IAEA-ND CM on “Prompt fission neutron spectra of major actinides”, 24-27. Nov. 2008

1. IAEA-ND CM on “Prompt fission neutron spectra of major actinides”, 24-27. Nov. 2008 Application of Multimodal Madland-Nix Model ・Evaluation of PFNSin JENDL-series ・Multimodal Random Neck-rupture Model : An Outline ・Refinements in the Madland-Nix Model 1) Multimodal fission, 2) Level density parameter considering the shell effect, 3) Asymmetry in νfor LF and HF, 4) Asymmetry in T for LF and HF ・Possible early neutrons：Neutron emission during acceleration　（NEDA) Takaaki Ohsawa (大澤孝明) Dept. of Electric & Electronic Engineering School of Science and Engineering Kinki University, Osaka, Japan

2. Prompt fission neuron spectra in JENDL-3.3 and JENDL/AC2008 JENDL-3.3 JENDL/AC2008 Th-232 Maxwellian [TM=Howerton-Doyas’ syst.] CCONE (O.Iwamoto) Pa-231 Maxwellian (taken from ENDF/B-V) CCONE U-233 Multimodal M-N (T.Ohsawa) Multimodal M-N [E≤5MeV], CCONE [E>5MeV] U-235 Multimodal M-N [E≤5MeV], Multimodal M-N [E≤5MeV], Preeq. spectrum by FKK model CCONE [E>5MeV] U-238 Multimodal M-N Multimodal M-N [E≤5MeV], CCONE [E>5MeV] Np-237 Maxwellian [TM: Baba(2000),Boikov(1994)] CCONE Pu-239 Multimodal M-N Multimodal M-N [E≤5MeV] CCONE [E>5MeV] Pu-241 Maxwellian [TM=Smith’s systematics] CCONE [E>5MeV] Am-241 Maslov’s evaluation (1996) Multimodal M-N [E≤6MeV], CCONE [E>6MeV] Am-242m Maslov’s evaluation (1997) Multimodal M-N [E≤6MeV], CCONE [E>6MeV] Cm-243 Maslov’s evaluation (1995) Multimodal M-N [E≤6MeV], CCONE[E>6MeV] Cm-245 Maslov’s evaluation (1996) Multimodal M-N [E≤6MeV], CCONE[E>6MeV]

3. Evaluated Nuclear Data for Actinides in the JENDL-series JENDL-3.3 JENDL/AC2008 JENDL-4 ・Released May 2002 ・62 nuclides ・Released March 2008 ・Ac –Fm (Z=89-100) ・79 nuclides ・Will be released in 2010 ・Slight revision(?) New 17 nuclides (T1/2 >1d) added

4. ProgramCCONE (by O. Iwamoto, JAEA) Main features ・”All-in-one” code for evaluation of nuclear data ・Witten in C++ for ease of extension & modification ・Architecture based on object oriented programming ・Coupled-channel theory ・Hauser-Feshbach theory including Moldauer effect ・DWBAfor direct excitation of vibrational states ・Two-component exciton model (Kalbach) ・Multi-particle emission fromthe CN with spin- and parity-conservation ・Double-humped fission barriers with consideration of collective enhancement of the level density ・Madland-Nix model (original implementation) cf. Osamu Iwamoto, J. Nucl. Sci. Technol. 44, 687 (2007)

5. MultimodalRandom Neck-ruptureModel [U.Brosa, S.Grossmann, A.Müller] Multichannel Fission Model Random Neck- Rupture Model [e.g. E.K.Hulet et al. 1989] [S.L.Whetstone,1959] “hybrid” Multimodal Random Neck-Rupture Model (BGM model)

6. Multimodal Random Neck-rupture Model Neck-rupture occurs randomly according to the Gaussian function Several distinct deformation paths ⇒ several pre-scission shapes S1 S2 SL [U. Brosa etal.1990]

7. Example:235U(n,f) [H.-H. Knitter et al. Z. Naturforsch,42a,760(1987)] Standard-2 Mass Yield Standard-1 Superlong Standard-1 TKE Standard-2 Superlong 3 modes overlapping → largest σ σ(TKE) 2 modes overlapping → larger σ single mode prevails → smaller σ

8. Justification of the MM-RNR model on the basis of deformation energy surface calc. [B. D. Wilkins et al., Phys. Rev. C14,1832 (1976)] N=86 (Meta-stable deformation; S2) Beta-deformation Spherical nucleus N N=82(S1) Z Z=50(S1) The nascent HF is likely to be formed close to these hollows

9. Application of the Multimodal RNR Model Multi-channel FissionModel Random Neck- Rupture Model Madland-Nix (LA) Model Multimodal RNR Model Summation Calculation Multimodal Madland-Nix Model Multimodal Analysis of DNY T. Ohsawa & F.-J. Hambsch, Nucl. Sci. Eng. 148, 50 (2004) T.Ohsawa et al., Nucl. Phys. A653, 17 (1999).

