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Shell Structure of Exotic Nuclei ( a Paradigm Shift?) Witold Nazarewicz (UTK, ORNL, UWS)

Shell Structure of Exotic Nuclei ( a Paradigm Shift?) Witold Nazarewicz (UTK, ORNL, UWS) University of Surrey, UK, Mar. 11, 2008. Introduction Shell structure revisited Nuclear Density Functional Theory Questions and Challenges, Homework Perspectives. Emphasis on: novel aspects

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Shell Structure of Exotic Nuclei ( a Paradigm Shift?) Witold Nazarewicz (UTK, ORNL, UWS)

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  1. Shell Structure of Exotic Nuclei (a Paradigm Shift?) Witold Nazarewicz (UTK, ORNL, UWS) University of Surrey, UK, Mar. 11, 2008 • Introduction • Shell structure revisited • Nuclear Density Functional Theory • Questions and Challenges, Homework • Perspectives Emphasis on: novel aspects recent results problems

  2. Introduction

  3. 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) • Closed orbits and s.p. quantum numbers • But… • Nuclear box is not rigid: motion is seldom adiabatic • The walls can be transparent

  4. Shell effects and classical periodic orbits Balian & Bloch, Ann. Phys. 69 (1971) 76 Bohr & Mottelson, Nuclear Structure vol 2 (1975) Strutinski & Magner, Sov. J. Part. Nucl. 7 (1976) 138 Trace formula, Gutzwiller, J. Math. Phys. 8 (1967) 1979 The action integral for the periodic orbit Condition for shell structure Principal shell quantum number Distance between shells (frequency of classical orbit)

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

  6. 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

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

  8. Nature 449, 1022 (2007) Phys. Rev. Lett. 99, 192501 (2007) No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32…

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

  10. 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

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

  12. 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 • Nuclear DFT • two fermi liquids • self-bound • superfluid

  13. Nuclear Local s.p. Densities and Currents isoscalar (T=0) density isovector (T=1) density isoscalar spin density isovector spin density current density spin-current tensor density kinetic density kinetic spin density + analogous p-p densities and currents

  14. Construction of the functional Perlinska et al., Phys. Rev. C 69, 014316 (2004) p-h density p-p density Most general second order expansion in densities and their derivatives pairing functional Not all terms are equally important. Some probe specific observables

  15. Example: Spin-Orbit and Tensor Force (among many possibilities) F j< • The origin of SO splitting can be attributed to 2-body SO and tensor forces, and 3-body force • R.R. Scheerbaum, Phys. Lett. B61, 151 (1976); B63, 381 (1976); Nucl. Phys. A257, 77 (1976); D.W.L. Sprung, Nucl. Phys. A182, 97 (1972); C.W. Wong, Nucl. Phys. A108, 481 (1968); K. Ando and H. Bando, Prog. Theor. Phys. 66, 227 (1981); R. Wiringa and S. Pieper, Phys. Rev. Lett. 89, 182501 (2002) • The maximum effect is in spin-unsaturated systems • Discussed in the context of mean field models: • Fl. Stancu, et al., Phys. Lett. 68B, 108 (1977); M. Ploszajczak and M.E. Faber, Z. Phys. A299, 119 (1981); J. Dudek, WN, and T. Werner, Nucl. Phys. A341, 253 (1980); J. Dobaczewski, nucl-th/0604043; Otsuka et al. Phys. Rev. Lett. 97, 162501 (2006); Lesinski et al., arXiv:0704.0731,… • …and the nuclear shell model: • T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001); Phys. Rev. Lett. 95, 232502 (2005) 28, 50, 82, 126 2, 8, 20 F j< j> j> Spin-saturated systems Spin-unsaturated systems

  16. acts in s and d states of relative motion acts in p states SO densities (strongly depend on shell filling) • Additional contributions in deformed nuclei • Particle-number dependent contribution to nuclear binding • It is not trivial to relate theoretical s.p. energies to experiment.

  17. Importance of the tensor interaction far from stability [523]7/2 Proton emission from 141Ho [411]1/2

  18. `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

  19. 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

  20. 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

  21. N. Michel et al. PRC 75, 0311301(R) (2007) 5He+n 6He 6He+n 7He WS potential depth decreased to bind 7He. Monopole SGI strength varied Overlap integral, basis independent! Anomalies appear at calculated thresholds (many-body S-matrix unitary) Scattering continuum essential see also Nucl. Phys. A 794, 29 (2007)

  22. Questions and challenges

  23. How to extend DFT to finite, self-bound systems? Intrinsic-Density Functionals J. Engel, Phys. Rev. C75, 014306 (2007) Generalized Kohn-Sham Density-Functional Theory via Effective Action Formalism M. Valiev, G.W. Fernando, cond-mat/9702247 B.G. Giraud, B.K. Jennings, and B.R. Barrett, arXiv:0707.3099 (2007); B.G. Giraud, arXiv:0707.3901 (2007)

  24. Can dynamics be incorporated directly into the functional? Example: Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas, Aurel Bulgac, Phys. Rev. A 76, 040502 (2007) See also: Density-functional theory for fermions in the unitary regime T. Papenbrock Phys. Rev. A72, 041603 (2005) Density functional theory for fermions close to the unitary regime A. Bhattacharyya and T. Papenbrock Phys. Rev. A 74, 041602(R) (2006)

  25. How to root nuclear DFT in a microscopic theory? ab-initio - DFT connection NN+NNN - EDF connection (via EFT+RG)

  26. Connections to computational science 1Teraflop=1012 flops 1peta=1015 flops (next 2-3 years) 1exa=1018 flops (next 10 years) Jaguar Cray XT4 at ORNL No. 2 on Top500 • 11,706 processor nodes • Each compute/service node contains 2.6 GHz dual-core AMD Opteron processor and 4 GB/8 GB of memory • Peak performance of over 119 Teraflops • 250 Teraflops after Dec.'07 upgrade • 600 TB of scratch disk space

  27. Example: Large Scale Mass Table Calculations Science scales with processors Jaguar@ M. Stoitsov, HFB+LN mass table, HFBTHO Even-Even Nuclei • The SkM* mass table contains 2525 even-even nuclei • A single processor calculates each nucleus 3 times (prolate, oblate, spherical) and records all nuclear characteristics and candidates for blocked calculations in the neighbors • Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration) Odd and odd-odd Nuclei • The even-even calculations define 250,754 configurations in odd-A and odd-odd nuclei assuming 0.5 MeV threshold for the blocking candidates • Using 10,000 processors - about 25 CPU hours

  28. A typical run for the whole even-even mass chart contains about 2731 different bound nuclear states which identify the ground states of 1527 even-even nuclei. At the end of the run: 2032 converge for up to 500 iterations 404 converge up to 1000 iterations 123 converge up to 2000 iterations 152 converge up to 6000 iterations 26 do not converge

  29. 0 1 0 - 1 1 0 - 2 1 0 - 3 1 0 - 4 1 0 - 5 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 Broyden Mixing 1 9 4 R n , H F B + L N , N = 2 0 s h S l y 4 + m i x e d p a i r i n g d - Error L i n e a r m i x i n g B r o y d e n M = 3 B r o y d e n M = 7 Number of iterations

  30. Bimodal fission in nuclear DFT A. Staszczak, J. Dobaczewski, W. Nazarewicz, in preparation S. Umar and V. Oberacker Phys. Rev. C 76, 014614 (2007) nucl-th/0612017 TDHF description of heavy ion fusion

  31. Conclusions Why is the shell structure changing at extreme N/Z ?Can we talk about shell structure at extreme N/Z ? Interactions Many-body Correlations Open Channels Thank You

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