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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives A Monte Carlo Simulation of Prompt Gamma Emission from Fission Fragments D. Regnier, O. Litaize, O. Serot CEA

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

A Monte Carlo Simulation of Prompt Gamma Emission from Fission Fragments

  • D. Regnier, O. Litaize, O. Serot

CEA Cadarache, DEN/DER/SPRC/LEPH

WONDER, 27/09/2012

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Table of contents

1

Introduction

2

Model 1: Uncoupled neutron and gamma emission Model Results & discussion

3

Model 2: Coupled neutron and gamma emission Model Results & discussion

4

Conclusion and perspectives

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Table of contents

1

Introduction

2

Model 1: Uncoupled neutron and gamma emission Model Results & discussion

3

Model 2: Coupled neutron and gamma emission Model Results & discussion

4

Conclusion and perspectives

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Gamma heating problematic

0,2 0,4 0,6 0,8 1 5 10 15 20 25 30 35 40 Distance from the core center (cm) Relative deposited energy

Photon Deposited Energy Neutron Deposited

Core Reflector

Figure 1: Relative neutron and photon heating in the Perle experiment (From Phd student S. Ravaux transport calculation with Tripoli-4.7) Figure 2: Perle experiment

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Prompt fission gamma data in evaluated files

Two spectra used for all the main fissionning isotopes

(n+239Pu, f) : baseda on Verbinski et al. measurement (1973) (n+235U, f) : basedb on Verbinski et al. measurement (1973)

  • aR. E. Hunter and L. Stewart, LA-4901 (1972)
  • bR. E. Hunter and L. Stewart, LA-4918 (1972)

Figure 3: JEFF-3.1.2 fission gamma spectrum for (n+239Pu, f)

Mγ= 7.78 γ/f

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Prompt fission gamma data in evaluated files

Two spectra used for all the main fissionning isotopes

(n+239Pu, f) : baseda on Verbinski et al. measurement (1973) (n+235U, f) : basedb on Verbinski et al. measurement (1973)

  • aR. E. Hunter and L. Stewart, LA-4901 (1972)
  • bR. E. Hunter and L. Stewart, LA-4918 (1972)

Figure 3: JEFF-3.1.2 fission gamma spectrum for (n+235U, f)

Mγ= 7.17 γ/f

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

FIFRELIN: A Monte Carlo simulation of fission fragments evaporation

T:

Fissioning nucleus

Figure 4:

Compound nucleus

(T= nuclear temperature)

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

FIFRELIN: A Monte Carlo simulation of fission fragments evaporation

T:

Fissioning nucleus

Figure 4:

Compound nucleus

T: pL pH Figure 5: Fully

accelerated fragments

(T= nuclear temperature)

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

FIFRELIN: A Monte Carlo simulation of fission fragments evaporation

T:

Fissioning nucleus

Figure 4:

Compound nucleus

T: pL pH Figure 5: Fully

accelerated fragments

Figure 6: Prompt

neutron emission

(T= nuclear temperature)

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

FIFRELIN: A Monte Carlo simulation of fission fragments evaporation

T:

Fissioning nucleus

Figure 4:

Compound nucleus

T: pL pH Figure 5: Fully

accelerated fragments

Figure 6: Prompt

neutron emission

Figure 7: Prompt

gamma emission

(T= nuclear temperature)

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Table of contents

1

Introduction

2

Model 1: Uncoupled neutron and gamma emission Model Results & discussion

3

Model 2: Coupled neutron and gamma emission Model Results & discussion

4

Conclusion and perspectives

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1

Approximation on neutron/gamma competition

1

Emit neutrons until a limit energy is reached, Elimit = Sn + Erot(J)

2

Decay by gamma and/or conversion electron emissions.

Sn Primary Fragments Entry region for Secondary Fragments Entry region for

n n n n n n n γ γ γ γ γ γ

E* J

γ γ γ γ

E*

lim

E(Yrast)

γ

discret levels γ statistical

}

}

Neutron emission

Energy sampled in a Weisskopf spectrum: χ(ǫn) ∝ σinv(ǫn) ǫn e−ǫn/T Total angular momentum: JA−1 = JA − 1/2

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1

Gamma emission

For one fission fragment

1

Departure from a known excited level (E∗

i , Ji, πi)

2

Decay probabilities calculation: Iγ(i → j) = Γγ(i → j) Γγ,tot (1) Γγ(i → j) = fXL(ǫγ)ǫ2L+1yfluctuation ρ(Ef, Jf, πf) (2)

3

Sample one transition

4

Gamma decay until a stable level is reached

Energy GS Ei J i

i

Continuum bound dE Experimental levels

Figure 8: Level scheme of the fission fragment

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1

Gamma emission

For one fission fragment

1

Departure from a known excited level (E∗

i , Ji, πi)

2

Decay probabilities calculation: Iγ(i → j) = Γγ(i → j) Γγ,tot (1) Γγ(i → j) = fXL(ǫγ)ǫ2L+1yfluctuation ρ(Ef, Jf, πf) (2)

