Fission Barriers in Compound Superheavy Nuclei Witold Nazarewicz University of Tennessee/ORNL APS April Meeting, Washing

1. Fission Barriers in Compound Superheavy Nuclei Witold Nazarewicz University of Tennessee/ORNL APS April Meeting, Washington DC February 13-17, 2010 Supported by by the Stewardship Science Academic Alliances NNSA grant DE-FG52-09NA29461 and by the NEUP grant DE-AC07-05ID14517 (sub award 00091100)

2. 240Pu 1938 - I. Joliot-Curie and P. Savitch, J. Phys. Rad. 9, 355 (1938) 1938 - Hahn & Strassmann, Naturwissenschaften 27, 11 (1939) 1939 - Meitner & Frisch 1939 - Bohr & Wheeler 1940 - Petrzhak & Flerov Fission N,Z elongation necking N=N1+N2 Z=Z1+Z2 split N2,Z2 N1,Z1

3. Why Focus on a Microscopic Nuclear Theory? • The nuclear problem is very complex, computationally difficult • Much of the progress in the past 50 years has been based on empirical models (most with microscopic degrees of freedom) tuned to experimental data • This highly limits our predictive capability • And it is difficult to estimate the uncertainties • Understanding of fission is important for basic science (nuclear structure, nuclear astrophysics) • Physics of fission has high societal relevance With a fundamental picture of nuclei based on the correct microphysics, we can remove the empiricism inherent today, thereby giving us greater confidence in science we produce

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. Microscopic description of complex nuclear decay: Multimodal fission • Staszczak, A.Baran, J. Dobaczewski, W.N., Phys. Rev. C 80, 014309 (2009)

6. Microscopic description of spontaneous fission Two-dimensional total energy surface for 258Fm in the plane of two collective coordinates: elongation, Q20, and reflection-asymmetry, Q30. Dashed lines show the fission pathways: symmetric compact fragments (sCFs) and asymmetric elongated fragments (aEFs). Nuclear shapes are shown as three-dimensional images that correspond to calculated nucleon densities. Two-dimensional total energy surface for 258Fm in the plane of two collective coordinates: elongation, Q20, and necking, Q40. Summary of fission pathway results obtained in this study. Nuclei around 252Cf are predicted to fission along the asymmetric path aEF; those around 262No along the symmetric pathway sCF. These two regions are separated by the bimodal symmetric fission (sCF + sEF) around 258Fm. In a number of the Rf, Sg, and Hs nuclei, all three fission modes are likely (aEF + sCF + sEF; trimodal fission). In some cases, labeled by two-tone shading with one tone dominant, calculations predict coexistence of two decay scenarios with a preference for one. Typical nuclear shapes corresponding to the calculated nucleon densities are marked. Calculated fission half lives of even-even fermium isotopes, with 242 ≤ A ≤ 260, compared with experimental data. A. Staszczak et al. Phys. Rev. C 80, 014309 (2009)

7. Fission barriers of compound superheavy nuclei • J. Pei, J. Sheikh, WN, A. Kerman, Phys. Rev. Lett. 102, 192501 (2009) • J. Sheikh, WN, J. Pei, Phys. Rev. C 80, 011302(R) (2009) • J.D. McDonnell, WN, and J.A. Sheikh, Proc. Fourth International Workshop On Nuclear Fission And Fission Product Spectroscopy, Cadarache, France, May, 13-16, 2009. AIP Conference Proceedings 1175, 371, (2009). Unique HFB solvers made this work possible: HFBAX: J.C. Pei et al., Phys. Rev. C 78, 064306 (2008) HFODD: J. Dobaczewski and P. Olbratowski, Comput. Phys. Commun. 158, 158 (2004); ibid.167, 214 (2005)

8. 226Ra 2008 238U 237Np 242Pu 245Cm 249Cf 2004 244Pu + 48Ca 243Am 248Cm hot fusion 2 events/year …also: 286,287114 48Ca+242Pu from LBNL From Y. Oganessian

10. Fission: isothermal or isentropic, or …? M. Diebel, K. Albrecht, and R.W. Hasse, Nucl. Phys. A 355, 66 (1981) M.E. Faber, M. Ploszajczak, and K. Junker, Acta Phys. Pol. B 15, 94 (1984) Numerical test

11. The lowest minimum warmer than the saddle point!

13. The damping factor can be meaningfully extracted:

14. Shell effects crucial!

16. Systematic Study of Fission Barriers of Excited Superheavy Nuclei • J. Sheikh, WN, J. Pei, Phys. Rev. C 80, 011302(R) (2009) • Focus on: • Mirror asymmetry and triaxiality at high temperatures • Systematic analysis of barrier damping

