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Transcript of | PAGE 1 2nd ERINDA Progress MeetingCEA | 10 AVRIL 2012 O. Serot, O. Litaize, D. Regnier...
| PAGE 12nd ERINDA Progress MeetingCEA | 10 AVRIL
2012
O. Serot, O. Litaize, D. Regnier
CEA-Cadarache, DEN/DER/SPRC/LEPh,
F-13108 Saint Paul lez Durance, France
CRPPrompt Fission Neutron
Spectra of Actinides
Introduction
Calculation procedure
Results on 252Cf(sf)
Results on 235U(nth,f)
Results on 239Pu(nth,f)
Conclusion and outlook
Plan
2
3
Calculation procedure
For each Fission Fragment:Determination of A, Z, KEDetermination of J, piDesexcitation of the Fission fragments
Calculation procedure
Sampling of the light fragment:
1 AL , ZL , KEL
Calculation procedure
4
Y(A,KE,Z)=Y(A) × Y(<KE>, KE) × Y(Z)
Pre Neutron Kinetic Energy
distribution
Nuclear charge distribution
Charge dispersion:
Most probable charge ZP taken from Walh evaluation and/or from systematic
1/12)2(σc 2Z
/c)Z(Z 2pe
cπ
1Y(Z)
Pre Neutron Mass
distribution
The mass and charge of the heavy fragment can be deduced:
AH=240-AL
ZH=94-ZL
Its kinetic energy (KEH) is deduced from momentum conservation laws
2AH , ZH , KEH
Calculation procedure
5
0 5 10 15 20 25 300.00
0.02
0.04
0.06
0.08
0.10
Pro
bab
ility
Spin
=9 h => <J>=10.8 =7 h => <J>=8.3
)/σ1/2)((J2
22
eσ2
1)(2JP(J)
L: spin cut-off of the Light fragment
H: spin cut-off of the Heavy fragment
Sampling of the spin parity of the light and heavy fragment:
3
(J)L
(J)H
Partitioning of the excitation energy between the two fragments
4
Calculation procedure
Total Kinetic Energy
(From Audi-Wapstra)
Total Excitation Energy
HL KEKETKE
)Z,B(A)Z,B(A)Z,B(AQ CNCNHHLL
The Total Excitation Energy (TXE) available at scission can be deduced:
At scission
After full acceleration of the
FF
The main part of the deformation at scission is assumed to be converted into intrinsic excitation energy during the FF acceleration phase (Ohsawa, INDS 251(1991))
Main assumptions
7
RotHL,
* E E TXE
CollSCGS
defSC
def*SC E βEβE E TXE
The FF are considered as a Fermi gas, the intrinsic excitation energy is therefore written as:
This intrinsic excitation energy will be used for the prompt neutron and gamma emissions
2HH
2LL
* Ta Ta E
Calculation procedure
0.5
1.0
1.5
2.0
RT=
TL/T
H
120/132
RTmin
RTmax
126/12678/174
Exemple on 252Cf(sf)
8
Calculation procedure
*γU
*e1
U
δW1 aa ** EU
W
a Asymptotic level density parameterEffective excitation energyShell corrections (Myers-Swiatecki, …)
Level density parameter calculated from Ignatyuk’s model:
Rotational Energy: ERot
J2
1)J(J E
2Rot
0.31β1 MR
5
2 2rigid J : quadrupole deformation
taken from Myers-Swiatecki
We have taken: with k=0.6rigidkJJ
9
Desexcitation of each fission fragment: A, Z, J, pi, E*, Erot5
Weisskopf Model (uncoupled)
Calculation procedure
• EL,H*=aTL,H
• Neutron evaporation spectrum:
• Neutron emission down to Sn(J) = Sn + Erot(J)
• Then Gamma emission simulated via level density + strength functions
5a
10
Desexcitation of each fission fragment: A, Z, J, pi, E*, Erot5
Hauser Feshbach formalism (coupled):
Level density used: Composite Gilbert Cameron ModelTn: from optical model potential of Koning Delaroche (Talys Code)T: obtained from the strength function formalism (Enhanced Generalized LOrentzian)
