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Physics-based Calculation of the Prompt Neutron Spectrum

Physics-based Calculation of the Prompt Neutron Spectrum ・ Brief Review of Fission Physics ・ Classification of Problems with Neutron Emission from FFs ・ Sequential Evaporation 　　　　　・ Angular Anisotropy in the CM-system of FF ・ Neutron emission During Acceleration

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Physics-based Calculation of the Prompt Neutron Spectrum

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  1. Physics-based Calculation of the Prompt Neutron Spectrum ・Brief Review of Fission Physics ・Classification of Problems with Neutron Emission from FFs ・Sequential Evaporation 　　　　　・Angular Anisotropy in the CM-systemof FF ・Neutron emission During Acceleration 　　　　　・Scission Neutrons ・Yrast levels ・Application of the Multimodal MN-Model to Bimodal Fission ・My interest in Thorium Utilization ・Summary Takaaki Ohsawa (大澤孝明) School of Science and Engineering Kinki University, Osaka, Japan

  2. Basic idea The calculation model of the PFNS should be grounded on the present knowledge of fission physics and be consistent with it. The fission process is a multi-stage, multi-facet phenomenon. Stage I: Deformation Stage III: Neutron emission Stage IV: DN & γ-emission Stage II: Saddle-to- Scission Prompt neutron are emitted from fragments of different property, each of which is formed by the deformation path it followed . γ n β

  3. Asymmetric fission (standard mode) Stage I: Deformation process •The nuclear deformation proceeds by way of a few distinct paths, defined by macroscopic and microscopic effects. Symmetric fission (superlong mode) Hartree-Fock-Bogoliubov calculation by H. Goutte et al., Phys. Rev. C71, 024316 (2005)

  4. Stage II: Saddle-to-Scission Transition Hypothesis of “Mis-alined Valleys” (Swiatecki & Bjørnholm (1972)) • Fission valley and fusion valley are separated by a ridge. • The nucleus transafers from fission (one-body) to fusion (two-body) valley (scission point). Hartree-Fock- Bogoliubov calc. (Bernard, Girod, Gogny (1991)) one-body ridge Most scission occurs around here. But scission point is not uniquely defined. →fluctuation in TKE two-body

  5. • Brosa visualized the scission process as stochastic breakup in the neck region of the deformed nucleus. • Several well-defined pre-scission shapes, together with uncertainty in the breakup point, bring about different energy partition. Standard-1 (S1) Standard-2 (S2) Superlong (SL) Different Q-values, Different mass distributions, Different average TKEs, Different st. dev. of TKEs, for different fission modes. Illustration by K. Nishio

  6. TKE and TXE Distributions of Primary Fragments (based on the data of H.-H. Knitter et al. for U-235(nth,f) ) TKE TXE Three groups of primary fragment pairs with different excitation energies. Since neutron emission starts from these three groups of primary FF pairs, prompt neutron emission calculation should take the fact into account.

  7. Stage III: Neutron Emission We can classify the problems relevant to prompt neutron emission as follows: ●Evaporation (equilibrium emission)? Fragment spin: <J> = 7 - 8 Isotropic in the CM- system of the FFs? A. From fully-accelerated FFs? Possible effect of the Yrast levels? B. During acceleration? (Less kinematic boost by the FFs) C. At the moment of scission? ●Non-equilibrium (non-adiabatic) emission? (Neutrons with E>20MeV: H.Märten & D.Seeliger, INDC(GDR)-17 - completely WRONG!)

  8. Evaporation: Sequential neutron emission from fragments with different temperaturesand with different properties. a) Temperature distribution: P(T) T1 T2 • Madland and Nix proposed to approximate the temperature distribution by a triangular distribution. • Mawxellian and Watt formulas are characterized by a single temperature → This assumption is justified only when the cooling due to particle emission is small. T Max. temp.→Tm

  9. b) Nuclear properties of the FFs: Original M-N model: Level density systematics A/8 A/10 a = A/C C = 8 – 11 (adjustable parameter) A/11 LF HF D.G.Madland & J.R.Nix, Nucl. Sci. Eng. 81, 213 (1982) Nowadays, Ignatyuk’ssuperfluid model with consideration of the shell effects is known to give better description of the LDP, thus eliminating the adjustable parameter C.

