Microscopic Description of Fission Process Witold Nazarewicz (PI) / Jordan McDonnell (speaker)

1. Microscopic Description of Fission Process Witold Nazarewicz (PI) /Jordan McDonnell (speaker) University of Tennessee SSAA grant DE-FG52-09NA29461 N,Z elongation necking N=N1+N2 Z=Z1+Z2 split N2,Z2 N1,Z1

2. http://www.phys.utk.edu/witek/fission/fission.html Funded 2003

3. UTK/ORNL Team 1 Permanent researcher: Witold Nazarewicz 2 PhD students: Jordan McDonnell, Nikola Nikolov 1Postdoc: JochenErler (will join the group in early 2011) 2 Visiting professors: AndrzejStaszczak and AndrzejBaran Arthur Kerman + Several foreign collaborators + UNEDF Nicolas Schunck Joined Nuclear Theory and Modeling Group at LLNL. Fall 2010 Fellow: DOE NNSA SSGF

4. Powerful phenomenology exists… • … but no satisfactory microscopic understanding of: • Barriers • Fission half-lives and mass/energy splits • Fission dynamics • Cross sections • … • What is needed? • Expertise in nuclear theory • Collaborative efforts focused on programmatic needs • Microscopic many-body techniques • Computational algorithms • Hardware

5. Augmented Lagrangian Method for Fission A. Staszczak et al., Eur. Phys. J. A 46, 85 (2010) The quadratic penalty method (QPM), frequently used in constrained DFT calculations for fission, often fails to deliver the requested average value of the collective operator with an acceptable accuracy. In the Augmented Lagrangian Method (ALM), a linear constraint is applied together with a quadratic penalty function, and this guarantees that the constrained calculations properly converge. The ALM has been implemented in UNEDF DFT solvers HFODD and HFBTHO solvers A comparison between the ALM (black squares) and the standard QPM (open squares) for the constrained self-consistent convergence scheme. The DFT calculations were carried out for the total energy surface of 252Fm in a two-dimensional plane of elongation, Q20, and reflection-asymmetry, Q30. Although QPM often fails to produce a solution at the required values of constrained variables on a rectangular grid, ALM performs very well in all cases. Two dimensional constrained calculations in a (Q20,Q30) plane for 252Fm performed with HFODD using the ALM. Compared with the standard quadratic penalty method, one can see interesting physics in the region which was inaccessible by the latter approach, namely the appearance of the second (fusion) valley at large values of Q30 separated from the spontaneous fission valley by a steep ridge.

6. Collective inertia B(q) and ZPE Abstract. Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

7. J.D. McDonnell et al. A highlight in 2011 SSAA Magazine! Potential energy surfaces are calculated for the spontaneous fission of light actinides with (finite-temperature) HF+BCS theory. The fission path favors more symmetric scission configurations as excitation energy increases.

9. Surface Symmetry Energy and NEDF Ph.D. of N. Nikolov, Phys. Rev. C, in press (2011)

11. Quality Control Integral to this project is the verification of methods and codes, the estimation of uncertainties, and assessment. • Verification and Validation • Cross-check of different theory methods and codes • Multiple DFT solvers; benchmarking • Uncertainty Quantification and • Error Analysis • Tools for correlation analysis to estimate errors and significance • Uncertainty analysis • Assessment • Development and application of statistical tools • Analysis of experimental data significance Earlier fit (some masses from systematics) Final fit

12. Annual LACM/Fission Workshops 2004 Annual Workshop Theoretical Description of the Nuclear Large Amplitude Collective Motion (with a focus on fission) March 17-19, 2004, Joint Institute for Heavy Ion Research, Oak Ridge Attended by 25 participants 2005 Annual Workshop The Second International Workshop on the Theoretical Description of the Nuclear Large Amplitude Collective Motion March 30 - 31, 2005, Joint Institute for Heavy Ion Research, Oak Ridge. Attended by 21 participants 2007 Annual Workshop The 1st JUSTIPEN-LACM Meeting March 5-8, 2007, Joint Institute for Heavy Ion Research, Oak Ridge Attended by 60 participants 2008 Annual Workshop The 2nd LACM-EFES-JUSTIPEN Meeting January 23-25, 2008, Joint Institute for Heavy Ion Research, Oak Ridge Attended by 70 participants 2009 Annual Workshop The 3rd LACM-EFES-JUSTIPEN Meeting February 23-25, 2009, Joint Institute for Heavy Ion Research, Oak Ridge Attended by 90 participants 2010 Annual Workshop The 4th LACM-EFES-JUSTIPEN Meeting March 15-17, 2010, Joint Institute for Heavy Ion Research, Oak Ridge Attended by 50 participants All meetings involved participants from NNSA/DP Laboratories (LANL, LANL, NNSA), as well as many students and post-docs. 2011 Annual Workshop The 5thLACM-EFES-JUSTIPEN Meeting March 15-17, 2011 http://massexplorer.org/justipen/

13. SUMMARY • There are fundamental problems in fission that cry to be solved • Basic science (nuclear structure, nuclear astrophysics) • Programmatic needs • Fission is a perfect problem for the extreme scale • Quantum many-body problem is tough! • We are developing a microscopic model that will be predictive • Fission probabilities • Properties of fission fragments • Cross sections • Level densities • Quantification of Margins and Uncertainties is important