From PhD thesis D. Regnier
Take into account the conservation laws for the energy, spin and parity of the initial and final states
The emission probabilities of prompt neutron and prompt gamma are given by:
The competition between neutron and gamma can be accounted for
Calculation procedure
nnnnnn Sε U1,A Z,ρ εT)dεP(ε
ε UA, Z,ρ εT)dεP(ε
)/( nn
E*L,H=aTL,H +Erot L,H
5b
11
Calculation procedure
5 free parameters for fission:L, H, RTmin, RTmax, Krigid
Weisskopf Model (uncoupled)
Hauser Feshbach formalism (coupled):
Level density model: CGCM, CTM, HFB
Neutron tramsmission coefficient: from optical model (Koning-Delaroche, Jeukenne-Lejeune-Mahaut)
Gamma transmission: based on strength function (EGLO : Enhanced Generalized Lorentzian; SLO : Standard Lorentzian; HFB
12
Some Results on 252Cf(sf)
Comparison : Weisskopf / Hauser-Feshbach
With the Hauser-Fescbach model:Impact of the level density Impact of the optical model used for the Tn calculation
Results / 252Cf(sf)
Input data (pre-neutron mass and kinetic energy) from Varapai
13
0.01 0.1 1 100.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Rat
io M
axw
(T
=1.
4197
)
Energy (MeV)
Fifrelin (Varapai_Coupled_V3) Fifrelin (Varapai_NonCouple_V2) Mannhart (1987)
Hauser-Fescbach model (coupled)L=9.5H=9.0RTmin=0.3RTmax=1.5krigid=0.75(Varapai_coupled_V3)
Weisskopf model (uncoupled)L=8.5H=10.2RTmin=0.7RTmax=1.4krigid=0.6(Varapai_uncoupled_V2)
Comparison : Weisskopf / Hauser-Feshbach
Results / 252Cf(sf)
14
Coupled Hauser-Fescbach :Impact of the level density model used
Coupled Hauser-Fescbach :Impact of the optical model used for the Tn calculation
Results / 252Cf(sf)
From David Regnier Thesis
From David Regnier Thesis
15
Coupled Hauser Feshbach model
Impact of the level density model on PFNS
Impact of the optical model used for the Tn calculation on PFNS
Results / 252Cf(sf)
From David Regnier Thesis
16
Calculation performed for the 235U(nth,f)
Hauser-Fescbach model (coupled)L=7.2H=8.4RTmin=0.9RTmax=1.3krigid=0.9
Input data (pre-neutron mass and kinetic energy) from Hambsch
Results / 235U(nth,f)
17
0 1 2 3 4 5 6 7 8-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Pro
ba
Neutron Number
Fifrelin (Hambsch_Coupled_V2) Boldeman (1985)
Results / 235U(nth,f)
Probability of neutron emission
18
140 150 160 170 180 190 2000
1
2
3
4
5
6
Ave
rag
e N
eutr
on
Mu
ltip
licit
y
Total Kinetic Energy (MeV)
Fifrelin Heavy (Hambsch_Couple_V2) Fifrelin Light (Hambsch_Couple_V2) Fifrelin Total (Hambsch_Couple_V2)
140 150 160 170 180 190 2000
1
2
3
4
5
6
Ave
rag
e N
eutr
on
Mu
ltip
licit
yTotal Kinetic Energy (MeV)
Fifrelin Total (Hambsch_Couple_V2) Nishio Maslin
Results / 235U(nth,f)
Average neutron multiplicity as a function of TKE
Slope=10.24 MeV/n Slope_Nishio=18.5 MeV/n
19
80 90 100 110 120 130 140 150 1600.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Ave
rag
e N
eutr
on
Mu
ltip
licit
y
Pre Neutron Mass
Fifrelin (Hambsch_Couple_V2) Maslin (1967) Nishio (1998) Boldeman (1971) Batenkov
Results / 235U(nth,f)
Average neutron multiplicity as a function of pre-neutron mass
20
Results / 235U(nth,f)
Prompt Fission Neutron Spectrum
0.01 0.1 1 100.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
Rat
io M
axw
(T
=1.