  10. Level Density : Ignatyuk’sSuperfluid Model ● 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）

  11. The LDP for FFs for different fragment excitation energies The LDP for neutron-rich nuclei 50Z A/10 30MeV 82N 10MeV At higher excitation energies, the structure due to shell effects become less pronounced but still persists. The shell effect persists for neutron-rich nuclei. The LDP for FFs for each fission mode were calculated considering their exc. energy and neutron-richness .

  12. Effect of the Level Density Parameters on the Spectrum ●The high-energy part of the spectrum is sensitive to the LDP, but the low-energy part is not. ●Ignatyuk’s LDP, without any artificial adjustment, gives good fit to the experimental data. This proves that Ignatyuk’s LDP is physically adequate.

  13. c) Asymmetry inν(A) Average number of neutrons emitted from a fragment for each mode • The number of neutrons emitted from the two FFs are not equal. • The CM-spectra of neutrons from Lf and HF are very different. Weighted average should be taken instead of the simple average.

  14. Neutron Spectra from LF and HF are very different CM mHvH＝mLvL LS HF LF • Kinematic boost is greater for LF, • leading to harder LF-spectra. 2. Higher inverse cross section for HF enhances emission of slow neutrons. HF S.S.Kapoor et al., Phys.Rev. 131, 283 (1963) LF

  15. MULTIF1

  16. Neutron spectra from three fission modes for U-235(nth,f) S1-spectrum – softest S2-spectrum – harder SL-spectrum – hardest

  17. Experimental data for U-235, Ein = 0.4 - 0.5 MeV •En<0.5 MeV： Two kinds of exp. data Higher:Nefedov（Starostov) [Obninsk] Lower: Johansson [Studsvik] • En>2 MeV： Two kinds of exp. data Higher:Adams [Harwell] Johansson [Studsvik] Lower: Nefedov（Starostov) [Obninsk]

  18. ●What are the reasons for the discrepancy in the region En< 0.5 MeV? Possibilities: 1. The exp. data are not accurate enough, due to scattered neutrons and/or low detection efficiency. 2. Possible existence of scission neutrons. 3. Angular anisotropy in neutron emission in the CM-system of FF. 4. Neutron emission during acceleration (NEDA), instead of after full acceleration. 5. Possible effect of “yrast levels”.

  19. 2. Possible Existence of Scission Neutrons ● C. Wagemans, “The Nuclear Fission Process” (1991): <νSCN>/<νp>= (1.1 ±0.3) % <ESCN>= (0.39 ±0.06) MeV for Cf-252(sf) ● O.I. Batenkov, M.V. Blinov et al., IAEA/CM on Phys. of Neutron Emission in Fission, Mito (1989), INDC(NDS)-220: <νSCN>/<νp> ~ 3 % ● A.S.Vorobyev, O.A.Shcherbakov et al. NIM 598, 795(2009): <νSCN>/<νp>< 5 % for U-235 at E0=thermal ● N.V. Kornilov et al., ND2007, Nice <νSCN>/<νp> ~ 25 % <ESCN>= 2.08 MeV for U-235 at E0=0.5 MeV ■ Uncertainties are still large in the data of fraction and average energy of scission neutrons.

  20. Multimodal Madland-Nix model + 3%-SCN ・With an assumption of 3 % of SCN with nuclear temperature T=0.3 – 0.5 MeV, the spectrum still remains within uncertainty of the experimental data.

  21. 5% of SCN is too much. ・SCN fraction as big as25% is not required to fit to the experimental data. ・ Scission neutron is an interesting phenomenon from physics point of view, and further investigation is needed to identify its characteristics. ・ But it should not be treated as a convenient tool for fitting.

  22. 3. Angular Anisotropy of Neutron Emission in the Fragment CM-system E = Ef + ε + 2(Ef ε)1/2cosθ The L-system energy The angle-dependent neutron spectrum in the CM- system b=W(θ)/W(90º) – 1 the anisotropy parameter: The L-system spectrum: → Numerical calculation

  23. • The angular anisotropy of neutron emission enhances the low-energy (E<0.6 MeV) and high-energy (E>4 MeV) parts of the spectrum, and diminishes the intermediate part. • The anisotropy parameter b should be studied more in relation to the spin and energy of the FFs.

