1 iaea / crp prompt neutron / 13-16th dec. 2011 olivier serot 1, olivier litaize 1, cristian...

1IAEA / CRP Prompt Neutron / 13-16th Dec. 2011

Olivier SEROT 1, Olivier LITAIZE 1 ,Cristian MANAILESCU 1, 2,

David REGNIER 1

1CEA Cadarache, Physics Studies Laboratory F-13108 Saint Paul Lez Durance

France

2University of Bucarest, Faculty of Physics, Bucharest-Magurele,

Romania

Investigation of the prompt neutron characteristics from a Monte Carlo

simulation of the fission fragment de-excitation


Introduction

Initial input data needed

Calculation procedure

Results on 252Cf(sf)

Results on 239Pu(n,f) and 240Pu(sf)

Conclusion and outlook

Plan


Context•Prompt neutron and prompt gamma spectra and their multiplicities are very important data for nuclear applications

•The evaluation files (JEFF,…) are not satisfactory:Lack of data, Same data for various fissioning nuclei, Dependence with the incident neutron not always taken into accountPrompt gamma spectra not enough accurate and strongly needed by nuclear energy …)

Our aim •Development of a Monte Carlo code able to simulate statistical decay of the fission fragments:

Various physical quantities can be investigated: (A,TKE), P(), E(A), N(,A)….

•Test models related to the emission process

Introduction



Example from Varapai’s thesis (2006) / Experiment performed on 252Cf(sf) at IRMM (Belgium)

Ionisation chamber

NE213

Y(A,KE,Z)=Y(A) × Y(<KE>, KE) × Y(Z)

Mass and KE distributions

Mass

Yield

<KE>

KE

Nuclear charge

distribution

Initial data needed for the code


Nuclear charge distribution

Most probable charge ZP

taken from Walh evaluation and/or from systematic

Charge dispersion:

z assumed independent of the mass

1/12)2(σc 2Z

/c)Z(Z 2pe

cπ

1Y(Z)

Wahl, Phys. Rev. 126 (1962) 1112

Sampling of a fission fragment (A, Z) with a kinetic energy KE

Y(A,KE,Z)=Y(A) × Y(<KE>, KE) × Y(Z)

These are the initial data

needed for the code

Mass and KE distributions: taken from Varapai’s thesis work



Sampling of the light fragment: 1

The mass and charge of the heavy fragment can be

deduced:AH=252-AL

ZH=98-ZL

Its kinetic energy (KEH) is sampled on the experimental kinetic energy distribution

2


AL , ZL , KEL

AH , ZH , KEH

Total Kinetic Energy

(From Audi-Wapstra)

Total Excitation Energy

HL KEKETKE

*H

*L EETKEBnEnQTXE

)Z,B(A)Z,B(A)Z,B(AQ CNCNHHLL

The Total Excitation Energy (TXE) available at scission can be deduced:3


At scission:

RotHL,

* E E TXE

CollSCGS

defSC

def*SC E βEβE E TXE

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))

The FF are considered as a Fermi gas, the intrinsic excitation energy can therefore be written as:

This intrinsic excitation energy will be used for the prompt neutron and gamma emissions

2HH

2LL

* Ta Ta E

Partitioning of the excitation energy between the two fragments4



*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:

RotH

RotL

2HH

2LL

* E- E- TXE Ta Ta E

Nuclear Temperature: RT=TL/TH

RT=1

RT=1.25

0.5

1.0

1.5

2.0

RT=

TL/T

H

120 / 132

126 / 126

78 / 174

RT=RT(A)


Rotational Energy: ERot

0.31β1 MR5

2 2rigid J

22Irrot βMR

8π

9J

: quadrupole deformation taken from Myers-Swiatecki

J : Moment of Inertia :Three

available options in FIFRELIN

Rigid body

Irrotational flow

J2

1)J(J E

2Rot

(Approximation of

the rotational energy)


Microscopic calculations from CEA-DAM (AMEDEE database) (on going)

Data taken from:http://www-phynu.cea.fr/science_en_ligne/

carte_potentiels_microscopiques/carte_potentiel_nucleaire.htm


J: Angular momentum:

Two available options

)/B1/2)((J 22

1)e(2JP(J)

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

Yie

ld (

arbi

trar

y un

it)

Spin

Light Heavy

(Vandenbosch – Huizenga)

7.2B

6B

Heavy

Light

(Wilhelmy et al., Phys. Rev. C5, 2041 (1972))


)/σ1/2)((J 22

1)e(2JP(J)

a~aU

A 01389.0 5/32 : spin cut-off

U: effective excitation energy corrected for pairing: Δ*EU


Example: Initial conditions in the plane (E*,J) obtained for the light and heavy primary

fragments 252Cf(sf)


Heavy Light

(J=0.5Jrigid )


Weisskopf spectrum

Z)1,a(A

SZ)(A,E)EZ,1,T(A n

**

2ε/T2

eT

εφ(ε)

where T is the temperature of the residual nucleus:

Neutron evaporation


5

Energy limit for the neutron emission:

Rotnn

* ES(J)SE

JES(J)SE Rotnnlim

E*

J

Yrastn ESE *

Yrastn ESE *


Prompt gamma emission


6

• Implementation of gamma cascade simulation methods which can be applied to a vast domain of isotopes

• Implementation of several nuclear models (level density, strength function, spin cutoff, density parameter...)