3409
)
Energy (MeV)
Fifrelin (Hambsch_couple_V2) Kornilov Lajtay/0.998 Starostov Trufanov
21
Calculation performed for the 239Pu(nth,f)Presented at Workshop GAMMA2, Oct. 2013
Standard IStandard IISuper LongRT Laws for each mode
Test the influence of the fission modes on the prompt neutron and gamma characteristics: case of the thermal neutron induced fission of 239Pu
Describe for each fission mode the n and characteristics
Results / 239Pu(nth,f)
2222
St. I St. II SL
<AH> 134.97 140.96 120.0
M 3.73 6.48 15.8
<TKE> 188.63 173.65 148.35
TKE 7.71 8.51 9.93
W (%) 22.83 76.60 0.57120 130 140 150 160
1E-5
1E-4
1E-3
0.01
0.1
Yie
ld
Pre Neutron Mass
Dematté (1997) Standard I Standard II Super Long Total
Main characteristics of the fission modes
Data taken from Dematté: PhD thesis, University of Gent, 1997(Standard III fission mode is neglected)
Very similar data were obtained by Schilleebeckx)
Results / 239Pu(nth,f)
23
120 124 128 132 136 140 144 148 152 156 160 1648
9
10
11
12
13
Dematte (1997) Schillebeckx (1992) Asghar (1978) SigmaTKE
TK
E [
MeV
]
Mass
120 124 128 132 136 140 144 148 152 156 160 164145
150
155
160
165
170
175
180
185
190
195
200
TKE Dematte (1997) Tsuchiya (2000) Surin (1971) Schillebeeckx (1992) Wagemans (1984)
TK
E [
MeV
]
Mass
23
Average Total Kinetic Energy
Width of the Total Kinetic Energy
Results / 239Pu(nth,f)
24
120 124 128 132 136 140 144 148 152 156 160140
150
160
170
180
190
200
210
220
TK
E [
MeV
]0.000
6.000E-04
0.001200
0.001800
0.002400
0.003000
0.003600
0.004200
0.004800
0.005400
0.006000
120 124 128 132 136 140 144 148 152 156 160140
150
160
170
180
190
200
210
2200.000
3.000E-04
6.000E-04
9.000E-04
0.001200
0.001500
0.001800
0.002100
0.002400
0.002700
0.003000
120 124 128 132 136 140 144 148 152 156 160100110120130140150160170180190200210220
Mass
TK
E [
MeV
]
0.000
1.010E-04
2.020E-04
3.030E-04
4.040E-04
5.050E-04
6.060E-04
7.070E-04
8.080E-04
9.090E-04
0.001010
120 124 128 132 136 140 144 148 152 156 160140
150
160
170
180
190
200
210
220
Mass
0.000
2.370E-04
4.740E-04
7.110E-04
9.480E-04
0.001185
0.001422
0.001659
0.001896
0.002133
0.002370
24
Standard I Standard II
Super Long Total
Results / 239Pu(nth,f)
25
Standard I
Standard II
Super Long
120 / 120
Standard II is governed by the deformed neutron shell (N=88) + spherical proton
shell (Z=50)
Standard I is governed by the spherical neutron shell (N=82) + spherical proton
shell (Z=50)
108 / 132
120 130 140 150 160
0.6
0.8
1.0
1.2
1.4
RT=
TL/
TH
Mass
120 130 140 150 160
0.6
0.8
1.0
1.2
1.4
RT=
TL/
TH
Mass
120 130 140 150 1600.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
RT=
TL/
TH
Mass
102 / 138
Super Long is a strongly deformed mode
Temperature Ratio Law: RT = TL/TH
Results / 239Pu(nth,f)
26
Prompt Neutron Multiplicity
80 90 100 110 120 130 140 150 1600.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Pro
mp
t N
eutr
on
Mu
ltip
licit
y
Pre Neutron Mass
Total Standard I Standard II Super Long
L H Tot
St. I 1.56 0.43 1.99
