Monte Carlo Simulation of Prompt Neutron Emission During Acceleration in Fission

1. IAEA/CRP on PFNS, Vienna, Dec. 13-16, 2011 Monte Carlo Simulation ofPrompt Neutron Emission DuringAcceleration in Fission ε q T.Ohsawa Kinki University Japanese Nuclear Data Committee

2. Prompt Fission Neutron Spectrum U-235(nth,f) U-235(nth,f) Overall agreement between Madland-Nix (MN) model calculation and experiments is good. Apparent discrepancy in the low-energy region (E<0.5 MeV).

3. What are the reasons for the discrepancy in the region En< 0.5 MeV? Possibilities: Uncertainties in the experimental data in the low-energy region. 2. Possible existence of scission neutrons. 3. Angular anisotropy in neutron emission in the CM-system of FF. 4. Possible effect of “yrast levels”. 5. Neutron emission during acceleration (NEDA), instead of after full acceleration. We should examine the possibilities from physics point of view.

4. 1. Uncertainties in experimental datain the low- energy region Uncertainties coming from ◆Scatted neutrons ◆ Low detection efficiency, … (after F.-J.Hambsch)

5. 2. Possible existence of scission neutrons. R. W. Fuller (1962)：　“volcano erupting” in the Fermi sea Recent work: N. Cârjan, P. Talou & O. Serot (2007)：　 Time-dep. Potential + 2D-Time-dep. Schrödinger eq. [N. Cârjan, P. Talou and O. Serot,Nucl. Phys. 792, 102 (2007)] ◆ The probability of occurrence and energy transfer in SCN emission should be treated on the physics ground, and not to be used as convenient tool for fittingto PFNS data.

6. 3. Angular anisotropy of emitted neutrons in the CM-system of FF. Experimental evidences: b=W(θ)/W(90º) – 1 >0 <J> = 7 - 8 More neutrons in the forward and backward directions ↓　　　　　　 　↓ Enhancement of High-energy and Low-energy wings Correlation between angle and energy [T. Ohsawa, INDC(NDS)-0541, p.71 (2009)]

7. 4. Possible effect of “yrast levels” Another effect of high angular momentum of FF: Transition to energy levels lower than yrast levels are prohibited. Soften the PFNS, the degree depending on Lower limit of energy after neutron evaporation

8. 5. Neutron Emission During Acceleration (NEDA) Neutron emission during acceleration Neutron emission after full acceleration Scission • Interest from Physics as well as Application point of view • In order to examine the NEDA effect, we have to analyze the competition: [A] Coulomb acceleration [deterministic process] [B] Neutron emission [stochastic process]

9. [A] Coulomb acceleration Relation between relative acceleration χand the time t after scission is described unambiguously by Eismont’s equation, once the FF charges and charge-center distance lare given. χ = KE / KEfinal vfinal =[2{(M-m)Mm}・1.44(Z-z)z/l]1/2 By treating the charge-center distance as a random variable, we can simulate the variance in TKE. l

10. [B] Neutron emission[stochastic process] • Monte Carlo approach is a suitable and effective method to treat the stochastic processes. • In order to simulate the competition accurately, it is important to evaluate the neutron emission timeτexactly. • τ is not a constant; rather it varies over a wide range, as will be shown later, depending on the excitation energy, level density and inverse reaction cross section. Level Density Formula • [T. Ericson, Adv. Phys. 9, 425 (1960)] Optical Model • τ were evaluated for four isobars with every mass number A of FF.

