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Structure of Exotic Nuclei Witold Nazarewicz (Tennessee) International School of Nuclear Physics

Structure of Exotic Nuclei Witold Nazarewicz (Tennessee) International School of Nuclear Physics 28th course: Radioactive Beams, Nuclear Dynamics and Astrophysics Erice, Italy, September 2006. Introduction: challenges and questions Microscopic nuclear structure theory

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Structure of Exotic Nuclei Witold Nazarewicz (Tennessee) International School of Nuclear Physics

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  1. Structure of Exotic Nuclei Witold Nazarewicz (Tennessee) International School of Nuclear Physics 28th course: Radioactive Beams, Nuclear Dynamics and Astrophysics Erice, Italy, September 2006 • Introduction: challenges and questions • Microscopic nuclear structure theory • Recent/relevant examples • 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. Effective Field Theory tells us that: • Short-range (high-k) physics can be integrated out (no need to worry about explicit inclusion of hard core when dealing with low-k phenomena) • Successive two-body scatterings with short-lived high-energy intermediate states unresolved → must be absorbed into three-body force • Power counting can be controlled • … but the operators have to be renormalized (i.e., consistent with the power counting) Weinberg’s Third Law of Progress in Theoretical Physics: “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!” D. Furnstahl, INT Fall’05

  4. Nuclear Structure: the interaction Effective-field theory (χPT) potentials: error bars provided Vlow-k: can it describe low-energy observables? • Quality two- and three-nucleon interactions exist • Not uniquely defined (local, nonlocal) • Soft and hard-core • The challenge is: • to understand their origin • to understand how to use them in nuclei Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003) N3LO: Entem et al., PRC68, 041001 (2003) Epelbaum, Meissner, et al.

  5. Ab initio Configuration interaction Density Functional Theory Bottom-up approaches to nuclear structure Roadmap Collective and Algebraic Models (top-down) Theoretical approaches overlap and need to be bridged

  6. Ab Initio Nuclear Structure Theory (with bare NN+NNN interactions) • Quantum Monte Carlo (GFMC) 12C • No-Core Shell Model 13C • Coupled-Cluster Techniques 16O • Unitary Model Operator Approach • Faddeev-Yakubovsky • Bloch-Horowitz • … The nucleon-based description works to <0.5 fm • Input: • Excellent forces based on the phase shift analysis • EFT based nonlocal chiral NN and NNN potentials • Challenges: • Interaction: NNN • How important is NNNN? See nucl-th/0606017for 4He estimates • How to extend calculations to heavier systems? • Treatment of weakly-bound and unbound states, and cluster correlations • First applications to reactions in GFMC, NCSM, CCM, …

  7. Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!) Honma, Otsuka et al., PRC69, 034335 (2004) and ENAM’04 Martinez-Pinedo ENAM’04 Challenges: Configuration space Effective Interactions Open channels

  8. Towards the Universal Nuclear Energy Density Functional (non-relativistic, relativistic) Walter Kohn: Nobel Prize in Chemistry in 1998 isoscalar (T=0) density isovector (T=1) density isoscalar spin density Local densities and currents + pairing… isovector spin density current density Construction of the functional: E. Perlinska et al. Phys. Rev. C 69, 014316 (2004) spin-current tensor density kinetic density kinetic spin density Example: Skyrme Functional Total ground-state DFT energy

  9. Nuclear DFT From Qualitative to Quantitative! 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!

  10. Why is the shell structure changing at extreme isospins? 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 • Long isotopic chains crucial • 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 • Open channels • Nuclei are open quantum systems • Exotic nuclei have low-energy decay thresholds • Coupling to the continuum important

  11. 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) • 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. • 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

  12. acts in s and d states of relative motion acts in p states SO densities (strongly depend on shell filling) J. Dobaczewski, nucl-th/0604043

  13. J. Dobaczewski, nucl-th/0604043 Skyrme-DFT • Additional contributions in deformed nuclei • Particle-number dependent contribution to nuclear binding • It is not trivial to relate theoretical s.p. energies to experiment. • Correlations (including g.s. correlations) are important!

