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IAEA-ND CM on “Prompt fission neutron spectra of major actinides”, Nov Application of Multimodal Madland-Nix Model ・ Evaluation of PFNS in 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 ν for 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

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Prompt fission neuron spectra in JENDL-3.3 and JENDL/AC2008 JENDL-3.3 JENDL/AC2008 Th-232 Maxwellian [T M =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 [T M : Baba(2000),Boikov(1994)] CCONE Pu-239 Multimodal M-N Multimodal M-N [E≤5MeV] CCONE [E>5MeV] Pu-241 Maxwellian [T M =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]

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

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Program CCONE (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 ・ DWBA for direct excitation of vibrational states ・ Two-component exciton model (Kalbach) ・ Multi-particle emission from the 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)

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

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

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

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

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

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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.

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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.

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

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

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

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

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Improvements in the Method Original Madland-Nix Model χ tot = ½{ χ L + χ H } Multimodal Madland-Nix Model (2) LDP : Shell effects on the LDP (Ignatyuk’s model) (1) Multimodal Fission: Energy partition in the fission process is very different for different fission modes (3) Asymmetry in ν : ν L ≠ν H (4) Asymmetry in T : T L ≠ T H because of the difference in deformation

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

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

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Decomposition of Primary FF Mass Distribution = 14.0 MeV 24.4 MeV 40.5 MeV 24.4 MeV 14.0 MeV

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

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

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

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(2) Shell Effects on LDP for FF

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

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

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(3) Asymmetry in ν for LF and HF: ν L (A) ≠ ν H (A) Saw-tooth structure

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

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

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Consideration of non-equality ν L (A) ≠ ν H (A) brings about a difference of ~10% at maximum in the spectrum

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(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, 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 = E int (L) + E def (L) + E int (H) + E def (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.

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E * CN =B n +E n E*L=aLT2LE*L=aLT2L E*H=aHT2HE*H=aHT2H E * L = E int L +E def L E * H = E int H +E def H TXE = + B n + E n ー TKE = a CN T 2 m = a L T 2 L + a H T 2 H =(a L R T 2 + a H )T 2 H where R T =T L /T H : temperature ratio

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Mode Standard-1 Standard-2 Superlong Nuclides Zr-102 Te-134 Sr-95 Xe-141 Pd-118 Pd-118 E R TKE E* LDP T L,i, T H,i Basic Fission Data for U-235(n th,f)

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Possible Early Neutrons

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Neutron Emission During Acceleration (NEDA) t = time after scission x = E/E k : ratio of the FF-KE relative to its final value E k s 0 = charge-center distance v k = final velocity =[2{(M-m)Mm} ・ 1.44(Z-z)z/s 0 ] 1/2 s0s0 t ・ Certain fraction of prompt neutrons may be emitted before full acceleration of FF [V.P. Eismont,1965] Z, M z,m

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

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

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

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Results of parameter search ： Best fit set of values that reproduce the experimental data for Cm-245(n th,f) is NEDA=0.3, TF=0.7

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NEDA factor increases with excitation energy

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Concluding Remarks 1.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 ν for 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.

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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.]

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

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

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

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NEDA increases with excitation energy General systematic relations : E R = (Z 2 /A 1/3 ) TKE Viola = (Z 2 /A 1/3 ) TXE = E R - TKE + B n + E n = (Z 2 /A 1/3 ) B n + E n As Z 2 /A 1/3 increases, TXE increases, which, in turn, means more NEDA effects for heavier actinides.

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Y (A, A f, E f * ) = C S1 [G(A, A S1, µ S1 s) + G(A, A f -A S1, µ S1 s)] + C S2 [G(A, A S2, s) + G(A, A f -A S2, s)] + C SL G(A, A f /2, µ SL s) Parameters : C S1 = N f (A f ) E f *, C S2 = 2.66( N f ) (A f ) E f *, C SL = 0.01exp(0.46 E f * ), A S1 = N f + 0.1Z f E f *, A S2 = E f *, s = ( N f ) E f *, µ SL = 1.4, µ S1 = N f exp[-(N f ) 2 ] exp[-|N f |], C = 100/( C S1 + C S2 + C SL /2 ) Five-Gaussian Representation of Fragment Mass Distribution by Wang & Hu

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Decomposition of Fission Fragment Mass Distribution Z=50N=82 N= MeV29.1MeV31.5MeVTXE=

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Location of Delayed Neutron Precursors （ Heavy Fragment Region ） N=82 Z=50

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At higher energies, successive neutron emission from “would-be” precursors (primary FFs) leads to loss of actual precursors T. Ohsawa et al., Proc. Int. Conf. on Nucl. Data for Sci. & Eng., Nice, France (2007)

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