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Fission at Intermediate Neutron Energies

Providing theoretical support for neutron cross sections measurements at the n_TOF facility at CERN to understand fission induced by intermediate energy nucleons. Utilizes fission detectors, PPAC detectors for measurements, and cascade-evaporation-fission models for simulations.

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Fission at Intermediate Neutron Energies

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  1. Fission at Intermediate Neutron Energies S. Lo Meo (a,c), D. Mancusi (b) , C. Massimi (c,d), G. Vannini (c,d), A. Ventura (c) • ENEA, Centro Ricerche Ezio Clementel, Bologna, Italy • CEA, Centre de Saclay, IRFU/SPhN, France • Istituto Nazionale di Fisica Nucleare, Bologna, Italy • Dipartimento di Fisica e Astronomia, Università di Bologna, Italy

  2. Intermediate Energy Fission 2 • Aim of the collaboration : • Theoretical support to the experimental campaign of neutron cross section measurements carried out since 2002 at the n_TOF(neutron time-of-flight) facility at CERN, Geneva.

  3. Intermediate Energy Fission 3 • The n_TOF facility • Neutrons with a broad energy spectrum ( ~10-2 eV < En < ~ 1 GeV) are produced by 20 GeV/c protons from the CERN Proton Synchrotron impinging on a lead block surrounded by a water layer acting as a coolant and a moderator of the neutron spectrum. • Neutron energies are measured by the time-of-flight method in a ~ 187 m flight path; hence the name of the collaboration. The neutron beam is used for measurements of neutron radiative capture and fission cross sections. • Basic reference: • C. Guerrero et al., Eur. Phys. J. A 49 (2013) 27

  4. Intermediate Energy Fission 4

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  6. Intermediate Energy Fission 6 • Fission detectors • Left: low-noise MicroMegas (MGAS) detector (1 fragment per fission), for cross sections only. • Right: set of parallel-plate avalanche counters (PPAC) (2 fragments per fission), can be used to measure angular distributions of fission fragments in addition to cross sections.

  7. Intermediate Energy Fission 7 • Fission cross sections are measured relative to235U(n,f) on the whole energy range from ~1 eV to ~ 1 GeV (left panel) and normalized to the evaluated σnf(235U) from ENDF/B-VIIup to 30 MeV and from JENDL/HE-2007 from 30 MeV to1 GeV (right panel). Data of 237Np(n,f) are from C.Paradela et al., Phys. Rev. C 82 (2010) 034601.

  8. Intermediate Energy Fission 8 • In measurements with PPAC detectors, not only fission cross section (left panel), but also angular anisotropy of fission fragments, W(00)/W(900), (right panel) can be determined. • Preliminary data of 232Th(n,f) by D. Tarrío et al. (2012).

  9. Intermediate Energy Fission 9 • Experimental vs. evaluated σnf(235U) at high energies (En > 50 MeV)

  10. Intermediate Energy Fission 10 • Fission induced by intermediate energy nucleons is usually considered as a two-stage process : • Fast intranuclear cascade, described as a succession of binary collisions, leading to the emission of fast nucleons, light fragments, pions, photons,… and leaving an excited residual nucleus, which decays by • Evaporation – fission (slow process). Different cascade-evaporation-fission models are available in the well-known simulation toolkit Geant4 ( version 9.6.0, November 2012).

  11. Intermediate Energy Fission 11 In the following plot the experimental cross section of the U-235(n,f) reaction in the energy range 100 < En < 200 MeV is compared with cross sections computed with different physics lists ( coupling of a high-energy string model, an intranuclear cascade and a de-excitation model ) using Geant4 default parameters. In particular, three cascade models are used : • Bertini model • Binary intranuclear cascade BIC (native model of Geant4) • Liège intranuclear cascade INCLXX .

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  13. Intermediate Energy Fission 13 The best comparison with experimental data is obtained with the Liège intranuclear cascade model INCLXX ; this is why Geant4 has been replaced in the analysis with much simpler stand-alone codes, basically a very recent version of the INCL model coupled with different evaporation-fission models, with the freedom of adjusting some crucial parameter in the latter for a better reproduction of experimental data. Summing up :

  14. Intermediate Energy Fission 14 • Theoretical tools for fission calculations at intermediate nucleon energies • (100 MeV – 2.5 GeV) : • Fast cascade stage : Liège intranuclear cascade model INCL++ (C++ version) • (A. Boudard, J. Cugnon, J.-C. David, S. Leray and D. Mancusi, Phys. Rev. C 87 (2013) 014606 andreferences therein)

  15. Intermediate Energy Fission 15 • Evaporation-fission of residual nuclei: • 1) GEMINI++ (C++ version) • (D. Mancusi, R.J. Charity and J. Cugnon, Phys. Rev. C 82 (2010) 044610 and references therein) • 2) ABLA07 • (A. Kelic, M.V. Ricciardi and K.-H. Schmidt, report INDC(NDS)-530, IAEA, Vienna, 2008, p. 181).

  16. Intermediate Energy Fission 16 • Main features of INCL++ • Target nucleus at the centre of a working sphere (WS) of radius Rmax = R0 + 8a , with R0the radius and a the diffuseness of target nucleus density. Incident nucleon located on the WS surface with its own impact parameter. Particles move along straight-line trajectories between collisions inside the WS. Binary collision model valid at Eproj > 100 MeV. Potential well inside the WS is isospin dependent, so that neutron and proton Fermi levels have the same energy. Potential well decreases with increasing nucleon energy and goes to zero at E ≈ 200 MeV.