  14. Coupling of nuclear structure and reaction theory (microscopic treatment of open channels) Thomas/Ehrman shift Proton Emitters • ab-initio description • continuum shell model • Real-energy CSM (Hilbert space formalism) • Gamow Shell Model (Rigged Hilbert space) • cluster models

  15. Continuum Shell Model -an old tool! • U. Fano, Phys. Rev. 124, 1866 (1961) • C. Mahaux and H. Weidenmüller: “Shell Model Approach to Nuclear Reactions” 1969 • H. W. Bartz et al., Nucl. Phys. A275, 111 (1977) • D. Halderson and R.J. Philpott, Nucl. Phys. A345, 141 • … • J. Okolowicz, M. Ploszajczak, I. Rotter, Phys. Rep. 374, 271 (2003) • Recent Developments: • SMEC • K. Bennaceur et al., Nucl. Phys. A651, 289 (1999) • K. Bennaceur et al., Nucl. Phys. A671, 203 (2000) • N. Michel et al., Nucl. Phys. A703, 202 (2002) • Y. Luo et al., nucl-th/0201073 • Gamow Shell Model • N. Michel et al., Phys. Rev. Lett. 89, 042502 (2002) • N. Michel et al., Phys. Rev. C67, 054311 (2003) • N. Michel et al., Phys. Rev. C70, 064311 (2004) • R. Id Betan et al., Phys. Rev. Lett. 89, 042501 (2002) • R. Id Betan et al., Phys. Rev. C67, 014322 (2003) • G. Hagen et al, Phys. Rev. C71, 044314 (2005) • Other approaches

  16. Resonant (Gamow) states Also true in many-channel case! outgoing solution complex pole of the S-matrix • Humblet and Rosenfeld, Nucl. Phys. 26, 529 (1961) • Siegert, Phys. Rev. 36, 750 (1939) • Gamow, Z. Phys. 51, 204 (1928)

  17. One-body basis Contour is discretized GSM Hamiltonian matrix is complex symmetric 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

  18. N. Michel, W.N., M. Ploszajczak, J. Rotureau

  19. Example: Spectroscopic factors and threshold effects in GSM One-nucleon radial overlap integral: One-nucleon radial overlap integral in GSM: usually approximated by a WS wave function at properly adjusted energy Spectroscopic factor in GSM: In contrast to the standard SM, the final result is independent of the s.p. basis. In usual applications, only one term remains Usually extracted from experimental cross section Prone to errors close to particle thresholds

  20. 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.

  21. Threshold anomaly (cont.) Studied experimentally and theoretically in various areas of physics: • pion-nucleus scattering • R.K. Adair, Phys. Rev. 111, 632 (1958) • A. Starostin et al., Phys. Rev. C 72, 015205 (2005) • electron-molecule scattering • W. Domcke, J. Phys. B 14, 4889 (1981) • electron-atom scattering • K.F. Scheibner et al., Phys. Rev. A 35, 4869 (1987) • ultracold atom-diatom scattering • R.C. Forrey et al., Phys. Rev. A 58, R2645 (1998) • Low-energy nuclear physics • charge-exchange reactions • neutron elastic scattering • deuteron stripping The presence of cusp anomaly could provide structural information about reaction products

  22. Coupling between analog states in (d,p) and (d,n) C.F. Moore et al. Phys. Rev. Lett. 17, 926 (1966)

  23. C.F. Moore et al., Phys. Rev. Lett. 17, 926 (1966)

  24. 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

  25. The non-resonant continuum is important for the spectroscopy of weakly bound nuclei (energy shifts of excited states, additional binding,…) • SFs, cross sections, etc., exhibit a non-perturbative and non-analytic behavior (cusp effects) close to the particle-emission thresholds. These anomalies strongly depend on orbital angular momentum • Microscopic CSM (GSM) fully accounts for channel coupling. Thresholds are not predetermined! Timofeyuk, Blokhintsev, Tostevin, Phys. Rev. C68, 021601 (2003) Non-Borromean two-neutron halos

  26. NSCL@MSU 2005

  27. Example: Surface Symmetry Energy Microscopic LDM and Droplet Model Coefficients: PRC 73, 014309 (2006)

  28. Collective potential V(q) • Presence of shell effects in metastable minima seems to be under control. • Important data needed to fix • the deformability of the NEDF: • absolute energies of SD states • absolute energies of HD states • Advantages: • large elongations • weak mixing with ND structures Different deformabilities!

