1. Lawrence Livermore National Laboratory Daniel Gogny’s Vision for a Microscopic Theory of Fission DRAFT Version 1 First Gogny Conference, December 2015 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. W. Younes

2. 2 LLNL-PRES-678798-DRAFT A NEET beginning  Met Gogny through John Becker (2003)  First project on Nuclear Excitation by Electronic Transition From there, we turned our attention to the fission problem…

3. 3 LLNL-PRES-678798-DRAFT Breaking down the problem: three stages of fission One nucleus Two nuclei Scission line = boundary

4. 4 LLNL-PRES-678798-DRAFT The big questions  How to describe initial states?  What are the appropriate collective d.o.f.?  How to describe the coupling between collective and intrinsic d.o.f.?  What is scission?  How to describe the fission process consistently across the scission boundary?  How to extract fission-fragment mass & energy distributions? Gogny tackled all these questions! Scission in particular would become the centerpiece of our collaboration Gogny tackled all these questions! Scission in particular would become the centerpiece of our collaboration

5. 5 LLNL-PRES-678798-DRAFT Some influential work J.-F. Berger et al., NPA502, 85 (1989) ➞ fission dynamics W. Norenberg, IAEA-SM-122/30, 51 (1969) ➞ molecular model of fission M. Warda et al., PRC 66, 014310 (2002) ➞ neck constraint H. Goutte et al., PRC 71, 024316 (2005) ➞ fragment mass and TKE P. Lichtner et al., PLB 45, 175 (1973) ➞ frag separation & asymm. as d.o.f. Dubray et al., PRC 77, 014310 (2008) ➞ fragment properties Dubray et al., PRC 77, 014310 (2008) ➞ fragment properties

6. 6 LLNL-PRES-678798-DRAFT A first brush with scission 240 Pu neck size, pre- and post-scission Lingering questions: Where is scission? Where are the missing fragment masses? Lingering questions: Where is scission? Where are the missing fragment masses?

7. 7 LLNL-PRES-678798-DRAFT The scission problem (semi-) classical picture K. T. R. Davies et al., PRC 16, 1890 (1977) K. T. R. Davies et al., PRC 16, 1890 (1977) 240 Pu, Q 30 free Quantum-mechanical description is non-local ⇒ fragments have “tails”

8. 8 LLNL-PRES-678798-DRAFT The scission problem, and a quantum-mechanical solution Sir John Lennard-Jones, Proc. Roy. Soc. A 198, 14 (1949): We are free to choose the representation in which we analyze HF (or HFB) results Younes & Gogny, PRL 107, 132501 (2011) Quantum localization Quantum-mechanical definition of scission Realistic fragment kinetic & excitation energies Dynamical description beyond scission Change in nature of collective d.o.f. near scission Quantum-mechanical definition of scission Realistic fragment kinetic & excitation energies Dynamical description beyond scission Change in nature of collective d.o.f. near scission

9. 9 LLNL-PRES-678798-DRAFT We need better collective coordinates near scission  In practice: there isn’t a one-to-one relation between Q 30 and A  As the nucleus nears scission, local constraints (constraints on the individual pre-fragments) become important  So, instead of Q 20 and Q 30, near scission we work with:

10. 10 LLNL-PRES-678798-DRAFT How do we get the probability of populating the scission points? 240 Pu collective levels from GCM Time evolution of probability current

11. 11 LLNL-PRES-678798-DRAFT Results: 239 Pu(n,f) fragment mass distributions for E n = 0-5 MeV Microscopic calc Schillebeeckx (92) GEF code, Schmidt et al. (11) Younes et al., Proc. ICFN5, p. 605 (2012)

12. 12 LLNL-PRES-678798-DRAFT Results: 235 U(n,f) fragment mass distributions for E n = 0-5 MeV Microscopic calc Straede (87) Younes et al., Proc. ICFN5, p. 605 (2012)

13. 13 LLNL-PRES-678798-DRAFT Calculating fragment energies  Static contribution, After quantum localization of pre-fragments: Integrate energy density for each fragment separately, allow each to relax to its minimum energy, difference gives excitation energy Coulomb energy gives kinetic energy  Dynamic contribution (pre-scission energy) Use flux in the fission direction ( d ) to give excitation/kinetic partition Q E CN E pre kinetic E diss excitation E int kinetic E def (1), E def (2) excitation From dynamic calculations From static calculations

14. 14 LLNL-PRES-678798-DRAFT Results: fragment energy distributions 235 U(n th,f) 239 Pu(n th,f) Younes et al., Proc. ICFN5, p. 605 (2012) Starting from protons, neutrons, and effective interaction: Results consistent with experiment! Starting from protons, neutrons, and effective interaction: Results consistent with experiment!

15. 15 LLNL-PRES-678798-DRAFT Where do we go from here?  The definition and evolution of the collective d.o.f. is an active area of research Y. Tanimura et al., PRC 92, 034601 (2015)  Moving away from density dependent interactions  Fragment properties in particle-number-projected calculations  The great unknown: coupling between collective and intrinsic d.o.f. R. Bernard et al., PRC 84, 044308 (2011)