  17. Intermediate Energy Fission 17 • Pauli blocking strictly applied in the first collision, stochastically applied in subsequent collision on the basis of final-state blocking factors → depletion of the Fermi sphere during the cascade stage. • Coalescence model based on phase space considerations permits formation and emission of light clusters(A < 8) in the cascade stage. • Possible excitation of nucleons to Δ resonances and subsequent production of pions, which can be reabsorbed or emitted through the WS → Eproj < 2.5 GeV. • Duration of cascade connected with the target mass by the empirical law tstop = 29.8 AT0.16fm/c (1 fm/c ≈ 3.3x10-24 sec).

  18. Intermediate Energy Fission 18 • Main features of GEMINI++ • Light particle evaporation described with the Hauser-Feshbach formalism (conservation of angular momentum). • An important ingredient of the decay width is the level density formula • ρ(E*,J) ~ (2J+1)exp[2√a(U,J)U] (Fermi gas-like) , • where U = E* - Erot (J) + δP (pairing correction) • anda(U) = ã(U)[1 + (δW/U)(1-exp(-ηU)] • (damping of shell correction δW according to Ignatyuk, but ã(U)contains energy-dependent long-range correlations)

  19. Intermediate Energy Fission 19 • ã(U) admits the limits • ã(0) = A/k0 , with k0 = 7.3 MeV, from neutron resonance counting, • ã(∞) = A/k∞, with k∞ = 12 MeV, from kinetic energy spectra of evaporated particles. • At intermediate energies it is taken of the form

  20. Intermediate Energy Fission 20 • Here, γ = 0.00493 exp (0.0332 A). • It is customary to assume that ãf(0), the level density parameter at the saddle point, used in fission calculations, is larger than ãn(0), the level density parameter used in neutron evaporation. The default value is ãf(0)/ ãn(0) =1.036. • Symmetric fission is described by Bohr-Wheeler decay width • ΓBW = ∫dερsad [E*- Bf (Jcn) – ε] / [2π ρcn(E*, Jcn)] • Binary decay (asymmetric fission) is described by Moretto’s conditional decay width • ΓZA = ∫dερsad [E*- BZA (Jcn) – ε]/[2π ρcn(E*, Jcn)] • where Z and A are charge and mass of one of the nascent fragments.

  21. Intermediate Energy Fission 21 • Main features of ABLA07 • Particle evaporation : Weisskopf-Ewing formalism with semiclassical correction for most probable orbital angular momentum. • Nuclear level density with collective enhancement factor : • ρ(E) = ρin(E) Kvib(E) Krot(E) • ρin(E) : constant temperature formula at low energy combined with Bethe formula at high energy, with shell and pairing corrections and Ignatyuk asymptotic level density parameter • ã = 0.073 A + 0.095 Bs A2/3 • with Bs the ratio of the surface of the deformed nucleus and a spherical one with same A.

  22. Intermediate Energy Fission 22 • High-energy fission : time-dependent fission width from approximate solution of one-dimensional Fokker-Planck equation in fission coordinate β : • Γf (t) = K(γ) ΓBW W(β = βs ; t , γ ) / W(β = βs ; t → ∞ , γ ) where : • K(γ) : Kramers factor depending on dissipation coefficient γ ; • ΓBW : Bohr – Wheeler fission width ; W : time-dependent distribution of fission coordinate β. • βs : fission coordinate at the saddle point. • Low-energy fission : standard two-humped fission barrier in the limit of full damping of resonances in intermediate well : • Γf = ΓA ΓB / (ΓA + ΓB ) .

  23. Intermediate Energy Fission 23 • Computational strategy • Parameters of fission models (basically ãf / ãn in GEMINI and ãf in ABLA) are calibrated on experimental (p,f) cross sections in the energy range 200 MeV – 1 GeV, given by Kotov et al., Phys. Rev. C 74 (2006) 034605 and are then applied to the calculation of (n,f) cross sections. • The theoretical ratios to the 235U(n,f) cross section are compared with the n_TOF ratios in the actinide region ( C. Paradela et al., Phys. Rev. C 82 (2010) 034601 ) and in the Pb-Bi region ( D. Tarrío et al., Phys. Rev. C 83 (2011) 044620).

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  26. Intermediate Energy Fission 26 • Mass distribution of fission fragments at En = 104.71 MeV (left panel) and En = 954.99 MeV (right panel) computed with INCL + ABLA07.

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  32. Intermediate Energy Fission 32 • Conclusions • INCL + ABLA07 is able to reproduce experimental (p,f) cross sections (Kotov 2006) and experimental ratios of (n,f) cross sections to 235U(n,f) (n_TOF data) in the Pb-Bi and actinide regions (with the exception of 237Np). • Absolute (n,f) cross sections are larger than those published by n_TOF in the energy region from 500 MeV to 1 GeV because of different normalization. • INCL + GEMINI is equivalent to the previous chain in the actinide region, but less satisfactory in the Pb-Bi region.

  33. Intermediate Energy Fission 33 • Outlook • Systematic analysis of (p,f) and (n,f) cross sections above 100 MeV for determination of ãf /ãn and other crucial parameters as a function of Z2/A. • Prediction of (n,f) cross sections to be measured by n_TOF. • Calculation of angular distributions of fission fragments.

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