  29. theory (DFT) experiment Er Pb deformed systems spherical systems Shell closure Ra U deformed systems octupole collectivity Average value: symmetry energy Stoitsov, Nazarewicz + Cakirli, Casten

  30. Example: High-spin intruder states S2n S2p Brown & Sherrill, MSU

  31. Intruder states in the sdpf nuclei 45Sc G. Stoitcheva et al., Phys. Rev. C73, 061304(R) (2006) deformed structures 28 f7/2 intruder states 20 d3/2 Zdunczuk et al.,Phys.Rev. C71 (2005) 024305 • Excellent examples of single-particle configurations • Weak configuration mixing • Spin polarization! • Experimental data available P. Bednarczyk et al., Acta Phys. Pol. B32, 747 (2001)

  32. spdf space 1p-1h cross-shell Antoine

  33. SM SM’ 0.4 SM’’ 0.2 ESM-EEXP (MeV) 0 -0.2 -0.4 44Sc 46Ti 47V 42Ca 42Sc 44Ti 40Ca 43Sc 45Sc 45Ti 44Ca 46V Pandya transformation on the cross shell ME Bansal, French, Phys. Lett. 11, 145 (1964); Zamick, Phys. lett. 19, 580 (1965) the isospin-dependent contribution to the excitation energy of a 1p-1h state sd fp sd fp Crucial for the island of inversion around 32Mg!

  34. Do very long-lived superheavy nuclei exist? What are their physical and chemical properties? How to get there? HRIBF 2005 What are the limits of atoms and nuclei?

  35. T. Nakatsukasa et al., Nucl. Phys. A573, 333 (1994) spin-flip Z-rich nuclei: Collective M1 strength Enhanced in deformed N=Z nuclei Probes T=1 physics (g9/2)2 excitation

  36. Collective or single-particle? Skin effect? Threshold effect? LAND-FRS Energy differential electromagnetic dissociation cross section Deduced photo-neutron cross section.

  37. 132Sn 130Sn 140Sn IS IV J. Terasaki, J. Engel, nucl-th//0603021 SKM*+QRPA+HFB

  38. A comprehensive description of nuclei and their reactions is coming Exotic nuclei are essential in this quest: they provide missing links Discussed: Origin of shell structure changes Many-body GSM treatment of structure and reactions Surface-dependence of the symmetry energy (masses, deformed states) Learning about cross-shell physics from intruder states The superheavies: how to get there? Quest for collective exotica THE END Conclusions

  39. SkO 0.15 Brandolini et al., PRC66, 021302 (2002) 0.10 6.5 SLy4 0.05 dEC=DEHF - DEHF [MeV] 0 (C) 6.0 -0.05 42Ca 43Sc 45Sc 46Ti 44Ti 40Ca 5.5 44Ca 44Sc 45Ti 47V 46V 42Sc 5.0 50Cr SkO SLy4 4.5 DE([f7/2]n) [MeV] SkO 46Ti off off on on SLy4 off on COULOMB SHIFT (W. Satula et. al) Relative Coulomb shift Coulomb: off on polarization of strong field Absolute Coulomb shift of terminating state ~500keV deformed g.s and spherical Imax Coulomb:

  40. 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 radioactive beams electron scattering relativistic heavy ions

  41. Spectroscopy of open systems: proton emitters • Non-adiabatic theory: • B.Barmore et al., Phys.Rev. C62, 054315 (2000) • A.T. Kruppa and WN, Phys. Rev. C69, 054311 (2004)

  42. distance excitation energy angular momentum (j-polarization) mass and charge N/Z ratio (isospin polarization) (e.g., the local central force)

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