1. Lawrence Livermore National Laboratory A Microscopic picture of scission DRAFT Version 1 March 15, 2010 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. Walid Younes

2. 2 Outline 1.Context for a microscopic theory of fission 2.Approaching scission 3.The nucleus near scission

3. 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 Many-body theory Fragment properties Fission-neutron spectrum Fission chain yields Fully-mic = HFB+TDGCM (more predictive, less acc) Mic+Stat. mech (more acc, less predictive) Informs/guides

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

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

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

7. 7 Fission and the role of collective coordinates: Q 20 and Q 30 240 Pu Most probable path

8. 8 Scission configurations in the Q 20 -Q 30 plane: 240 Pu hot fission Criterion: sudden drop In neck size Complex scission line shape Younes & Gogny, PRC 80, 054313 (2009)

9. 9 A more detailed view: the Q 40 collective coordinate Q 20 -Q 40 map for Q 30 = 0 b 3/2 well-defined troughs barrier between valleys Focus on symmetric fission

10. 10 A more detailed view: barrier between fusion & fission in Q 20 -Q 40 Physical Sciences Directorate - N Division 240 Pu, symmetric fission ~ 5.6 MeV barrier at Q 20 = 320 b, disappear gradually exit near 300 b (cold), 580 b (hot) or anywhere in between Berger et al., NPA 428, 23 (1984)

11. 11 Caveat: the Q 30 = 30 b 3/2 case barrier low, with gaps dynamics  can exit early Barrier from Q 20 -Q 40 map Q 40 analysis  exit points  fragment properties

12. 12 Controlling the approach to scission: the Q N coordinate 240 Pu, most prob. Q 30, hot fission 7.6-MeV discontinuity Calc at discontinuity with Q N discontinuity  large error in fragment properties Q N ~ neck size  controlled approach to scission discontinuity  large error in fragment properties Q N ~ neck size  controlled approach to scission Younes & Gogny, PRC 80, 054313 (2009)

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

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

15. 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 (Q N ) 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 E int = E HFB -E HFB (L)-E HFB (R)-E coul Work in representation that minimizes fragment tails EE Scission occurs as soon as E int =  E Scission can occur with Q N  0 Caveats: simplified 1D picture multi-dim fission  smaller  E available (Berger et al., NPA428, 23 (1984)) Scission occurs as soon as E int =  E Scission can occur with Q N  0 Caveats: simplified 1D picture multi-dim fission  smaller  E available (Berger et al., NPA428, 23 (1984)) Younes & Gogny, AIP proceedings 1175, 3 (2009)/arXiv:0910.1804v1

16. 16 Identifying the pre-fragments: choice of representation Q N = 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 E int

17. 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 unlocalized qp

18. 18 Tail reduction at scission: Q 20 = 365 b, Q 30 = 60 b 3/2, Q N = 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. 19 Results: comparison with observables for 239 Pu(n th,f) Total kinetic energy (expt data have  ~ 10 MeV) 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. 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. 21 Non-adiabatic separation of fragments  Start from HFB for 240 Pu with Q 20 = 350 b, Q N = 2  Apply unitary transform to localize those sp wave functions that extend into the complementary fragment (Younes & Gogny, arXiv:0910.1804v)  Translate pre-fragment densities ( Younes & Gogny, PRC 80, 054313 )  Calculate the energy

22. 22 The molecular-like microscopic picture of scission  Sharp drop at Q 20 = 370 b for adiabatic calc (hot fission)  Non-adiabatic calcs for different starting Q 20, Q N Scission barrier decreases with Q 20 and Q N For hot fission, scission barrier disappears between Q N = 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. 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(- E tot /T coll ) Z L,A L, ,T int Z H,A H, ,T int d T coll

24. 24 The semi-microscopic approach: Mass yields 236 U(n th,f) using LDM (Wilkins et al., 1976) 236 U(n th,f) using LDM (Wilkins et al., 1976) 239 Pu(n th,f) using microscopic theory (Our work, in progress…) 239 Pu(n th,f) using microscopic theory (Our work, in progress…) 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 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. 25 Conclusions  Quantitative, microscopic picture of scission is essential for a predictive theory of fission  Near scission, new collective d.o.f. become relevant (Q N, 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. 26 Application: interaction energy for 240 Pu symmetric fission Densities at large and small Q N Interaction energies as function of Q N This is nonsense! E int between well-separated fragments should be small, not > 3 GeV

27. 27 Caveat: topology of the PES and the need for fission dynamics Q 20 -Q 40 map for Q 30 = 60 b 3/2 valleys well separated again exit near Q 20 = 370 b