragment foreach mode
* */ /L H L HE E Partition of the TXE
1
0
( ) ( ) exp( / )ck T T d
1E-3 0.01 0.1 1 100
10000
20000
30000
40000
50000
HF
Rea
ctio
n C
ross
Sec
tion
(mb)
Neutron Energy (MeV)
Zr-101 (S2) Cs-141 (S2) Tc-107 (S1) Te-135 (S1)
LF
Am-241(n,f) , En= 2MeV
The inverse reaction cross sections for HFs are higher than those for LFs in the low energy region. (according to the optical model calc.)
Gauss-Legendrequadrature over ε and T
Gauss-Laguerre quadrature
LS-spectrum:2
2
( )
2
( )
0
1( , , ) ( )
2
( ) exp( / )
f
f
m
E E
f c c
f m E E
T
N E E dE T
k T T T dT
NEDA increases with excitation energy
General systematic relations :
ER = 0.2197(Z2/A1/3)- 114.37 TKEViola = 0.1189(Z2/A1/3) + 7.3 TXE = ER -TKE + Bn + En
= 0.1008(Z2/A1/3) - 121.67 +Bn + En
As Z2/A1/3 increases, TXE increases, which, in turn, means more NEDA effects for heavier actinides.
Y (A, Af , Ef*) = CS1[G(A, AS1, µS1s) + G(A, Af -AS1, µS1s)]
+ CS2[G(A, AS2, s) + G(A, Af -AS2, s)] + CSLG(A, Af /2, µSLs) Parameters : CS1 = 59.3 - 0.263 Nf - 0.017(Af -235.7) Ef
*, CS2 = 2.66(169.9 - Nf) + 0.19(Af - 232.6) Ef
*, CSL = 0.01exp(0.46 Ef
*), AS1 = 82.3 + 0.293Nf + 0.1Zf - 0.03 Ef
*, AS2 = 141.0 - 0.053 Ef
* , s = 5.7 - 0.24(149.9 - Nf ) + 0.12 Ef
*, µSL = 1.4, µS1 = 1.884 -0.0094Nf + 0.267exp[-(Nf -142.5)2] + 0.114exp[-|Nf -146.8|], C = 100/( CS1 + CS2 + CSL/2 )
Five-Gaussian Representation of Fragment Mass Distribution by Wang & Hu
80 90 100 110 120 130 140 150 1600.01
0.1
1
10
Superlong (0.3%)
F
issi
on
yie
ld (
%)
Primary fragment mass number
B C D E
Am-241(n,f) En=2MeV
Total
Standard-1 (21.0%)
Standard-2 (78.6%)
Decomposition of Fission Fragment Mass Distribution
Z=50 N=82N=50
54.6MeV29.1MeV31.5MeVTXE=
80 100 120 140 1600
2
4
6
8
Cm-245(n,f), En=thermal
TOTAL S1 S2 SL
Fis
sio
n Y
ield
(%
)
Mass Number (u)
Location of Delayed Neutron Precursors ( Heavy Fragment Region )
N=82
Z=50
139Te
138Te
137Te
136Te
135Te
n
n
n
n
If E*(En)>Bn + <η >then neutron emission occurs.
Exc. energy of the residual nucleus:E(i-1)
*(En) =E(i-1)*(En)ー(Bn + <η >)
Precursor
Precursor
Precursor
Non-precursor
Non-precursor
The non-precursor becomesa precursor.
The precursor becomes a non-precursor.
If E(k)*(En)>Bn +<η >then neutron emission occurs.
At high incident energy, more and moreprecursors are lost.
1.4s(β )
2.49s(β )
17.5s(β )
0.343s(β )
At higher energies, successive neutron emission from “would-be” precursors (primary FFs) leads to loss of actual precursors
T. Ohsawa et al., Proc. Int. Conf. on Nucl. Data for Sci. & Eng., Nice, France (2007)