3

Sample one transition

4

Gamma decay until a stable level is reached

Energy GS Ei J i

i

Continuum bound dE Iγ

1 Iγ 2 Iγ 3 Iγ 4 Iγ 5

Experimental levels

Figure 8: Level scheme of the fission fragment

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1

Gamma emission

For one fission fragment

1

Departure from a known excited level (E∗

i , Ji, πi)

2

Decay probabilities calculation: Iγ(i → j) = Γγ(i → j) Γγ,tot (1) Γγ(i → j) = fXL(ǫγ)ǫ2L+1yfluctuation ρ(Ef, Jf, πf) (2)

3

Sample one transition

4

Gamma decay until a stable level is reached

Energy GS Ei J i

i

Continuum bound dE Eγ Experimental levels

Figure 8: Level scheme of the fission fragment

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1

Gamma emission

For one fission fragment

1

Departure from a known excited level (E∗

i , Ji, πi)

2

Decay probabilities calculation: Iγ(i → j) = Γγ(i → j) Γγ,tot (1) Γγ(i → j) = fXL(ǫγ)ǫ2L+1yfluctuation ρ(Ef, Jf, πf) (2)

3

Sample one transition

4

Gamma decay until a stable level is reached

Energy GS Ei J i

i

Continuum bound dE Iγ

1

Iγ

2

Iγ

3

Experimental levels

Figure 8: Level scheme of the fission fragment

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1

Gamma emission

For one fission fragment

1

Departure from a known excited level (E∗

i , Ji, πi)

2

Decay probabilities calculation: Iγ(i → j) = Γγ(i → j) Γγ,tot (1) Γγ(i → j) = fXL(ǫγ)ǫ2L+1yfluctuation ρ(Ef, Jf, πf) (2)

3

Sample one transition

4

Gamma decay until a stable level is reached

Energy GS Ei J i

i

Continuum bound dE Eγ Experimental levels

Figure 8: Level scheme of the fission fragment

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1: Results for the 252Cf spontaneous fission

1 2 3 4 5 6 Energy (MeV) 0.1 1 10 Nγ / fission / MeV

Chyzh (2012) Verbinski (1973) FIFRELIN Model 1 (2012)

Figure 9: Total prompt gamma spectrum

FIFRELIN: ν = 3.78 n/f Mγ = 8.0 γ/f Etot

γ

= 8.1 MeV Etot

elec = 39 keV

(σstat < 0.1%) Experiments: ν = 3.76 ± 0.03 n/f Mγ ≃ 8 ± 0.4 γ/f Eγ,tot ≃ 7 ± 0.4 MeV

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1: Results for the 252Cf spontaneous fission

0.5 1 1.5 Energy (MeV) 2 4 6 8 10 12 Nγ / fission / MeV

Chyzh (2012) Verbinski (1973) FIFRELIN Model 1 (2012)

Figure 10: Fifrelin prompt gamma spectrum in the fragment frame (same resolution as Verbinski measurements)

Verbinski et al. experimental setup

Detection threshold: 140 keV Thin sample : ≃ 200µg.cm−2 ⇒ Doppler effect

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1: Results for the 252Cf spontaneous fission

0.5 1 1.5 Energy (MeV) 2 4 6 8 10 12 Nγ / fission / MeV

Chyzh (2012) Verbinski (1973) FIFRELIN Model 1 (2012)

Figure 11: Fifrelin prompt gamma spectrum in the laboratory frame (same resolution as Verbinski measurements)

Assumptions: 4π detection of gamma emitted. Isotropic emission of gamma rays in the fragment frame. No kinetic energy loss in target. Lorentzian transformation.

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1: Level density and strength function influence

Level density models:

1 2 3 4 5 6 Energy (MeV) 0.1 1 10 Nγ / fission / MeV

Verbinski (1973) HFB - EGLO CGCM - EGLO CTM - EGLO

CTM: Constant temperature CGCM: Composite Gilbert-Cameron HFB: Microscopic calculation Strength function models:

1 2 3 4 5 6 Energy (MeV) 0.1 1 10 Nγ / fission / MeV

Verbinski (1973) HFB - EGLO HFB - SLO HFB - HFB

SLO: Standart Lorentzian EGLO: Enhanced Generalized Lorentzian HFB: Microscopic calculation

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1: Angular momentum of the fragments

Sn Primary Fragments Entry region for Secondary Fragments Entry region for n n n n n n n γ γ γ γ γ γ E* J γ γ γ γ E* lim E(Yrast) γ discret levels γ statistical

}

}

⇒ Low energy part of the spectrum highly sensitive to Jinit

In FIFRELIN

Before neutron emission: P(J) = (J + 1/2) σ2(T) e

(J+1/2)2 2σ2(T)

¯ JH = 6.6, ¯ JL = 5.9 During neutron emission: JA−1 = JA − 1/2

Ref Wilhelmy1,2(1972) Skarsvag1,2(1980) Mukhopadhyay1,2(2012 ) ¯ JL 7 6 ≃ 5 ¯ JH 8.4 5.3 ≃ 12

Table 1: Average angular momentum of primary fragments from 252Cf SF

1: Only even-even post-neutron fragments are considered. 2: Estimation of the uncertainty: ±2.

