Study of the (n,γf) process on Pu...Esther Leal Cidoncha, WONDER-2018, 8-12 October, 2018. TWO-STEP...

Study of the (n,γf) process on 239Pu

Esther LEAL CIDONCHA, Gilles NOGUERE, Olivier BOULAND and Olivier SEROTCEA/DEN/CAD/DER/SPRC/LEPh

WONDER-2018 8-12 October 2018

CEA/Cadarache (France)

Esther Leal Cidoncha, WONDER-2018, 8-12 October, 2018.

INTRODUCTION: REACTION CHANNELS

1/16

• The compound nucleus may decay by:

• Neutron emission (n,nʼ)

• γ-ray emission (n,γ)

• Fission (n,f)

ChannelReaction

Slow neutron-induced reactions


INTRODUCTION: REACTION CHANNELS

1/16

Slow neutron-induced reactions• The compound nucleus may decay by:

• Neutron emission (n,nʼ)

• γ-ray emission (n,γ)

• Fission (n,f)

• γ-ray emission + Fission (n,γf)

σn

σf

σγ

ChannelReaction


INTRODUCTION: FISSION CHANNELS

2/16

Slow neutron-induced reactions

J.E. Lynn, P. Talou and O. Bouland, PRC 97, 064601 (2018)

• If a γ is emitted before fission then the available excitation energy to the FF is lower and less prompt neutrons are emitted => anticorrelation between prompt neutron emission and γ multiplicities.

• Double-humped fission barrier:


INTRODUCTION: FISSION CHANNELS

3/16

Slow neutron-induced reactions• Double-humped fission barrier: • If a γ is emitted before fission

then the available excitation energy to the FF is lower and less prompt neutrons are emitted => anticorrelation between prompt neutron emission and γ multiplicities.

10 20 30 40 50E (eV)

0,68

0,7

0,72

0,74

0,76

0,78

! p

Gwin v1 (1984)Gwin v2 (1984)Frehaut (1973)

0,01 0,1 1 100,75

0,76

0,77



NEUTRON-INDUCED FISSION IN 239PU

4/16

• The 239Pu(n,f) cross section can be described by:

σf(En) = σ(En)(n,f) + σ(En)(n,γf)

• Partial fission width:

σ γ(En) ·Γγf

Γγ

?

Γγ f (E*, J π ) = dεγ ρ(E

* − εγ , J fπ (− )Xl ) × Γγ Xl (εγ )Pf (E

* − εγ , J fπ (− )Xl )

0

E*

∫J f = J − l

J + l

∑Xl∑

multipolarity(E1,M1)

fissionprobability

nuclearlevel

density

E* = Einc + Bn π (M1)-π (E1)

Residual excitation energy



NEUTRON-INDUCED FISSION IN 239PU

5/16

• Direct fission channels

• Two-step fission channels

Jπ = 0+

Jπ = 1+

Γ 1f (0+)

Γ 2f (0+)

Γ f (1+)

Jπ = 0+

Jπ = 1+

Γ γf (0+)

Γ γf (1+)

Resonances 0+

Dominate:

Resonances 1+

• The 239Pu(n,f) cross section can be described by:

σf(En) = σ(En)(n,f) + σ(En)(n,γf)

σ γ(En) ·Γγf

Γγ

?

• Partial fission widths in the R-Matrix Theory:


CONRAD RESONANCE ANALYSIS OF 239PU DATA

6/16

[2] J.E. Lynn, P. Talou and O. Bouland, PRC 97, 064601 (2018)

• New resonance analysis with the CONRAD* (COde for Nuclear Reaction Analysis and Dated Assimilation) R-Matrix code including:

• Two-step fission contribution from Trochon [1] vs. Bouland [2] => Γ γf

• The evaluated file of the fission cross section considers the Jπ=1+ resonances as being produced only through direct fission reactions.

• Direct reactions contribution from the evaluations => Γ γ , Γ f and Γ n

• Prompt neutron multiplicity (νp) reproduced including the two-step fission process.

[1] Trochon, Proc. 3rd Symp. Physics and Chemistry of Fission, Rochester, New York, Aug. 13-17 (1973)* Developed at CEA/Cadarache

• Multiple analysis:• Total cross section • Capture cross section • Fission cross section • Total neutron multiplicity• Prompt neutron multiplicity (Frehaut and Gwin experimental data)

• Resonance parameters:

• Free parameters:• ν nγf

• ν0 and ν1

• Normalization of experimental data


TWO-STEP FISSION CONTRIBUTION (Γ γf)

7/16

• Calculation of Γ γf from Trochon [1]:

• Calculation of Γ γf from Bouland [2]:

• Double-humped fission barrier.

• A low-lying M1 resonance known as the scissors mode has been also taken into account.