  24. 4. Neutron Emission During Acceleration (NEDA) ・Certain fraction of prompt neutrons may be emitted before full acceleration of FF [V.P. Eismont, Sov. At. Energy 19, 1000 (1965)] ●Time after scission t as a function of x = E/Ek, the ratio of the FF-KE relative to its final value Ek ●Decay of the FFs by neutron emission [T. Ericson, Advances in Nuclear Physics 6, 425 (1960)] If n-emission time > acceleration time t → NE after full acceleration  <t→NE during acceleration

  25. Fair chance of competition between FF acceleration and neutron emission for S2-mode. Fragment acceleration (doesn’t depend on fission mode) Pu-239(nth,f) Decay by neutron emission (strongly depend on fission mode)

  26. • NEDA effect enhances low-energy part of the spectrum. •The degree of enhancement depends on the neutron emission time. Pu-239(nth,f) Ratio to Maxwellian (T=1.42 MeV) Neutron Energy (MeV)

  27. 5. Effect of the Yrast level on the decay of a high-spin nucleus Fragment angular momentum <J>= 7 - 8ħ High-energy neutron emission may be suppressed by the yrast level. Initial excited states n E n n Yrast line : the lowest available states for a given angular momentum I. (No internal excitation below the line. It works something like the “ground state” for the angular momentum.) n n x γ(E2) Bn This possibility should be examined by Monte Carlo simulation with consideration of angular momentum conservation. I

  28. Application of the Multimodal Madland-Nix Model to Bimodal Fission Interests in Heaviest Actinides • Sudden switchover from asymmetric to symmetric fission • ーWhat will be the impact of the modal change • on the PFNS? 2. Recent interest in heavy actinides in astronuclearphysics ーFormation and fission of heavy actinides should be considered in the nucleosynthesis in supernovae.

  29. Sudden switchover from asymmetric to symmetric fission Fm-isotopes Cf Es Fm Md No Lr Rf Ha N=158 N=158

  30. Deformation Energy Surface for Fm-258 New path leading to elongated fragments (S1) Old path 50% 50% New path leading to spherical fragments (SS) P.Moller et al., Nucl. Phys. A492, 349 (1989)

  31. 2. Nucleosynthesis in Supernovae Fission Recycling r-process

  32. Fission Recycling Effects on the Abundance of Elements in the Solar System With neutron multiplication but without fission fragments With neutron multiplication and with fission fragments I. V. Panov et al., Astronomy Letters 34, 189 (2008) Note: Synthesis of elements in the universe is similar to nuclear transmutation in the reactor core, resulting in similar equations describing the processes.

  33. S1 SS For Fm-258(sf), S1 : SS = 50% : 50% S1 SS Hulet et al., Phys. Rev. C40, 770 (1989)

  34. Energy Balance in Fission • Total energy release is high (~250 MeV at max.) for Fm-isotopes. • Coulomb repulsion energy (≈TKE) is also high due to higher fragment charge. • SuperShort mode is restricted in a narrow region due to energetic reason. •For U-235, shell regions are separated; this favors asymmetric fission.

  35. Results of Multimodal Madland-Nix Model Calculation for Fm (1) • For Fm-257, fission is governed by S1-mode, hence the PFNS is also characterized by the hard spectrum peculiar to this mode.

  36. Results of Multimodal Madland-Nix Model Calculation for Fm (2) • For Fm-258, the contributions of SS and S1 are 50-50. (van Aarleet al. 1998) • However, since more neutrons are emitted from S1-mode, the PFNS is still dominated by S1-mode.

  37. • Sudden softening of the spectra for Fm-259 is due to complete switchover to the SuperShort mode (cold fission). • Thus, fission modal change causes a big change in PFNS.

  38. Integral Test of Nuclear Data Core systems: 900 cases were selected out of ICSBEP (Int’l Criticality Safety Benchmark Evaluation Project) Handbook, including various reactor-types, fuels, spectra (thermal, fast, intermediate,…) Codes: •MVP (Continuous Energy Monte Carlo Calculation Code) was used to perform accurate calculation for systems with complicated core geometry • Sensitivity analysis codes CBG, MOSRA-SAGEP, SVS were used to extract information from the benchmark tests

  39. In JENDL-4, ▪ No big change has been made for major actinides. ・For MA, Maslov’s evaluations in JENDL-3.3 were superseded by new evaluations by O.Iwamoto. Ref.) G. Chiba, K. Okumura, Benchmark Tests of Nuclear Data Files for Development of JENDL-4, JAEA-Research-089 (2008) O. Iwamoto et al., PHYSOR’08 (2008); T. Mori, Proc. of Nuclear Data Symposium (2005)