• First tests on single isotopes providing deexcitation spectra and multiplicities

Preliminary spectra for 252Cf spontaneous fission

From D. Regnier, Workshop Novi Sad Nov. 2011


RTLH E*lim inertia <>L <>H <>tot

1.00 Sn - 1.82 2.44 4.26

1.25 Sn - 2.28 1.93 4.21

Vorobyev et al. (2004) 2.05 1.70 3.76

With RT=1 and Elim=Sn (no rotational energy) ( ):

Saw-tooth not reproduced and more neutrons are emitted from heavy fragment (in conflict with experiment)

(A)

Results 252Cf(sf)

With RT=1.25 and Elim=Sn (no rotational energy) ( ):

Ratio L/H in better agreement with experiment



1.25 Sn+Ero

t

J=JRigid

2.181.83 4.01

1.25 Sn+Ero

t

J=JIrrot 1.06 0.46 1.52

1.25 Sn+Ero

t

J=0.5*JRigid 2.07 1.71 3.77

Vorobyev et al. (2004) 2.05 1.70 3.76Strong impact of the rotational energy:

With rigid model ( ): overestimation of the total neutron multiplicity

With fluid model ( ): completely wrong!

With J=0.5 JRigid ( ):more satisfactory

(A)

Results 252Cf(sf)



RT(A) Sn+Erot J=0.5JRigid 2.06 1.70 3.76

Vorobyev et al. (2004) 2.05 1.70 3.76

With a temperature ratio depending on A (RT=RT(A)):

Reasonable agreement with the experimental data except in the [155-170] mass region

Average multiplicities are very well reproduced

(A)

Results 252Cf(sf)


Good agreement with Budtz-Jorgensen data except in the very high TKE energy (could be due to scission neutron (see Kornilov 2004))

Slope:

In agreement with Budtz (88) and Nifenecker (73)

Strong differences are observed between Light and heavy fragments

MeV/n13TKE / υ 1

(TKE)

Results 252Cf(sf)


Results 252Cf(sf)

From O. Litaize, Novi Sad, Nov. 2011)


(A)

Good agreement with Budtz data, except in [125-140] mass region

Discrepancy also observed by Kornilov (2007) and Lemaire (2005)

Results 252Cf(sf)


Neutron Spectrum in the Laboratory

Could be improved by accounting for the Energy dependence of the inverse process of compound

nucleus formation in the Weisskopf spectrum (going on)

Nice agreement between 0.5 and 7 MeV

(within 5%)<E> = 2.13 MeV (Reference)<E> = 2.14 MeV (This work)

Results 252Cf(sf)


Heavy

0 1 2 3 4 5 6 7 80.0

0.1

0.2

0.3

0.4

0.5

P(

)

Vorobyev (2004) This work

Light Total

P

Good agreement with Vorobyev’s

data

Results 252Cf(sf)


< E > = 7.06 ± 0.35 (Pleasonton-2001)

< E > = 6.7 ± 0.4 (Nardi-1973)

< E > = 6.84 ± 0.3 (Verbinski-1973)

< E > = 7.08 MeV (Fréhaut-89)

< E > = 6.77 MeV (This work)

E(A)

Results 252Cf(sf)


Talou et al., PHYSICAL REVIEW C 83, 064612 (2011)C. Manailescu et al., Nuclear Physics A867 (2011) 12-40

78 / 162

120 / 120

120 125 130 135 140 145 150 155 160 1650.4

0.6

0.8

1.0

1.2

1.4

1.6

RT

= T

L/T

H

Heavy Mass

Temperature ratio law

Results 239Pu(n,f)

Fifrelin

108 / 132


239Pu(n,f))

80 90 100 110 120 130 140 150 1602345678

[M

eV]

Mass Number

80 90 100 110 120 130 140 150 16040

60

80

100

120

<K

E>

[M

eV]

80 90 100 110 120 130 140 150 1600

2

4

6

8

Yie

ld [

%]

Initial Input Data(Wagemans)

Results 239Pu(n,f)

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

Fifrelin Batenkov 2004 Tsuchiya 2000 Nishio 1995 Apalin 1965 Walh

Pro

mp

t N

eutr

on

Mu

ltip

licit

y

Mass Number


150 160 170 180 190 200 2100

1

2

3

4

5

Pro

mp

t N

eutr

on

Mu

ltip

licit

y

Total Kinetic Energy [MeV]

Tsuchiya 2000 Fifrelin

239Pu(n,f))

80 90 100 110 120 130 140 150 1602345678

[M

eV]

Mass Number

80 90 100 110 120 130 140 150 16040

60

80

100

120

<K

E>

[M

eV]

80 90 100 110 120 130 140 150 1600

2

4

6

8

Yie

ld [

%]


