The limits of the nuclear landscape Witold Nazarewicz (U. Tennessee/ORNL/Warsaw)

1. The limits of the nuclear landscape Witold Nazarewicz (U. Tennessee/ORNL/Warsaw) APS April Meeting 2012, Atlanta, GA • Introduction • General principles • The landscape • Theoretical challenges • Nuclear DFT • The limits • Perspectives

2. 2007 NSAC Long Range Plan The Frontiers of Nuclear Science The intellectual drivers of nuclear physics today 14 questions in 2007 LRP • Fundamental aspects (reduction) • Nature of building blocks • Nature of fundamental interactions • Self-organization of building blocks (emergence) • Nature of composite structures and phases • Origin of simple patterns in complex systems • Societal applications

3. Resolution Hot and dense quark-gluon matter Hadron structure Hadron-Nuclear interface ab initio Nuclear structure Nuclear reactions CI Effective Field Theory DFT Third Law of Progress in Theoretical Physics by Weinberg: “You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you’ll be sorry!” Nuclear astrophysics New standard model Applications of nuclear science collective models

4. The Nuclear Landscape superheavy nuclei proton drip line neutron drip line • Protons and neutrons formed 10-6s-1s after Big Bang • H, D, He, Li, Be, B formed 3-20 min after Big Bang • Other nuclei born later in heavy stars and supernovae probably known up to oxygen 82 known up to Z=91 Z=118, A=294 126 protons terra incognita 50 82 neutron stars 28 20 50 stable nuclei 8 28 2 20 known nuclei 8 2 neutrons

5. The Nuclear Landscape… http://physics.aps.org/articles/v3/44 …as seen by the QCD phase diagram …as seen by astrophysicists Pethick and Ravenhall, Annu. Rev. Nucl. Part. Sci. 45, 429 (1995)

6. The Nuclear Landscape …as seen by Jefferson Lab W. Henning Doug Higinbotham A: 0, …, 1, 1, 2, 4, 208Pb, ∞

7. …as seen by chemists Periodic Table of Elements 2012 Lv Cn 113 115 118 117 116 112 Fl 114 IUPAC names 113: Ununtrium, Uut 115: Ununpentium, Uup 117: Ununseptium, Uus 118: Ununoctium, Uuo Z=112: Copernicium Z=114: Flerovium; Z=116: Livermorium

8. Happy the man who has been able to discern the cause of things Virgil, Georgica Theories Models • A third rate theory forbids • A second rate theory explains after the fact • A first rate theory predicts • A. Lomonosov

9. Physics of nuclei is demanding Input Forces, operators, parameters Many-body dynamics Open channels 11Li 208Pb 298U

10. The Nuclear Many-Body Problem Eigenstate of angular momentum, parity, and ~isospin talks by Steven Pieper and Bob Wiringa in 2010 coupled integro-differential equations in 3A dimensions

11. The nuclear landscape as seen by theorists … dimension of the problem Interfaces provide crucial clues

12. Guiding principles shell gap shell gap shell • NN interaction is short-ranged, spin- and isospin-dependent • Nucleonic mean fields and single-particle motion provide zeroth-order picture • Shell structure • Mean fields can break symmetry of nuclear Hamiltonian • Appearance of emergent behavior and collective modes • Symmetry-driven many-body coupling schemes • Correlations and quasiparticles • Quantum corrections • Openness • (Band) structures labeled by quantum numbers of the internally broken symmetries • Time scale of single-particle and collective motion not very different

13. microscopic mesoscopic empirical Triple Portrait of Cardinal Richelieu, Philippe de Champaigne (c. 1640), National Gallery, London

14. Old paradigms revisited. Crucial input for theory Magicity is a fragile concept Forces Many-body dynamics Open channels N=20 N=28 talk by Rick Casten in 2011 Shell energy from A. Gade M. Bender et al. Phys. Lett. B 515, 42–48 (2001)

15. Forces Many-body dynamics Open channels Living on the edge… Correlations and opennesszeroth-order picture questioned

16. Mean-Field Theory ⇒ Density Functional Theory Electronic DFT: Hohenberg, Kohn (Nobel1999), Sham… Bohr-Mottelson, Landau-Migdal, Bogoliubov-Belyaev, Brueckner, Negele-Vautherin, Baranger, Strutinski… Degrees of freedom: nucleonic densities • two fermi liquids • self-bound • superfluid • continuum space crucial Nuclear DFT: • mean-field ⇒ one-body densities • zero-range ⇒ local densities • finite-range ⇒ gradient terms • particle-hole and pairing channels • Self-consistency guaranteed via HFB equations • Time-dependent extension: TDDFT • Has been extremely successful. A broken-symmetry generalized product state does surprisingly good job for nuclei. • Broken symmetries imply the existence of collective degrees of freedom (shape-, pairing-, spin-, isospin-deformations) Scott Bogner Eliminates, describes, predicts…

17. Nuclear Density Functional Theory: applications Traditional (limited) functionals provide quantitative description BE differences Mass table dm=0.581 MeV Goriely, Chamel, Pearson: HFB-17 Phys. Rev. Lett. 102, 152503 (2009) Cwiok et al., Nature, 433, 705 (2005)

18. Description of observables and model-based extrapolation • Systematic errors (due to incorrect assumptions/poor modeling) • Statistical errors (optimization and numerical errors) Erler et al.