St. II 1.71 1.48 3.19
SL 2.67 3.72 6.39
Total 1.68 1.25 2.93
Experimental and evaluated data
Tot
Boldeman 2.879 ± 0.060
Holden 2.881 ± 0.009
JEFF- 3.1.1 2.87
FIFRELIN Results
Results / 239Pu(nth,f)
27
80 90 100 110 120 130 140 150 1600.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Pro
mp
t N
eutr
on
Mu
ltip
licit
y
Pre Neutron Mass
FIFRELIN (Total) Batenkov (2004) Apalin (1965) Tsuchiya (2000) Nishio (1995)
Reasonable agreement between FIFRELIN calculation and the experimental data can be obtained
Best agreement is achieved with data from Batenkov (2004)
In the [115-120] mass region, the observed high experimental multiplicity could be reproduced by increasing the contribution of the Super Long fission mode
In the very asymmetric mass region, the St. III fission mode seen by Schillebeeckx could be interesting to add
Prompt Neutron Multiplicity
Results / 239Pu(nth,f)
28
150 160 170 180 190 2000
1
2
3
4
5
6
7
8
Linear Regression for Sta1_NuTOTst1:Y = A + B * X
Parameter Value Error------------------------------------------------------------A 24.9192 0.09482B -0.1219 5.20615E-4------------------------------------------------------------
Linear Regression for Sta2_NuTOTst2:Y = A + B * X
Parameter Value Error------------------------------------------------------------A 21.31452 0.08813B -0.1045 5.0009E-4------------------------------------------------------------
P
TKE [MeV]
TOT_St1 TOT_St2
Prompt Neutron Multiplicity
Results / 239Pu(nth,f)
Different slopes obtained for each fission modes
150 160 170 180 190 2000
1
2
3
4
5
6
7
P
TKE [MeV]
Heavy_St2 Light_St2 TOT_St2
Different slopes obtained for Light and Heavy fragment
29
Prompt Fission Neutron Spectrum
0.01 0.1 1-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Sp
ectr
um
[M
eV-1]
Outgoing Neutron Energy [MeV]
Standard I Standard II Super Long
5 100.001
0.01
0.1
1
Standard I Standard II Super Long
Sp
ectr
um
[M
eV-1]
Outgoing Neutron Energy [MeV]
Rather similar average energy for both St. I and St. II modes
But, differences can be observed in the low and high energy part of the spectrum
Results / 239Pu(nth,f)
30
Results / 239Pu(nth,f)
Prompt Neutron Spectrum: Ratio to Maxwellian with T=1.32
0.01 0.1 1 100.4
0.6
0.8
1.0
1.2
1.4
Outgoing Neutron Energy [MeV]
FIFRELIN (Total) Nefedov 85 Lajtai 1985 Starostov 1985 Bojcov 1983
0.01 0.1 1 100.4
0.6
0.8
1.0
1.2
1.4
Standard I Standard II Super Long
Rat
io t
o M
axw
ellia
n (
T=
1.32
)
Outgoing Neutron Energy [MeV]
<En>lab [MeV]
JEFF-3.1.2
St. I 2.19
St. II 2.13
SL 2.43
Total 2.14 2.11
31
0.01 0.1 1 100.4
0.6
0.8
1.0
1.2
1.4
Outgoing Neutron Energy [MeV]
FIFRELIN (with Fission modes) FIFRELIN (without Fission mode) Nefedov 85 Lajtai 1985 Starostov 1985 Bojcov 1983
Prompt Neutron Spectrum: Ratio to Maxwellian with T=1.32
Comparison with / without Fission modes
Results / 239Pu(nth,f)
32
80 90 100 110 120 130 140 150 160
1
2
3
4
5
6
7
8
9
Ave
rag
e G
amm
a M
ult
iplic
ity
Pre Neutron Mass
