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A Microscopic picture of scission

A Microscopic picture of scission. March 15, 2010. Walid Younes. DRAFT Version 1. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Outline.

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A Microscopic picture of scission

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  1. A Microscopic picture of scission March 15, 2010 WalidYounes DRAFT Version 1 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  2. Outline • Context for a microscopic theory of fission • Approaching scission • The nucleus near scission

  3. Overview of LLNL program • Goal: predict fission-fragments properties (energies, shapes, yields) as a function of incident energy • Two complementary approaches • Common to both: what is the microscopic picture of scission? • Crucial to understanding the entire fission process • Crucial to the extraction of realistic fragments properties Fully-mic = HFB+TDGCM (more predictive, less acc) Fission-neutron spectrum Fragment properties Many-body theory Informs/guides Fission chain yields Mic+Stat. mech (more acc, less predictive)

  4. Physical Sciences Directorate - N Division Fully microscopic approach to fission: The Big Picture PES Time-evolving wave packet Finite-range eff. interaction Statics Frag props Scission id Fission times HFB Collective Hamiltonian Fission yields Constraints Yield-avg’ed frag props dynamics TDGCM + qp d.o.f. Coll-intr coupling Based on highly successful BIII program Non-adiabatic Higher E Fully microscopic, quantum-mechanical, dynamic approach Effective interaction is the only phenomenological input

  5. Past successes Predicts 238U(,f) TKE to 6% Predicts/explains cold & hot fission Reproduces yields for 238U(,f) Predicts realistic Fission times Berger et al. NPA 502, 85 (1989) CPC 63, 365 (1991) Goutte et al., PRC 71 , 024316 (2005)

  6. Approaching scission • What are the relevant degrees of freedom near scission • Discontinuities along the path to scission?

  7. Fission and the role of collective coordinates: Q20 and Q30 Most probable path 240Pu

  8. Scission configurations in the Q20-Q30 plane: 240Pu hot fission • Criterion: sudden drop • In neck size • Complex scission line • shape Younes & Gogny, PRC 80, 054313 (2009)

  9. A more detailed view: the Q40 collective coordinate Focus on symmetric fission Q20-Q40 map for Q30 = 0 b3/2 • well-defined troughs • barrier between valleys

  10. Physical Sciences Directorate - N Division A more detailed view: barrier between fusion & fission in Q20-Q40 240Pu, symmetric fission • ~ 5.6 MeV barrier at Q20 = 320 b, disappear gradually • exit near 300 b (cold), 580 b (hot) or anywhere in between • Berger et al., NPA 428, 23 (1984)

  11. Caveat: the Q30 = 30 b3/2 case Barrier from Q20-Q40 map • barrier low, with gaps • dynamics  can exit early Q40 analysis  exit points  fragment properties

  12. Controlling the approach to scission: the QN coordinate 240Pu, most prob. Q30, hot fission Calc at discontinuity with QN 7.6-MeV discontinuity Younes & Gogny, PRC 80, 054313 (2009) • discontinuity  large error in fragment properties • QN ~ neck size  controlled approach to scission

  13. Identifying scission • How do we identify scission microscopically? • How do we identify the pre-fragments? • What are the fission-fragment properties?

  14. The path to refining our microscopic picture of scission • distinguishes pre and post configurations • doesn’t pinpoint scission Geometric criterion (e.g., neck size) • pinpoints scission • adiabatic treatment of scission Interaction-energy criterion Microscopic, non-adiabatic treatment Molecular-like picture ( variation of interaction energy)

  15. Energy-based criterion for identifying the scission configuration • Idea: scission occurs as soon as there is enough energy in system to overcome attractive interaction between fragments • Use neck size (QN) as constraint to approach scission • Identify s.p. wavefunctions for left and right fragments • tot1 + 2 + 212, with 12 0 at large separation • Calculate Eint = EHFB-EHFB(L)-EHFB(R)-Ecoul • Work in representation that minimizes fragment tails • Scission occurs as soon as Eint = E • Scission can occur with QN 0 • Caveats: • simplified 1D picture • multi-dim fission  smaller E available (Berger et al., NPA428, 23 (1984)) E Younes & Gogny, AIP proceedings 1175, 3 (2009)/arXiv:0910.1804v1

