Exploring Exotic Nuclei: Unveiling Shell Structure Paradigm Shifts

1. Shell Structure of Exotic Nuclei (a Paradigm Shift?) Witold Nazarewicz (University of Tennessee/ORNL) ANL Physics Division Colloquium, March 2007 • Introduction • Shell structure, mean filed, and one-body motion • Interactions • Many-body correlations • Open channels • Summary

2. One-body field • Not external (self-bound) • Hartree-Fock Shells • Product (independent-particle) state is often an excellent starting point • Localized densities, currents, fields • Closed orbits and s.p. quantum numbers • Typical time scale: babyseconds (10-22s) • Nuclear box is not rigid: motion is seldom adiabatic

3. 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)

4. Shell energy (correction) (a useful concept rooted in the one-body picture) e Swiatecki, 1963 Strutinsky, Nucl. Phys. 95, 420 (1967) Brack et al., Rev. Mod. Phys. 44, 320 (1972) high density; instability shell and subshell closures smooth part fluctuating part

5. Degeneracy, stability, symmetry breaking The concept of magicity can be generalized to the case of deformation: magic deformed nuclei Magic nucleus: the least degenerate among its neighbors The genaral rule: In quantal systems degeneracy leads to reduced stability. Thus even an infinitely small perturbation of a degenerate system produces a final response in the system due to rearrangement of many close-lying states. • Jahn-Teller Effect (1936) • Symmetry breaking and deformed (HF) mean-field

6. Pronounced shell structure (quantum numbers) Shell structure absent shell gap shell gap M. Brack et al., Phys. Rev. Lett. 79, 1817 (1997) shell space 95% chaotic Poincare surface of section of classical trajectories with Lz = 0 at deformation of asymmetric saddle (B). closed trajectory (regular motion) trajectory does not close

7. 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.

8. Many splendid examples of s.p. motion at large deformations Dynamical symmetries and multiclustering in superdeformed and hyperdeformed nuclei, RHO, Phys. Rev. Lett. 68, 154 (1992)

9. Bimodal fission nucl-th/0612017 A. Staszczak, J. Dobaczewski W. Nazarewicz, in preparation 132Sn + 132Sn

10. Fission pathways in the nuclear density functional theory A. Staszczak, J. Dobaczewski W. Nazarewicz, in preparation All intrinsic symmetries can be broken Motion non-adiabatic

11. Honma, Otsuka et al., PRC69, 034335 (2004) and ENAM’04 Martinez-Pinedo ENAM’04

12. 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.

14. 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 • 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; polarizations • 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 • Impact on in-medium Interactions

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) • 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

16. J. Dobaczewski, nucl-th/0604043 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. • Correlations (including g.s. correlations) are important!

17. J.P. Schiffer et al., PRL 92 (2004) 162501 Z=50, 51 Prog. Part. Nucl. Phys, in press; nucl-th/0701047 Energy differences extracted from calculated masses 1g7/2 almost filled 1h11/2 almost empty

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 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 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 Michel et al.:Virtual states not included explicitly in the GSM basis Phys. Rev. C 74, 054305 (2006)

21. 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

22. 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. This is of particular interest for neutron-rich nuclei

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

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

25. N. Michel et al. PRC (R), in press; nucl-th/0702021 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

26. Many-body OQS calculations correctly predict the Wigner-cusp and channel-coupling threshold effects. This constitutes a very strong theoretical check for the GSM approach. The spectroscopic factors defined in the OQS framework through the norm of the overlap integral, exhibit strong variations around particle thresholds. Such variations cannot be described in a standard CQS SM framework that applies a "one-isolated-state" ansatz and ignores the coupling to the decay and scattering channels. In the GSM model calculations, the contribution to SF from a non-resonant continuum can be as large as 25%.

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

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

29. 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)

30. What are the limits of s.p. motion? Crazy topologies of light nuclei due to the threshold effects Crazy topologies of superheavy nuclei due to the Coulomb frustration

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

32. EXTRAS

33. 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

34. 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)

36. “Spin-orbit splitting” in GSM Influence of configuration mixing and continuum coupling

37. 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

38. Empirical Proton-Neutron Interactions and Nuclear Density Functional Theory Stoitsov, Cakirli, Casten. Nazarewicz, Satula, PRL, in press; nucl-th/0611047 Average value: symmetry energy

39. theory (DFT) experiment Er Pb deformed systems spherical systems Shell closure Ra U deformed systems octupole collectivity