Results 239Pu(n,f)


239Pu(n,f))

80 90 100 110 120 130 140 150 1602345678

[M

eV]

Mass Number

80 90 100 110 120 130 140 150 16040

60

80

100

120

<K

E>

[M

eV]

80 90 100 110 120 130 140 150 1600

2

4

6

8

Yie

ld [

%]


Results 239Pu(n,f)

0 1 2 3 4 5 6 7 8 9 100.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Sp

ectr

um

Neutron energy [MeV]

Fifrelin Starostov 1983 JEFF-3.1.1


80 100 120 140 1600

2

4

6

8

10

Yie

lds

[%]

Post neutron emission Mass Number

MC Bail 2009 Schmitt 84

239Pu(n,f))

Mass yield (post neutron):Comparaison Fifrelin /

Measurements performed at ILL on Lohengrin mass sepctrometer)

Results 239Pu(n,f)


JEFF 3.1.1 Fifrelin

Total energy less the energy of neutrinos

199.073 +/- 1.090 MeV

197.975 MeV

Kinetic energy of fragments(post-neutron)

175.78 +/- 0.40 MeV 175.05 MeV

Total energy released by the emission of "prompt" gamma rays

6.75 +/- 0.47 MeV 6.69 MeV

Total energy released by the emission of "prompt" neutron

6.06 +/- 0.10 MeV 6.00 MeV

Average prompt neutron multiplicity

2.87 n/f 2.92 n/f

Mean neutron energy in Lab 2.11 MeV 2.05 MeV

Results 239Pu(n,f)

239Pu(n,f))


Results Comparison 239Pu(n,f) / 240Pu(sf)

0.1 1 101E-4

1E-3

0.01

0.1

1

Sp

ectr

um

[/M

eV]

Neutron energy [MeV]

239Pu(n,f)

240Pu(sf)

80 90 100 110 120 130 140 150 1600.0

0.5

1.0

1.5

2.0

2.5

3.0

239Pu(n,f)

240Pu(sf)

Neu

tro

n M

ult

iplic

ity

Mass Number

• 239Pu(n,f): Wagemans et al. • 240Pu(sf): Dematte et al.

Initial Data:

Same fissioning nucleus, but with different excitation energy


A Monte Carlo code has been recently developed in order to investigate prompt fission neutrons and gamma properties.

The available excitation energy of the fission fragments used for neutrons and gamma emission is calculated by accounting for their rotational energies.

The fission fragment evaporation process is simulated using two main assumptions:

(i) the partitioning of the excitation energy between primary fragments is performed by adopting a mass dependent temperature ratio law which has been established from physical grounds;

(ii) a spin dependent excitation energy limit is considered for neutron emission.

The main features of the prompt neutrons (energy spectrum, average neutron multiplicity, distribution of the prompt neutron multiplicity …) as well as the excitation energy available for prompt-gamma emission are nicely reproduced.

Conclusion


We plan to upgrade the code by:

Accounting for realistic fission fragment moment of inertia (going on by using AMEDEE database)

Accounting for the inverse process of compound nucleus formation involved in the Weisskopf spectrum (going on)

Temperature ratio law: depending on the mass and the fission modes (Standard I and II)

Possible additional neutron source (scission neutron)

The treatment of the gamma emission in order to get the prompt gamma spectrum (going on)

Outlook


S. Lemaire et al., [Phys. Rev. C, 72(2), 024601 (2005)];

hypothesis H1: RT=TL/TH=1: doesn’t work hypothesis H2: partitioning of the excitation energy between the two fragments from experimental data: <>(A), <>(A) and <E>(A): less predictive

P. Talou et al., [CNR 2009]RT values for each fission mode

P. Talou et al., Phys. Rev. C83, 064612 (2011)

Randrup and Vogt, [Phys. Rev. C80, 044611, 2009 + Phys. Rev. C80, 024601, (2009)]

Similar Monte Carlo codes already exist:

Annexe

34IAEA / CRP Prompt Neutron / 13-16th Dec. 2011 34

80 90 100 110 120 130 140 150 160 170120

130

140

150

160

170

180

190

200

210

220

230

24080 90 100 110 120 130 140 150 160 170

120

130

140

150

160

170

180

190

200

210

220

230

240

Qmax <TKE>

mass number A

TK

E (

MeV

)

0.1

1

2

3

4

5

6

7

8

(A,TKE)

Annexe


Annexe


80 90 100 110 120 130 140 150 1600.0

0.5

1.0

1.5

2.0

2.5

Pro

mp

t N

eutr

on

Mu

ltip

licit

y

Mass Number80 85 90 95 100 105 110 115 120

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

RT=

TL/

TH

Mass Number

240Pu(sf)

P=2.10 (black)

P=2.07 (red)

P=2.13 (green)

Influence of the RT law on neutron multiplicityExemple: 240Pu(sf)

Annexe

1 iaea / crp prompt neutron / 13-16th dec. 2011 olivier serot 1, olivier litaize 1, cristian...

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