  16. Identifying the pre-fragments: choice of representation QN = 0.01 • HFB solution defined up to unitary trans • Free to choose representation • Arbitrary rep can lead to large frag tails • With microscopic def of fragments, we see the tails • Tail-minimizing rep (via orthogonal transformation of s.p. wave funcs) • produces reasonable Eint

  17. Choosing a representation that minimizes tails • Define localization parameter • For a pair of states: • Identify pairs of states (i,j) and angle  such that • Gives 1 for completely localized qp 0 for completely unlocalizedqp

  18. Tail reduction at scission: Q20 = 365 b, Q30 = 60 b3/2, QN = 1.55 Before wave function localization After wave function localization • Operation does not affect total energy, but allows • identication of left and right pre-fragments • definition of a separation distance • calculation of interaction energy

  19. Results: comparison with observables for 239Pu(nth,f) Total kinetic energy (expt data have  ~ 10 MeV) Average neutron multiplicity Remarkable results for a parameterless calculation! Younes & Gogny, AIP proceedings 1175, 3 (2009)/arXiv:0910.1804v1

  20. The molecular-like picture of scission • Competition between attractive nuclear and repulsive Coulomb forces creates scission valley and barrier • Requires non-adiabatic calculation, otherwise no scission barrier: • stop HFB calcs at config where there is almost no nuclear interaction between pre-fragments • “freeze” pre-fragment configs • separate by translation • sudden approximation W. Nörenberg, IAEA-SM-122/30, 51 (1969).

  21. Non-adiabatic separation of fragments • Start from HFB for 240Pu with Q20 = 350 b, QN = 2 • Apply unitary transform to localize those sp wave functions that extend into the complementary fragment (Younes & Gogny, arXiv:0910.1804v) • Translate pre-fragmentdensities (Younes & Gogny, PRC 80, 054313) • Calculate the energy

  22. The molecular-like microscopic picture of scission • Sharp drop at Q20 = 370 b for adiabatic calc (hot fission) • Non-adiabatic calcs for different starting Q20, QN • Scission barrier decreases with Q20 and QN • For hot fission, scission barrier disappears between QN = 1 and 2 • This is still a static picture • TDGCM  dynamics • Pre-scission energy available to overcome scission barrier • Some of that energy may be taken up by collective transverse d.o.f. (Berger et al., NPA428, 23 (1984)) and, possibly, intrinsic excitations

  23. Application: microscopic Wilkins model for mass yields • Based on Wilkins et al., PRC 14, 1832 (1976). (See also S. Heinrich thesis) • Static microscopic calcs of fragments at many deformations • Calculate energy of two-fragment system as a function of separation d • Identify distance d at scission such that • Boltzmann factor gives probability distributions: exp(-Etot/Tcoll) d ZH,AH,b,Tint ZL,AL,b,Tint Tcoll

  24. The semi-microscopic approach: Mass yields 239Pu(nth,f) using microscopic theory (Our work, in progress…) 236U(nth,f) using LDM (Wilkins et al., 1976) • Already better than LDM. Should improve with: • proper treatment of anti-symmetrization • more fragments included • intrinsic temperature • revisit Pauli blocking in odd-A and odd-odd nuclei

  25. Conclusions • Quantitative, microscopic picture of scission is essential for a predictive theory of fission • Near scission, new collective d.o.f. become relevant (QN, d) • Molecular-like picture of fission provides solid framework to understand scission • Requires the identification of left and right pre-fragments and their interaction energy • Microscopic definition of scission • Sudden approximation at scission • Non-adiabatic separation of the fragments

  26. Application: interaction energy for 240Pu symmetric fission Densities at large and small QN Interaction energies as function of QN This is nonsense! Eint between well-separated fragments should be small, not > 3 GeV

  27. Caveat: topology of the PES and the need for fission dynamics Q20-Q40 map for Q30 = 60 b3/2 • valleys well separated again • exit near Q20 = 370 b

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