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The Wonderful World of Exotic Nuclei (extremes of the nuclear many-body problem)

The Wonderful World of Exotic Nuclei (extremes of the nuclear many-body problem) Witold Nazarewicz (Tennessee) LNS MIT Colloquium, November 2006. Introduction Neutron-rich terra incognita Unifying structure and reaction aspects The super-heavy land Summary.

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The Wonderful World of Exotic Nuclei (extremes of the nuclear many-body problem)

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  1. The Wonderful World of Exotic Nuclei (extremes of the nuclear many-body problem) Witold Nazarewicz (Tennessee) LNS MIT Colloquium, November 2006 • Introduction • Neutron-rich terra incognita • Unifying structure and reaction aspects • The super-heavy land • Summary

  2. 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

  3. Ab initio Configuration interaction Density Functional Theory Bottom-up approaches to nuclear structure Roadmap Theoretical approaches overlap and need to be bridged

  4. Physics of large neutron excess Interactions Many-body Correlations Open Channels • Interactions • Isovector (N-Z) effects: search for missing links • Poorly-known components of the effective interaction come into play (tensor) • Long isotopic chains crucial (SO) • Configuration interaction • Mean-field concept questionable for dripline nuclei • Asymmetry of proton and neutron Fermi surfaces gives rise to new couplings (Intruders and the islands of inversion) • New collective modes • Open channels • Nuclei are open quantum systems • Exotic nuclei have low-energy decay thresholds • Coupling to the continuum important • Virtual scattering • Physics of unbound states • Interaction modified

  5. Old paradigms, universal ideas, are not correct First experimental indications demonstrate significant changes No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32… Near the drip lines nuclear structure may be dramatically different.

  6. n n p p p n Skins and Skin Modes … and pairing modes…

  7. IS IV 132Sn 130Sn 140Sn Collective or single-particle? Skin effect? Threshold effect? J. Terasaki, J. Engel, SKM*+QRPA+HFB LAND-FRS

  8. `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 Unique geometries of light nuclei due to the threshold effects The nucleus is a correlated open quantum many-body system Environment: continuum of decay channels Spectra and matter distribution modified by the proximity of scattering continuum

  9. 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

  10. SMEC SM Hilbert space formulation : Shell Model Embedded in the Continuum (1999) [A] Shell Model Hilbert Space (CQS) [n] n-particle scattering continuum space

  11. Resonant (Gamow) states outgoing solution complex pole of the S-matrix • Gamow, Z. Phys. 51, 204 (1928) • Siegert, Phys. Rev. 36, 750 (1939) • Humblet and Rosenfeld, Nucl. Phys. 26, 529 (1961) Rigged Hilbert space formulation of SM : Gamow Shell Model (2002)

  12. One-body basis Contour is discretized GSM Hamiltonian matrix is complex symmetric non-resonant continuum bound, anti-bound, and resonance states J. Rotureau et al., DMRG Phys. Rev. Lett. 97, 110603 (2006) Virtual states not included explicitly in the GSM basis Michel et al., Phys. Rev. C (2006) nucl-th/0609016

  13. Example: Threshold anomaly E.P. Wigner, Phys. Rev. 73, 1002 (1948), the Wigner cusp G. Breit, Phys. Rev. 107, 923 (1957) A.I. Baz’, JETP 33, 923 (1957) R.G. Newton, Phys. Rev. 114, 1611 (1959). A.I. Baz', Ya.B. Zel'dovich, and A.M. Perelomov, Scattering Reactions and Decay in Nonrelativistic Quantum Mechanics, Nauka 1966 A.M. Lane, Phys. Lett. 32B, 159 (1970) S.N. Abramovich, B.Ya. Guzhovskii, and L.M. Lazarev, Part. and Nucl. 23, 305 (1992). • The threshold is a branching point. • The threshold effects originate in conservation of the flux. • If a new channel opens, a redistribution of the flux in other open channels appears, i.e. a modification of their reaction cross-sections. • The shape of the cusp depends strongly on the orbital angular momentum. a+X a1+X1 at Q1 a2+X2 at Q2 an+Xn at Qn a+X

  14. 5He+n 6He 6He+n 7He WS potential depth decreased to bind 7He. Monopole SGI strength varied WS potential depth varied Anomalies appear at calculated thresholds (many-body S-matrix unitary) Scattering continuum essential

  15. http://www.llnl.gov/pao/news/news_releases/2006/NR-06-10-03.htmlhttp://www.llnl.gov/pao/news/news_releases/2006/NR-06-10-03.html

  16. "Why would you want to go to the moon? Why do you want to go to the top of Mount Everest? Finding it experimentally is something new, something interesting. It helps the theorists understand what really works in their theories." “Unfortunately, the atoms lived less than a millisecond before decaying, first into element 116, then 114, then 112 and finally fragmenting completely. It wasn't unexpected, but atomic physicists believe, for theoretical reasons, that atoms with 120 or 126 protons might be a lot more stable. Of course, they were saying that about element 114 a few years ago, and it didn't pan out.”

  17. What are the limits of atoms and nuclei?

  18. Liquid-drop energy 264108 8 4 0 310126 -4 298114 -8 -0.4 0 0.4 0.8 b2

  19. region of spherically shell stabilised nuclei („island of stability“) 208Pb region of deformed shell stabilised nuclei around Z=108 and N=162 Quantum stabilization P. Moller, LANL

  20. W. Loveland

  21. HRIBF 2005 Do very long-lived superheavy nuclei exist? What are their physical and chemical properties? How to get there?

  22. Nuclear DFT From Qualitative to Quantitative! Negele, Kerman S. Cwiok, P.H. Heenen, W. Nazarewicz Nature, 433, 705 (2005) • Deformed Mass Table in one day! • HFB mass formula: m~700keV • Good agreement for mass differences UNEDF (SCIDAC-2) will address this question!

  23. Superheavy Elements in Nuclear DFT long-lived SHE

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

  25. Unusual topologies of superheavy nuclei due to the Coulomb frustration

  26. Crazy topologies of superheavy nuclei…

  27. rods 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. Liquid crystal structure? deformed nuclei Skyrme HF with SLy4, Magierski and Heenen, Phys. Rev. C 65, 045804 (2002)

  28. A comprehensive description of nuclei and their reactions is coming Exotic nuclei are essential in this quest: they provide missing links Conclusions Thank You • Bridging theoretical approaches • Bridging ab-initio and SM (effective interactions) • Ab initio and DFT (nuclear matter, density dependence) • EFT, RGT and DFT (effective operators) • Fermionic and Bosonic (algebraic) • Bridging structure with reactions (in both directions) • Bridging finite with bulk CSM NDFT

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