Standard I Standard II Super Long
80 90 100 110 120 130 140 150 1600
1
2
3
4
5
6
7
8
9
Ave
rag
e G
amm
a M
ult
iplic
ity
Pre Neutron Mass
Fifrelin (=[0-infinity]) Fifrelin (=[0.140-infinity]) Pleasonton (1973)
FIFRELIN with =[0 – infinity]
Prompt Gamma Multiplicity
Results / 239Pu(nth,f)
FIFRELIN with =[0 – infinity]
0.1 1 10
0
2
4
6
8
10
12
Sp
ectr
um
[/f
issi
on
/ M
eV]
Gamma Energy [MeV]
Standard I Standard II Super Long
0 1 2 3 4 5 6 7 81E-4
1E-3
0.01
0.1
1
10
Gam
ma
Sp
ectr
um
[ /f
issi
on
/ M
eV]
Gamma Energy [MeV]
Verbinski 1973 FIFRELIN
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40
1
2
3
4
5
6
7
8
9
10
11
12
Gam
ma
Sp
ectr
um
[ /f
issi
on
/ M
eV]
Gamma Energy [MeV]
Verbinski 1973 FIFRELIN
Prompt Gamma Spectrum
Structures at low energy are visible for both St. I and St. II modesFails to reproduce the high energy part (above 5 MeV)
Results / 239Pu(nth,f)
34
[MeV] T [ns] M/f Etot [MeV] [MeV]
St. I 140 keV-inf. 10 6.80 6.63 0.98
St. II 140 keV-inf. 10 7.30 6.86 0.94
SL 140 keV-inf. 10 7.39 7.90 1.07
Total 140 keV-inf. 10 7.19 6.81 0.95
Experimental Compilation from David Regnier
FIFRELIN Calculation
Excellent agreement with Verbinski’s data
Results / 239Pu(nth,f)
35
Q TKEpre
TKEpost
TXETotal
E*Light
E*Heavy
(Erot)Light
(Erot)Heavy
TNE TGE
St. I 203.3 188.3 186.5 21.53 12.85 5.92 2.41 0.35 7.017 7.311
St. II 196.2 173.5 171.1 29.22 13.40 11.94 2.71 1.16 6.806 7.424
SL 201.1 148.3 144.6 59.3 22.17 33.53 2.59 1.01 7.949 8.341
Total 197.85 176.74 174.46 27.64 13.32 10.69 2.64 0.97 6.86 7.40
JEFF 3.1.1
Total energy less the energy of neutrinos
199.073 +/- 1.090 MeV
Kinetic energy of fragments(post-neutron)
175.78 +/- 0.40 MeV
Total energy released by the emission of "prompt" gamma rays
6.75 +/- 0.47 MeV
Total energy released by the emission of "prompt" neutron
6.06 +/- 0.10 MeV
Average fragment remaining energy due to metastableStILight FF = 0.04626 Heavy FF= 0.5323
StIILight FF = 0.1808Heavy FF= 0.2812
SLLight FF = 0.08083Heavy FF= 0.3699
Results / 239Pu(nth,f)
36
Conclusion
Many new developments have been done in the Monte Carlo code FIFRELIN (in the frame of David REGNIER’s thesis)
The prompts neutron and gamma spectra obtained are in reasonable with experiments for: 252Cf(sf), 235U(nth,f) and 239Pu(nth,f)
The Hauser-Feshbach formalism used for the desexcitation of the fission fragments is the better model to get both prompt neutron and gamma spectra
It is recommended to use the CGCM for the level densitythe KD optical model for the Tn calculationthe EGLO for the strength function
It seems promising to use as input data (pre neutron mass and kinetic energy) the one deduced from the fission mode analysis
38
Hauser-Fescbach model (coupled)L=9.5H=9.0RTmin=0.3RTmax=1.5krigid=0.75(Varapai_V3)
0.01 0.1 1 10
1
Rat
io M
axw
(T
=1.
4197
)
Energy (MeV)
Mannhart (1987) Fifrelin (Varapai_Coupled_V3) Fifrelin (Varapai_couple_V1)
Hauser-Fescbach model (coupled)L=8.5H=10.2RTmin=0.7RTmax=1.4krigid=0.6(Varapai_V1)