Shell Structure of Exotic Nuclei ( a Paradigm Shift?)

1. Shell Structure of Exotic Nuclei (a Paradigm Shift?) Witold Nazarewicz (University of Tennessee/ORNL) LLNL Seminar, August 20, 2007 • Introduction • The nuclear many-body problem • Shell structure revisited • The nucleus: correlated, open quantum system • Perspectives Emphasis on: novel aspects recent results problems

3. Distance heavy nuclei Energy few body quarks gluons vacuum quark-gluon soup QCD nucleon QCD few body systems free NN force many body systems effective NN force The Nuclear Many-Body Problem Energy, Distance, Complexity Different degrees-of-freedom radioactive beams electron scattering relativistic heavy ions

4. How do protons and neutrons make stable nuclei and rare isotopes? What is the origin of simple patterns in complex nuclei? What is the equation of state of matter made of nucleons? What are the heaviest nuclei that can exist? When and how did the elements from iron to uranium originate? How do stars explode? What is the nature of neutron star matter? How can our knowledge of nuclei and our ability to produce them benefit the humankind? Life Sciences, Material Sciences, Nuclear Energy, Security Questions that Drive the Field Physics of nuclei Nuclear astrophysics Applications of nuclei

5. Recent years: very successful period for theory of nuclei • many new ideas leading to new understanding • new theoretical frameworks • exciting developments • high-quality calculations • The nucleon-based description works to <0.5 fm • Effective Field Theory/Renormalization Group provides missing links • Accurate ab-initio methods allow for interaction tests • Quantitative microscopic nuclear structure • Integrating nuclear structure and reactions • High-performance computing continues to revolutionize microscopic nuclear many-body problem: impossible becomes possible

6. Weinberg’s Laws of Progress in Theoretical Physics From: “Asymptotic Realms of Physics” (ed. by Guth, Huang, Jaffe, MIT Press, 1983) First Law: “The conservation of Information” (You will get nowhere by churning equations) Second Law: “Do not trust arguments based on the lowest order of perturbation theory” Third Law: “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!”

8. Ab initio: GFMC, NCSM, CCM (nuclei, neutron droplets, nuclear matter) • Quantum Monte Carlo (GFMC) 12C • No-Core Shell Model 13C • Coupled-Cluster Techniques 40Ca • Faddeev-Yakubovsky • Bloch-Horowitz • … • Input: • Excellent forces based on the phase shift analysis • EFT based nonlocal chiral NN and NNN potentials deuteron’s shape GFMC: S. Pieper, ANL 1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed The nucleon-based description works to <0.5 fm

9. Shell effects and classical periodic orbits • One-body field • Not external (self-bound) • Hartree-Fock Shells • Product (independent-particle) state is often an excellent starting point • Localized densities, currents, fields • Typical time scale: babyseconds (10-22s) • Nuclear box is not rigid: motion is seldom adiabatic • Closed orbits and s.p. quantum numbers The action integral for the periodic orbit

10. Pronounced shell structure (quantum numbers) Shell structure absent shell gap shell gap shell closed trajectory (regular motion) trajectory does not close

11. Shells 10 experiment experiment 0 Nuclei theory -10 Shell Energy (MeV) theory 0 20 28 50 -10 discrepancy 82 126 0 diff. 1 experiment -10 20 60 100 Number of Neutrons 0 58 92 198 138 -1 Shell Energy (eV) Sodium Clusters spherical clusters theory 1 0 -1 deformed clusters 50 100 150 200 Number of Electrons P. Moller et al. S. Frauendorf et al. • Jahn-Teller Effect (1936) • Symmetry breaking and deformed (HF) mean-field

13. Modern Mean-Field Theory = Energy Density Functional mean-field ⇒ one-body densities zero-range ⇒ local densities finite-range ⇒ gradient terms particle-hole and pairing channels • Hohenberg-Kohn • Kohn-Sham • Negele-Vautherin • Landau-Migdal • Nilsson-Strutinsky

14. From Qualitative to Quantitative! • Nuclear DFT • two fermi liquids • self-bound • superfluid • Deformed Mass Table in one day! • HFB mass formula: m~700keV • Good agreement for mass differences UNEDF SciDAC-2