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Effect of an increase of post-neutron fragment J

0.5 1 1.5 2 Energy (MeV) 1 10 Nγ / fission / MeV

Verbinski (1973) HFB - EGLO +1 hbar +2 hbar +3 hbar

Figure 12: Prompt gamma spectrum for the spontaneous fission of 252Cf

For a good agreement of low energy part of the gamma spectrum post-neutron angular momentum are found to be: JL ≃ 8, JH ≃ 9

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

From model 1 to model 2 ...

Model 1 results: Good agreement of neutron observables with experiments. First prediction of a prompt gamma fission spectrum. Overestimation of total gamma energy (Eγ,tot) ? Prompt gamma spectrum too hard. Remaining questions: Neutron emission before gamma emission ? Average ∆J = 1/2 during a neutron emission ? Initial total angular momentum of the fission fragments ? Validity of a Weisskopf spectrum at low excitation energy ?

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Table of contents

1

Introduction

2

Model 1: Uncoupled neutron and gamma emission Model Results & discussion

3

Model 2: Coupled neutron and gamma emission Model Results & discussion

4

Conclusion and perspectives

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 2

Transition probability

p(i → j) = Γ(i → j) Γtot

γ + Γtot neutron

(3) ⇒ Neutron and gamma emission competition

Neutron width calculation

Γn(i → j) = Tl,j(ǫn)yfluctuation 2πρ(Ef, Jf, πf) (4) Tl,j(ǫn) are provided by a Talys-1.4

  • ptical model calculation using a

Koning-Delaroche spherical potential

Energy A GS Ei J i

i

A-1 Sn GS dE

Figure 13: Possible decay

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 2: Preliminary results for the 252Cf SF

< ǫn > in FF frame (MeV) ν E* for neutron (MeV) Vorobyev (2005) 3.76 ± 0.03 Model 1 1.34 3.78 25.7 Model 2 1.23 4.0 27.4

Table 2: Neutron results

< ǫγ >(MeV) Mγ Eγ,tot (MeV) Chyzh (2012) 0.94 8.16 7.8 Model 1 1.0 8.0 8.1 Model 2 0.86 7.5 6.4

Table 3: Gamma results

New observables provided by the model 2

1

∆Jn= 0.1 /n

2

Average number of gamma emitted before the last prompt neutron: ≃ 4.10−3γ/f (1γ every 250 fissions)

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1 vs Model 2 for the 252Cf spontaneous fission

1 2 3 4 5 6 Energy (MeV) 0.1 1 10 Nγ / fission / MeV

Chyzh (2012) Verbinski (1973) FIFRELIN Model 1 (2012) FIFRELIN Model 2 (2012)

Figure 14: Total prompt gamma spectrum

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Model 1 vs Model 2 for the 252Cf spontaneous fission

0.5 1 1.5 2 Energy (MeV) 10 Nγ / fission / MeV

Chyzh (2012) Verbinski (1973) FIFRELIN Model 1 (2012) FIFRELIN Model 2 (2012)

Figure 14: Total prompt gamma spectrum

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Influence of parameters and models

Strength function γ

∆ν < 1% ∆ǫγ ≃ 12% ∆Eγ,tot ≃ 1% Shape of the gamma spectrum impacted

Level density

∆ν ≃ 3% ∆ǫγ ≃ 6% ∆Eγ,tot ≃ 4% Shape of the gamma spectrum impacted

Angular momentum of primary FF

High sensitivity of main observables, +2 leads to: ν: −1% ǫn: −2 % Eγ,tot: +0.7 MeV ǫγ: −7 % Mγ: +20%

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Table of contents

1

Introduction

2

Model 1: Uncoupled neutron and gamma emission Model Results & discussion

3

Model 2: Coupled neutron and gamma emission Model Results & discussion

4

Conclusion and perspectives

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Realized for the moment:

Implementation of two main cascade models, work on neutron/gamma competition. Implementation and comparison of several models of level density and strength function. Optimization in speed and memory of the code, parallelization. Calculation of several observables of the fission process ( post-neutron fragments data, multiplicity for a given fragmentation ...).

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Perspectives:

Impact of the optical model used for neutron transmission calculation. Investigation on the energy balance between neutron and gamma emission. Calculation of observables with high sensitivity to angular momentum: anisotropy gamma. Measurements at ILL before end of 2012. . . . Other application scope: Neutron capture calculation: spectrum, multiplicity, branching ratio...

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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Introduction Model 1: Uncoupled neutron and gamma emission Model 2: Coupled neutron and gamma emission Conclusion and perspectives

Thank you for your attention !

  • D. Regnier, O. Litaize, O. Serot - CEA Cadarache, DEN/DER/SPRC/LEPH

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