o. serot, o. litaize, d. regnier cea-cadarache, den/der/sprc/leph,

| 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


For each Fission Fragment:Determination of A, Z, KEDetermination of J, piDesexcitation of the Fission fragments


Sampling of the light fragment:

1 AL , ZL , KEL


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


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


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


0.5

1.0

1.5

2.0

RT=

TL/T

H

120/132

RTmin

RTmax

126/12678/174

Exemple on 252Cf(sf)

8


*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)


• 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


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


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


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)


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)


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


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


Average neutron multiplicity as a function of pre-neutron mass

20


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)


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


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


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


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


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



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



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


Sp

ectr

um

[M

eV-1]


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


30


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


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


Rat

io t

o M

axw

ellia

n (

T=

1.32

)


<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


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


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


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


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]


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)


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


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


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

37

Annexe

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)

39

Experimental data baseon prompt gamma rays

40

Influence:Spin cut-off on P(nu)

Model Weisskopf238U(n,f)

(Same trend observed with HF coupled)

From O. Litaize et al., ND2013

o. serot, o. litaize, d. regnier cea-cadarache, den/der/sprc/leph,

Documents

intrinsic excitation

level density model

neutron emission

rotational energy

ignatyuks model

zlits kinetic energy

prompt gamma

optical model koningdelaroche