18. J.D. McDonnell, WN, J.A. Sheikh 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.

19. Surface Symmetry Energy and NEDF N. Nikolov, N. Schunck, W. Nazarewicz Leading terms in the leptodermous expansion Surface-symmetry term poorly determined in standard DFT, but crucial role in neutron-rich nuclei Mass A ~ 190 Deformation properties of LD driven by surface-symmetry term in neutron-rich nuclei ! Fission properties of neutron-rich U isotopes affected by poorly known assym Actinides Surface Surface-symmetry Curvature Coulomb (HF) 236U 248U 260U 270U 298U

20. Research goals, mid-term (1) • Applications of modern adiabatic and time-dependent theories • Use modern NEDF optimized for deformation effects • Investigate excitation energy dependence • Perform action minimization on many-dimensional meshes • Develop symmetry restoration schemes for DFT • Increase the number of collective coordinates in GCM, including pairing channel • Develop time-dependent framework for fission from excited states (T>0): ATDHFB and TDHFB

21. Collective inertia B(q) and ZPE Various prescriptions for collective inertia and ZPE exist: GOA of the GCMRing and P. Schuck, The Nuclear Many-Body Problem, 1980 ATDHF+Cranking Giannoni and Quentin, Phys. Rev. C21, 2060 (1980); Warda et al., Phys. Rev. C66, 014310 (2002) Goutte et al., Phys. Rev. C71, 024316 (2005) A.Baran et al., nucl-th/0610092 HFODD+BCS+Skyrme Recently, a nice progress with full ATDHFB inertia….

22. Research goals, mid-term (2) • Tests of non-adiabatic approaches • Non adiabatic tunneling, properly accounts for level crossings and symmetry breaking effects (collective path strongly influenced by level crossings). ATDHF not adequate • Evolution in an imaginary time • The lifetime is expressed by the sum of bounces • Difficulty in solving the periodic mean-field equations (fission bounce equations) • Important role of pairing correlations (restore adiabaticity) • Unclear how to restore broken symmetries bounce trajectory governing fission J. Skalski: Phys. Rev. C 77, 064610 (2008) Nuclear fission with mean-field instantons ATDHFB inertia

23. Fission was chosen as a principal research directions at workshop for computing at the extreme scale, see the summary report: http://extremecomputing.labworks.org/nuclearphysics/PNNL_18739_onlineversion_opt.pdf

24. Priority Research Direction: Fission Theory Scientific and computational challenges Summary of research direction Scientific: Tunneling and time-dependent dynamics of complex heavy nuclei. Computational: Implementation of highly nonlinear, nonlocal, multi-dimensional system of time-dependent integro-differential equations. Develop efficient solvers for the time-dependent (deterministic and stochastic) nuclear superfluid density functional theory (DFT). Solve the multi-dimensional optimization problem for collective action. Develop algorithms to compute bounce trajectories in imaginary time. Uncertainty quantification for complex nuclear processes. Potential impact on Nuclear Physics Problems that arise in NNSA/ASC? Expected Scientific and Computational Outcomes Validate and predict fission cross sections, fragment mass and energy distributions. Provide microscopic guidance (extrapolation capability) for phenomenological models of fission. Microscopic input to materials damage simulations. Neutron and photon spectra for stockpile simulation validation and nonproliferation. Scientific: Microscopic description, based on realistic internucleon interactions, of nuclear fission process. Explanation of tunneling motion of a many-body system. Computational: New fast multiresolution methods for the nuclear DFT. Implementation of new Importance Sampling Techniques for the time-dependent stochastic evolution equations.

25. Microscopic description of nuclear fission process Drivers: Improved understanding, validate and predict fission cross sections , fragment mass and energy distributions; neutron and photon spectra prediction; Uncertainty Quantification for complex nuclear processes Applications: Advanced Reactors, Stockpile Stewardship, Nuclear Forensics Prediction, Diagnostics Validation, Verification Present Exascale Peta

26. SUMMARY • Microscopic description of multimodal fission • Isentropic fission barriers and shell structure • Impact of shell effects on survival probability of superheavy compound nuclei • 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 tunneling is tough • We are developing a microscopic model that will be predictive • Fission probabilities • Properties of fission fragments • Cross section Thank You

27. Backup

28. Particle gas component Can be removed Its magnitude is related to particle width P. Bonche, S. Levit, and D. Vautherin, Nucl. Phys. A 427, 278 (1984); 436, 265 (1985)