11. Initial Conditions for Monte Carlo Simulation (1) • 1. Multimodal Random Neck-Rupture Model was used to generate the mass , charge, TKE distributions of the primary fission fragments. 235U(n,f): 3 fission modes S1 S2 SL • Superposition of the modal distributions gives the total distribution. [K. Nishio] • Scission shape parameters were taken from H.-H. Knitter et al.(1987)for U-235

12. Initial Conditions for Monte Carlo Simulation (2) 2. TKE distribution was converted into the TXE distribution • Given the TKE distribution for a fission mode, the distribution of the charge-center distance is obtained. • The TXE distribution is calculated from energy-conservation relation. TXE =ER(ZH,AH,ZL,AL) + Bn + En – TKE

13. Initial Conditions for Monte Carlo Simulation (3) 3. Partition of the TXE between the two fragments Three working hypothesesin accordance with P.Talouet al. (2007) H0Equipartition of Energy H1Equitemperature assumption H2Partition according to ν(AL,H)

14. ε • Monte Carlo Code “NEDAEMON” • Select fission mode (S1, S2, SL, …) • Condition for Neutron Emission q • Sampling of (AL , ZL , TKE, I) • Neutron Spectrum in the CM-system • Calculation of ER, TXE, etc. • Mass formula • TEX Partition (H0, H1, H2) Random sampling • Cascade Process • Neutron Emission Time τ • Transformation into L-system • FF Acceleration Time t • NEDA Probability P(X), … • Excitation Energy of the Residual Nucleus • Accumulation of calculated data(Total of 109events) • PFNS calc. [NEDAPEK] l

15. Results (1) Frequency Distribution of the Number of Emitted Neutrons • The agreement with measured data as well as with other MC calculations is rather good, irrespective of the hypothesis H0, H1, H2. → Estimation of TXE in the present analysis is adequate.

16. Results (2) The Average Number of Neutrons Emitted from FF of Mass A • The saw-tooth structure is reproduced, without ad hoc adjustment. • Among the 3 hypotheses, H2 gives the best representation. → The following calculations were done with H2.

17. Results (3) The Neutron Emission Time as a Function of Mass for 235U Under different hypothesis For different fission modes H2 Our findings are: • The neutron emission time τvaries over a wide range from fragment to fragment. • The gross structure is caused by the shell effects on the LDP and Sn. • Fluctuations between neighboring FF is due to even-odd effect.

18. Results (4) NEDA probability as a function of χ NEDA probability is high at the final stage of accele- ration. A certain fraction of neutrons are certainly emitted before full acceleration. 235U(nth,f) The average value for 252Cf(sf) is ~16%, due to higher Q- value. χ 235U(nth,f) Integral NEDA probability

19. Results (5) PFNS with Consideration of NEDA Effect (Code NEDAPEK) ◆Single-fragment neutron spectrum ◆Modal neutron spectrum for mode i ◆Total neutron spectrum (summed over possible modes)

20. Results (6) PFNS with and without consideration of NEDA NEDA enhances the low-energy wing

21. Results (7) Angular anisotropy of emitted neutrons in the CM-system of FF [T. Ohsawa, INDC(NDS)-0541, p.71 (2009)] Two possibilities: b=0.05 C. Budtz-Jørgensenet al., INDC(NDS)-220, 181 (1989) b=0.1 V.F. Gerasimenkoet al., INDC(NDS)-220, 283 (1989) Result：→ Next page

22. NEDA + Anisotropy Taking into account the CM-anisotropy of neutron emission, in addition to NEDA-effect, in the multimodal Madland-Nix model, significantly enhances the low-energy componentand improves the agreement with experimental data in the region less than 0.5 MeV.

23. Conclusions Monte Carlo simulation of competition of Coulomb acceleration and neutron emission was made to examine the possibility of NEDA. 2. The initial condition for starting the Monte Carlo calculation was sampled from Multimodal Random Neck-Rupture model. 3. The simulation showed that~10% of neutrons were emitted before 90%-acceleration for 235U(nth,f); and ~16% for 252Cf(sf). 4. Existence of NEDA-neutrons enhances the low-energy wing of the PFNS. Consideration of CM-angular anisotropy of neutron emission, in addition to NEDA, further increases the low-energy component of the spectra and improves the agreement with experimental data in the region <0.5 MeV..

24. That’s it. Thanks!