10. Fluctuations Observed in the Fission Yield in the Resonance Region for U-235 [F.-J. Hambsch] Precursors are localized, because they have a structure of closed shell + loosely bound neutrons outside of the core.

11. Fluctuation in the Precursor Yields in the Resonance Region of U-235 The precursor yields in the LF-S2-region are considerably decreased. This brings about decrease in the delayed neutron yield at the resonance.

12. Fluctuation in the Delayed Neutron Yields for U-235 -3.5% cf. T. Ohsawa and F.-J. Hambsch, Nucl. Sci. Eng. 148, 50 (2004)

13. Slight decrease in thermal & resonance regions Sudden decrease in the 4 - 7MeV region

14. Models of PFNS 1. Maxwellian 2. Watt 3. Madland-Nix (LA) model CM-spectrum: S.S.Kapoor et al., Phys. Rev. 131, 283 (1963)

15. LS-spectrum: 4. Cascade Evaporation Model Märten & Seeliger Hu Jimin Criteria for choosing a model for evaluation: 1.Accuracy 2. Simplicity 3. Predictive power 5. Hauser-Feshbach Model Browne & Dietrich Gerasimenko 6. Monte Carlo Simulation Dostrovsky, Fraenkel (1959) Lemaire, Talou, Kawano, Chadwick, Madland

16. Improvements in the Method Original Madland-Nix Model χtot= ½{ χL+ χH } (1) Multimodal Fission: Energy partition in the fission process is very different for different fission modes (2) LDP : Shell effects on the LDP (Ignatyuk’s model) (4) Asymmetry in T : T L ≠ TH because of the difference in deformation (3) Asymmetry inν: νL≠νH Multimodal Madland-Nix Model

17. Asymmetric fission (standard mode) (1) Multimodal Fission Model Each different deformation path leads to different scission configuration, therefore to different energy partition. Symmetric fission (superlong mode) S1 S2 SL Hartree-Fock-Bogoliubov calc. by H.Goutte et al., Phys. Rev. C71, 024316(2005)

18. Standard-1 Multimodal Fission Process 235U(n,f), Ein=thermal 134 102 ER=194.5MeV TKE=187MeV 18.3% Standard-2 81.6% 141 95 236 ER=184.9MeV TKE=167MeV 0.007% Superlong 118 118 ER : calc. with TUYY mass formula (Tachibana et al., Atomic & Nucl. Data Tables, 39, 251 (1988) ) TKE : Knitter et al., Naturforsch, 42a, 786 (1987) ER=190.9MeV TKE=157MeV Average fragment mass

19. Decomposition of Primary FF Mass Distribution 40.5 MeV <TXE>= 14.0 MeV 14.0 MeV 24.4 MeV 24.4 MeV

20. S1-spectrum – softest S2-spectrum – harder SL-spectrum －hardest

21. Comparison with experiment for U-235(nth,f) ●Modal spectrum : ●Total spectrum : wi: mode branching ratio This evaluation is contained in JENDL-3.3 & JENDL/AC2008 and will also be in JENDL-4.

22. At higher incident energies the spectrum becomes harder due to 1. Higher excitation energies of the FFs. 2. Increase in the S2- component.

23. (2) Shell Effects on LDPfor FF

24. Ignatyuk’s LDP ●Shell effects on the LDP vary according to the mass and excitation energy of the FFs. (1) Asymptotic value : Effective excitation energy : Excitation-energy dependence : Shell correction : Eq.(1) is a transcendental eq.→Solve it numerically! （IGNA3 code）

25. Effect of the Level Density Parameter on the Spectrum LDP has a great effect on the spectrum, esp. in the higher energy region.

26. (3) Asymmetry in ν for LF and HF: νL(A) ≠ νH(A) Saw-tooth structure

27. Madland- Nix: New modal spectra: This is important because the neutron spectra from the LF and HF are very different!

28. mHvH＝mLvL CM LS HF LF 1. The LF travels faster than the HF. Two effects 2. Low energy neutrons are more easily emitted from HFs than from LFs. HF S.S.Kapoor et al., Phys.Rev. 131, 283 (1963) LF

29. Consideration of non-equality νL(A) ≠ νH(A) brings about a difference of ~10% at maximum in the spectrum

30. (4) Asymmetry in the Nuclear Temperatures ・T. Ohsawa, INDC(NDS)-251 (1991), IAEA/CM on Nuclear Data for Neutron Emission in the Fission Process, Vienna, 1990. p.71. ・T. Ohsawa and T. Shibata, Proc. Int. Conf. on Nucl. Data for Science and Technology, Juelich, 1991, p.965 (1992), Springer-Verlag. ・P. Talou, ND2007, Nice (2008) ●Total excitation energy of the FF: TXE= Eint (L) + Edef (L) + Eint (H) + Edef (H) at the scission-point = E*(L) + E*(H) at the moment of neutron emission The nuclear temperatures of the two FFs at the moment of neutron emission are generally not equal, if the deformation is different at scission.

