| PAGE 1 2nd ERINDA Progress MeetingCEA | 10 AVRIL 2012 O. Serot, O. Litaize, D. Regnier CEA-Cadarache, DEN/DER/SPRC/LEPh, F Saint Paul lez Durance, France CRP Prompt Fission Neutron Spectra of Actinides

Introduction Calculation procedure Results on 252 Cf(sf) Results on 235 U(n th,f) Results on 239 Pu(n th,f) Conclusion and outlook Plan 2

3 Calculation procedure For each Fission Fragment: Determination of A, Z, KE Determination of J, pi Desexcitation of the Fission fragments Calculation procedure

Sampling of the light fragment: 1 A L, Z L, KE L Calculation procedure 4 Y(A,KE,Z)=Y(A) × Y(,  KE ) × Y(Z) Pre Neutron Kinetic Energy distribution Nuclear charge distribution Charge dispersion: Most probable charge Z P taken from Walh evaluation and/or from systematic Pre Neutron Mass distribution

The mass and charge of the heavy fragment can be deduced: A H =240-A L Z H =94-Z L Its kinetic energy (KE H ) is deduced from momentum conservation laws 2 A H, Z H, KE H Calculation procedure 5  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 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 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 Calculation procedure 120/132 RT min RT max 126/12678/174 Exemple on 252Cf(sf)

8 Calculation procedure Asymptotic level density parameter Effective excitation energy Shell corrections (Myers-Swiatecki, …) Level density parameter calculated from Ignatyuk’s model: Rotational Energy: E Rot  : quadrupole deformation taken from Myers-Swiatecki We have taken:with k=0.6

9 Desexcitation of each fission fragment: A, Z, J, pi, E*, Erot 5 Weisskopf Model (uncoupled) Calculation procedure E L,H *=aT L,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*, Erot 5 Hauser Feshbach formalism (coupled): Level density used: Composite Gilbert Cameron Model Tn: 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 E* L,H =aT L,H +E rot L,H 5b

11 Calculation procedure 5 free parameters for fission:  L,  H, RT min, RT max, K rigid 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 Hauser-Fescbach model (coupled)  L =9.5  H =9.0 RT min =0.3 RT max =1.5 k rigid =0.75 (Varapai_coupled_V3) Weisskopf model (uncoupled)  L =8.5  H =10.2 RT min =0.7 RT max =1.4 k rigid =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) From David Regnier Thesis

16 Calculation performed for the 235U(nth,f) Hauser-Fescbach model (coupled)  L =7.2  H =8.4 RT min =0.9 RT max =1.3 k rigid =0.9 Input data (pre-neutron mass and kinetic energy) from Hambsch Results / 235U(n th,f)

17 Results / 235U(n th,f) Probability of neutron emission

18 Results / 235U(n th,f) Average neutron multiplicity as a function of TKE Slope=10.24 MeV/n Slope_Nishio=18.5 MeV/n

19 Results / 235U(n th,f) Average neutron multiplicity as a function of pre-neutron mass

20 Results / 235U(n th,f) Prompt Fission Neutron Spectrum

21 Calculation performed for the 239Pu(n th,f) Presented at Workshop GAMMA2, Oct Standard I Standard II Super Long R T 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 239 Pu Describe for each fission mode the n and  characteristics Results / 239Pu(n th,f)

22 St. ISt. IISL MM  TKE W (%) 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(n th,f)

23 Average Total Kinetic Energy Width of the Total Kinetic Energy Results / 239Pu(n th,f)

24 Standard I Standard II Super LongTotal Results / 239Pu(n th,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 / / 138 Super Long is a strongly deformed mode Temperature Ratio Law: R T = T L /T H Results / 239Pu(n th,f)

26 Prompt Neutron Multiplicity L H Tot St. I St. II SL Total Experimental and evaluated data Tot Boldeman2.879 ± Holden2.881 ± JEFF FIFRELIN Results Results / 239Pu(n th,f)

27 Reasonable agreement between FIFRELIN calculation and the experimental data can be obtained Best agreement is achieved with data from Batenkov (2004) In the [ ] 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(n th,f)

28 Prompt Neutron Multiplicity Results / 239Pu(n th,f) Different slopes obtained for each fission modes Different slopes obtained for Light and Heavy fragment

29 Prompt Fission Neutron Spectrum 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(n th,f)

30 Results / 239Pu(n th,f) Prompt Neutron Spectrum: Ratio to Maxwellian with T=1.32 lab [MeV] JEFF St. I2.19 St. II2.13 SL2.43 Total

31 Prompt Neutron Spectrum: Ratio to Maxwellian with T=1.32 Comparison with / without Fission modes Results / 239Pu(n th,f)

32 FIFRELIN with  =[0 – infinity] Prompt Gamma Multiplicity Results / 239Pu(n th,f)

FIFRELIN with  =[0 – infinity] Prompt Gamma Spectrum Structures at low energy are visible for both St. I and St. II modes Fails to reproduce the high energy part (above 5 MeV) Results / 239Pu(n th,f)

34  [MeV]  T [ns]M   /f  E  tot [MeV]   [MeV] St. I 140 keV-inf St. II 140 keV-inf SL 140 keV-inf Total 140 keV-inf Experimental Compilation from David Regnier FIFRELIN Calculation Excellent agreement with Verbinski’s data Results / 239Pu(n th,f)

35 QTKE pre TKE post TXE Total E* Light E* Heavy (Erot) Light (Erot) Heavy TNETGE St. I St. II SL Total JEFF Total energy less the energy of neutrinos / MeV Kinetic energy of fragments (post-neutron) / MeV Total energy released by the emission of "prompt" gamma rays / MeV Total energy released by the emission of "prompt" neutron / MeV Average fragment remaining energy due to metastable StI Light FF = Heavy FF= StII Light FF = Heavy FF= SL Light FF = Heavy FF= Results / 239Pu(n th,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(n th,f) and 239Pu(n th,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 density the KD optical model for the Tn calculation the 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 =9.5  H =9.0 RT min =0.3 RT max =1.5 k rigid =0.75 (Varapai_V3) Hauser-Fescbach model (coupled)  L =8.5  H =10.2 RT min =0.7 RT max =1.4 k rigid =0.6 (Varapai_V1)

39 Experimental data base on prompt gamma rays

40 Influence: Spin cut-off on P(nu) Model Weisskopf 238U(n,f) (Same trend observed with HF coupled) From O. Litaize et al., ND2013