15. Bimodal fission in nuclear DFT nucl-th/0612017 A. Staszczak, J. Dobaczewski W. Nazarewicz, in preparation

16. Magicity is a fragile concept Near the drip lines nuclear structure may be dramatically different.

17. First experimental indications demonstrate significant changes No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32…

18. Prog. Part. Nucl. Phys. 59, 432 (2007)

19. Neutron Drip line nuclei 6He 4He 8He HUGE D i f f u s e d PA IR ED 5He 7He 9He 10He

20. `Alignment’ of w.b. state with the decay channel Thomas-Ehrmann effect 4946 12C+n 3/2 3685 3502 3089 1/2 2365 1943 12C+p 16O 1/2 13C7 13N6 The nucleus is a correlated open quantum many-body system Environment: continuum of decay channels 7162 6049 Spectra and matter distribution modified by the proximity of scattering continuum

21. Unique geometries of light nuclei due to the threshold effects Exotic decay channels Miernik et al. (Warsaw-MSU-Tennessee)

22. The importance of the particle continuum was discussed in the early days of the multiconfigurational Shell Model and the mathematical formulation within the Hilbert space of nuclear states embedded in the continuum of decay channels goes back to H. Feshbach (1958-1962), U. Fano (1961), and C. Mahaux and H. Weidenmüller (1969) • unification of structure and reactions • resonance phenomena generic to many small quantum systems coupled to an environment of scattering wave functions: hadrons, nuclei, atoms, molecules, quantum dots, microwave cavities, … • consistent treatment of multiparticle correlations Open quantum system many-body framework Gamow (complex-energy) Shell Model (2002 -) N. Michel et al, PRL 89 (2002) 042502 R. Id Betan et al, PRL 89 (2002) 042501 N. Michel et al, PRC 70 (2004) 064311 G. Hagen et al, PRC 71 (2005) 044314 Continuum (real-energy) Shell Model (1977 - 1999 - 2005) H.W.Bartz et al, NP A275 (1977) 111 R.J. Philpott, NP A289 (1977) 109 K. Bennaceur et al, NP A651 (1999) 289 J. Rotureau et al, PRL 95 (2005) 042503

24. Physics of the large neutron excess Interactions Many-body Correlations Open Channels • Interactions • Isovector (N-Z) effects • Poorly-known components come into play • Long isotopic chains crucial • Configuration interaction • Mean-field concept often questionable • Asymmetry of proton and neutron Fermi surfaces gives rise to new couplings (Intruders and the islands of inversion) • New collective modes; polarization effects • Open channels • Nuclei are open quantum systems • Exotic nuclei have low-energy decay thresholds • Coupling to the continuum important • Virtual scattering • Unbound states • Impact on in-medium Interactions

25. What is the next magic nucleus beyond 208Pb?

26. Superheavy Elements in Nuclear DFT long-lived SHE

27. Crazy topologies of superheavy nuclei due to the Coulomb frustration

28. Experiment Future major facilities Existing major dedicated facilities TRIUMF GSI NSCL GANIL ISOLDE RIKEN HRIBF FRIB Radioactive Ion Beam Facilities Worldwide

29. Computing Nuclear theorists are embarking on a comprehensive study of all nuclei based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, and the massive use of the computer power available at this moment in time. The prospects look good: we are witnessing breakthrough calculations of nuclear properties that the previous two generations of scientists had only begun to dream about.

30. Conclusions The study of nuclei makes the connection between the Standard Model, complex systems, and the cosmos Old paradigms revisited • Exciting science • Interdisciplinary (quantum many-body problem, cosmos,…) • Relevant to society (national security, energy, medicine…) • Theory gives the mathematical formulation of our understanding and predictive ability • Experiment provides insights and verification (FRIB) • New-generation computers provide unprecedented opportunities Thank You

31. EXTRAS

32. Rigged Hilbert space Gamow Shell Model (2002) One-body basis J. Rotureau et al., DMRG Phys. Rev. Lett. 97, 110603 (2006) non-resonant continuum bound, anti-bound, and resonance states Michel et al.:Virtual states not included explicitly in the GSM basis Phys. Rev. C 74, 054305 (2006)