31. E*L= Eint L +Edef L E*CN=Bn+En E*L=aLT2L E*H=aHT2H E*H= Eint H +Edef H TXE=<ER> + Bn + En ー TKE = aCNT2m = aLT2L + aHT2H =(aLRT2 + aH)T2H where RT=TL/TH : temperature ratio

32. Basic Fission Data for U-235(nth,f) ModeStandard-1Standard-2Superlong NuclidesZr-102Te-134Sr-95Xe-141Pd-118Pd-118 ER194.49 184.86 190.95 TKE 187 167 157 E*8.39 10.51 11.74 9.11 22.89 22.89 LDP11.43 8.89 10.31 13.25 11.79 11.79 1.05 1.31 1.47 1.14 2.86 2.86 TL,i, TH,i 0.861.09 1.06 0.83 1.39 1.39

34. Possible Early Neutrons

35. Neutron Emission During Acceleration (NEDA) ・Certain fraction of prompt neutrons may be emitted before full acceleration of FF [V.P. Eismont,1965] t =time after scission x = E/Ek: ratio of the FF-KE relative to its final value Ek s0= charge-center distance vk= final velocity=[2{(M-m)Mm}・1.44(Z-z)z/s0]1/2 t s0 z,m Z, M

36. Time Scale of Neutron Emission Neutron emission time from an excited nucleus of excitation energy U and binding energy Bn [T. Ericson, Advances in Nuclear Physics 6, 425 (1960)] If n-emission time >acceleration time t 　　　　　　　　　　　　　　 → NE after full acceleration <t →NE during acceleration

37. NEDA is possible, at least in the Standard-2 fission

38. Empirical Examination Parametric survey ● Define two parameters: 　・NEDA factor ： fraction of neutrons emitted during acceleration 　・Timing factor TF ： the ratio E/Ek at which neutrons are emitted ● Then find the best set of parameters that reproduce the experimental data.

39. Results of parameter search： Best fit set of values that reproduce the experimental data for Cm-245(nth,f) isNEDA=0.3, TF=0.7

40. NEDA factor increases with excitation energy

41. Concluding Remarks • Madland-Nix model,refined by considering • 1) multimodal nature of the fission process • 2) appropriate LDP with inclusion of the shell effect • 3) asymmetry in νfor LF & HF • 4) asymmetry in T for LF & HF • provides a good representation of the spectra for major • actinides in the first chance fission region where • multimodal analyses have been done. • 2. In order to further improve the accuracy and extend the • predictive power of the method, it is necessary to have • a better knowledge on the systematics of the multimodal • parameters for more fissioning systems. • 3. Mode detailed study should be undertaken in order to • solve the pre-scission/scission neutrons or neutron • emission during acceleration.

46. Justification of the Triangular Temperature Distribution with Sharp Cutoff The approximate validity of this model is based on a specific relationship between the FF neutron separation energy and the width of the initial distribution of FF excitation energy. [Terrell; Kapoor et al.]

47. Mis-alined Fission and Fusion Valleys Mis-alined Valleys [W.J.S. Swiatecki & S. Bjornholm, Phys. Rep.4C, 325 (1972) ] ・Fission and fusion valleys are separated by a ridge. ・The nucleus gets over the ridge somewhere from the fission to fusion valley. Hartree-Fock- Bogoliubov calc. [J.F. Bernard, M. Girod, D. Gogny, Comp. Phys. Comm. 63, 365 (1991)] Scission occurs some- where around here.

48. Pre-scission shapes Average number of neutrons emitted from a fragment for each mode S1 S2 SL Partition of the TXE T.-S.Fan et al., Nucl. Phys. A591,161 (1995)

49. The inverse reaction cross sections for HFs are higher than those for LFs in the low energy region. (according to the optical model calc.) LS-spectrum: Gauss-Legendre quadrature over ε and T Gauss-Laguerre quadrature

50. NEDA increases with excitation energy General systematic relations : ER= 0.2197(Z2/A1/3)- 114.37 TKEViola = 0.1189(Z2/A1/3) + 7.3 TXE =ER-TKE+Bn+En = 0.1008(Z2/A1/3) - 121.67 +Bn+ En As Z2/A1/3 increases, TXEincreases, which, in turn, means more NEDA effects for heavier actinides.