19. The limits: Skyrme-DFT Benchmark 2012 288 ~3,000 Asymptotic freedom ? How many protons and neutrons can be bound in a nucleus? Literature: 5,000-12,000 from B. Sherrill Skyrme-DFT: 6,900±500syst Erler et al.

20. Quadrupole ground-state shape deformations

21. Example: Large Scale Mass Table Calculations Skyrme-DFT mass table, embarrassingly parallel • 5,000 even-even nuclei, 250,000 HFB runs, 9,060 processors – about 2 CPU hours • Full mass table: 20,000 nuclei, 12M configurations — full JAGUAR Cray XT5

22. Exotic topologies of superheavy nuclei: Coulomb frustration Self-consistent calculations confirm the fact that the “pasta phase” might have a rather complex structure, various shapes can coexist, at the same time significant lattice distortions are likely and the neutron star crust could be on the verge of a disordered phase. A challenge is to assess stability of such forms

23. LACM, Fission: the ultimate challenge Stability of the heaviest nuclei, r-process, advanced fuel cycle, stockpile stewardship… Optimized Functionals Large-scale DFT Collective dynamics PRC 85, 024304 (2012) PRC 84, 054321(2011) Confrontation with experiment; predictions PRC 80, 014309 (2009) Numerical Techniques PRC 80, 014309 (2009) PRC 78, 014318 (2008)

24. P. Pyykkö: A suggested Periodic Table up to Z ≤ 172, based on Dirac-Fock calculations on atoms and ions, Phys. Chem. Chem. Phys. 13, 161-168 (2011) “Half of chemistry is still undiscovered. We don't know what it looks like and that's the challenge” The limit of mass and charge is still undiscovered. We don't know what it looks like and that's the challenge.

25. The challenge: isovector fields, quest for isovector indicators Neutron skin: Antiprotonic atoms: Proton elastic scattering: Piekarewicz et al., PRC arXiv:1201.3807 S. Abrahamyan et al. (PREx Collaboration), Phys. Rev. Lett. 108, 112502 (2012) Strong correlation between the dipole polarizability aD and neutron skin predicted by DFT : PRC C 81, 051303(R) (2010) PREx: FW(q) RCNP: aD A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011) Theory: • Next: • PREx(II) • New PREx measurement for 48Ca… • RCNP data on aD in 48Ca… Systematic error dominates

26. Microscopic calculations of isospin-breaking corrections to superallowed b-decay Superallowed Fermi 0+ →0+-decay studies Kobayashi and Maskawa: … for "the discovery of the origin of broken symmetry, which predicts the existence of at least three families of quarks in nature." Impressive experimental effort worldwide 0.9999(6) nuclear meson decay Isospin-projected DFT W. Satuła et al., PRL 106, 132502 (2011) Towner and Hardy 2010

27. Future: large multi-institutional efforts involving strong coupling between physics, computer science, and applied math http://unedf.org/ Theory is developing new statistical tools to deliver uncertainty quantification and error analysis for theoretical studies as well as for the assessment of new experimental data. Such technologies are essential as new theories and computational tools are explicitly intended to be applied to entirely new nuclear systems and conditions that are not accessible to experiment.

28. Some nuclei are more important than others - + - + - + tests of fundamental laws of nature nuclear structure + - + - 45Fe 149Tb astrophysics applications 18F,22Na 225Ra Over the last decade, tremendous progress has been made in techniques to produce and describe designer nuclei, rare atomic nuclei with characteristics adjusted to specific research needs and applications a prototypical nuclear physicist…

29. Very special thanks as well to: Principal Collaborators • Jacek Dobaczewski • Andras Kruppa • Nicolas Michel • Marek Płoszajczak • P.-G. Reinhardt • Wojtek Satuła • Nicolas Schunck • Andrzej Staszczak • Tamas Vertse • … • Stefan Ćwiok • Georg Leander • Mario Stoitsov • Zdzisław Szymański • Cyrus Baktash • Carroll Bingham • Peter Butler • Larry Cardman • Rick Casten • Bob Chapman • David Dean • Jerry Draayer • Jurek Dudek • Dick Furnstahl • Jerry Garrett • Carl Gross • Joe Hamilton • Paul-Henri Heenen • Robert Janssens • Kenichi Matsuyanagi • Erich Ormand • Thomas Papenbrock • Ingemar Ragnarsson • Lee Riedinger • Mark Riley • Kris Rykaczewski • Brad Sherrill • Soren Sorensen • Ramon Wyss • … Thank you !!!

30. Outlook The study of atomic nuclei makes the connection between the fundamental building block of matter, complex systems, and the cosmos • Exciting • Interdisciplinary • Relevant Over the last decade, tremendous progress has been made in techniques to produce rare atomic nuclei with characteristics adjusted to specific research needs. Guided by unique data on short-lived nuclei, we are embarking on a comprehensive study of all nuclei based on the most accurate knowledge of nuclear interactions, the most reliable theoretical approaches, and the massive use of the computer power available at this moment in time. The prospects are excellent. Thank You