[2] J.E. Lynn, P. Talou and O. Bouland, PRC 97, 064601 (2018)[1] Trochon, Proc. 3rd Symp. Physics and Chemistry of Fission, Rochester, New York, Aug. 13-17 (1973)

• Single-humped fission barrier.

• Only E1 transitions are considered.

• E1 transitions are considered.


EXPERIMENTAL DATA (νp)

8/16

• Frehaut and Gwin experimental data:

10 20 30 40 50E (eV)

0,68

0,7

0,72

0,74

0,76

0,78

! p

Gwin v1 (1984)Gwin v2 (1984)Frehaut (1973)

0,01 0,1 1 100,75

0,76

0,77


EXPERIMENTAL DATA (νp)

9/16

• Problem: how to threat Frehaut data (histogram/pointwise) better description with pointwise.

0 10 20 30 40 50E (eV)

0,68

0,7

0,72

0,74

0,76

0,78

! p

Frehaut pointwise Frehaut histogram


CONRAD RESULTS OF νp UP TO 50 EV

10/16

• Comparison of results obtained threating Frehaut data as histogram/pointwise.

with Γ γf from Trochon

0,68

0,7

0,72

0,74

0,76

0,78

! p

0 10 20 30 40 50E (eV)

-4-2024

Res

idua

l

Frehaut histogrampointwise

0,68

0,7

0,72

0,74

0,76

0,78

! p

0 10 20 30 40 50E (eV)

-4-2024

Res

idua

l

histogrampointwise

with Γ γf from Bouland

• CONRAD results from the fit below 50 eV of Frehaut data:



11/16

0,68

0,7

0,72

0,74

0,76

0,78

! p

0 10 20 30 40 50E (eV)

-4-202

Res

idua

l

Frehaut with Γ γf from Boulandwith Γ γf from Trochon

< ν 0 > = 2.891 ± 0.002

< ν 1 > = 2.867 ± 0.002

< ν nγf > = 2.61 ± 0.02

< ν 0 > = 2.888 ± 0.002

< ν 1 > = 2.866 ± 0.002

< ν nγf > = 2.43 ± 0.03

N Frehaut = 0.9963 ± 0.0007

N Frehaut = 0.9965 ± 0.0007

• Output parameters:

• CONRAD results from the fit below 50 eV of Frehaut data:



12/16

• CONRAD results from the fit below 50 eV of Gwin data:

0,750,7520,7540,7560,7580,76

0,7620,7640,7660,7680,77

! p

10 15 20 25 30 35 40E (eV)

-4-2024

Res

idua

l

0,7580,7590,76

0,7610,7620,7630,7640,7650,7660,767

! p

0,01 0,1 1E (eV)

-4-2024

Res

idua

l

Gwin with Γ γf from Boulandwith Γ γf from Trochon


RESULTS OF νp UP TO 50 EV

13/16

• Final results up to 50 eV:

Frehaut (normalized)with Γ γf from Boulandwith Γ γf from Trochon

J=1

J=1J=1

J=1J=1

J=1

J=1

J=1


RESULTS OF νp UP TO 50 EV

14/16

• The spin contribution can reproduce the data at low energies.• The ν nγf contribution reproduces the dips of the νp up to 50 eV.

J=1

J=1 J=1


J=1


DISCUSSION ABOVE 50 EV

15/16

h_ex

pEn

tries

1

36M

ean

0

.753

6R

MS

0

.014

25

p!0.

660.

680.

70.

720.

740.

760.

780.

80.

820.

840.

86

Counts

01020304050h_

exp

Entri

es

136

Mea

n

0.7

536

RM

S

0.0

1425

const = 50.1 +/- 6.6mean = 0.7564 +/- 0.0009sigma = 0.0095 +/- 0.0009

• Large dispersion in the experimental data from Frehaut at E > 50eV.

ν nγf contribution

=> New experimental data are required.• Large error bars from Gwin experimental data => not reliable.

Large dispersion

1.2%

50 eV

• Frehaut data with high νp can not be described by the equations.



CONCLUSIONS AND PERSPECTIVES

16/16

• Large dispersion (1.2%) in the experimental data from Frehaut at E > 50eV.• Frehaut data with high νp can not be described by the equations.• Large error bars from Gwin experimental data => not reliable.

• Experimental data:

• To implement this model in CONRAD.

• Model:

CONCLUSIONS

PERSPECTIVES

• Incompatibility in the normalization between Gwin and Frehaut datasets.

• Do not reproduce the data in the full energy range (above 50 eV).• The inclusion of Γ γf from Trochon/Bouland produces similar results.

• Lower < ν nγf > with Bouland data.

=> New experimental data are required.

Study of the (n,γf) process on Pu...Esther Leal Cidoncha, WONDER-2018, 8-12 October, 2018. TWO-STEP...

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