  40. My interest in Thorium Fuel Utilization • Molten-Salt Reactor • - As a MA Burner • - As a Plutonium Burner Reactor core HEX Proposed Concept of A Small-sized [150 MWe] MSR “FUJI” U233 Pa233 Pa-reservoir

  41. 2. Reactor Physics Experiments Using Thorium - KUCA (Kyoto University Critical Assembly) • Central Test Zone (Th-232) + Surrounding Driver Zone (EU) • Spectral Shift Experiments by changing moderator-to-fuel ratio • Accelerator Driven System with Thorium-target (planned) • Verification of nuclear data (JENDL, ENDF/B) was done through k-eff, reaction rate distribution, neutron flux distribution. • Some problems have been found in the thermal and resonance capture cross sections. These problems have already been solved in JENDL-3.3.

  42. Conversion ratio & Pa-233 pile-upin the U-233-fueled & Pu(6%Th)-fueled MSR cores Without the reprocessing unit, the conversion ratio decreases with the burn-up time, leveling off at an equilibrium value 0.73. This is due to the pileup of Pa-233 in the core, which leads to loss of Pa-233 by neutron absorption.

  43. In-core Accumulation of U-233, U-234 etc. U-233-fueled core Pu-fueled core 233Pa(n,γ)234Pa→

  44. Accumulation of Pa-233 in the thermal core is not desirable, due to two reasons: 1- From neutron economy point of view, a considerable fraction* of neutrons are lost by Pa-233(n,γ), rather than by Th-232(n,γ). This also reduces the neutron flux in the core region. (* ~1.9% at 131 days of burn-up) 2- From fuel economy point of view, capture by Pa-233 implies loss of Pa-233 that would otherwise convert into U-233. For Th-loaded hard-spectrum ADS, Pa-233 can fission to produce energy.

  45. Summary • The Multimodal Madland-Nix Model provides a method of • calculating the PFNS, based on the multimodal analysis of fission. • Therefore it can be applied to evaluation of PFNS for actinides • and transactinides as well as for exotic nuclides far from beta- • stability line. 2. The methodology incorporates requirements from basic physics, such as energy conservation and shell effects, as well as other aspects of fission physics, such as mass and TKE distributions. 3. In order to finalize the remaining question of scission neutrons, and angular anisotropy of neutron emission, multi-parameter coincident measurement of angular and energy distributions of neutrons and FFs are required.

  46. 4. For Th-cycle nuclides, the quantity as well as quality of nuclear data is not so good as for U-Pu cycle. The author hopes some experimentalists will take on the work of measuring the PFNS, as well as mass & TKE distributions for Th-232, Pa-233 and U-233 with improved accuracy.

  47. • Mass and TKE distributions are consistently described as a superposition of components of a few fission modes of different properties. • Therefore, naturally, the TXE of FFs are different for different fission modes. TXE = ER + Ein + Bn - TKE • The shell correction energies demonstrate that the fission process is strongly governed by the fragment shell effects.

  48. • Experimental measurements and analyses have been done for (n,f), (sf) and (p,f) for many nuclides over wide range of energy up to Ep=200 MeV. Np-237(n,f) • Multimodal random-neck rupture (MM-RNR) model is, at present, the only model that can give consistent description of the 2D- distributions of mass and TKE of FFs. P. Siegler, F.-J. Hambsch et al. Nucl. Phys. A679 (2000) Gorodisskiy et al., Ann. Nucl. Energy 35 (2008)

  49. (1) Multimodal Nature : Experimental Evidence TKE Distribution for Various Fragment Mass Intervals ・TKE distributions for a fixed mass interval are distinctively different, and represented well with Gaussian functions U-235 S2 ・Charge-center distance deduced from the most probable TKE: S1 AD(fm) mode 13216.92 S1 140 17.37 S2 120 18.93 SL SL R.Müller et al. Phys. Rev. C29,885 (1984)

  50. Some Relevant Problems (1) How to consider neutrons emitted from numerous fragments of diverse excitation energy and of different nuclear properties? ●Single-modal approach: Madland & Nix, NSE 81(1982): Typical LF & HF ●Multimodal approach: Ohsawa et al., Nucl. Phys. A653 (1999); A665 (2000) ▪ 3 - 5 fission modes (Standard-1, -2, -3, Superlong, Super-asym.) ▪ Consider “average fragments” for each mode The physical properties were determined by seven-point approximation .

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