Structure of Exotic Nuclei Witold Nazarewicz (UT/ORNL) NSCL User Workshop 2005

1. The ultimate goal of the physics of nuclei is to develop a unified, predictive theory of nucleonic matter Structure of Exotic Nuclei Witold Nazarewicz (UT/ORNL) NSCL User Workshop 2005 • Introduction • Roadmap • Why Exotic Nuclei? • Examples • Summary

2. http://www.orau.org/ria/RIATG/ Theory roadmap

3. Shell Model Ab Initio Density Functional Theory What are the missing pieces? asymptotic freedom…

4. proton drip line neutron drip line Precision measurements on light nuclei Changes in shell structure for very neutron-rich nuclei Nuclear structure below 100Sn Isospin physics: EOS, masses, moments, reaction mechanism, Astro… Nuclear Landscape 126 stable nuclei 82 r-process known nuclei terra incognita 50 protons 82 rp-process 28 20 50 8 28 neutrons 2 20 8 2

5. Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!) • Challenges: • Configuration space 1024 is not an option!!!! Smarter solutions are needed • DMRG • Monte Carlo • Factorization methods • Hybridization with the mean-field theory • Effective interactions • Modifications of interactions in neutron-rich nuclei • Microscopic effective forces for cross-shell systems • Open channels!

6. Interactions: Shell Model on the interface… different behavior for N=Z and N>Z nuclei Intruder states in the sdpf nuclei Gergana Stoitcheva et al. Zdunczuk et al., Phys.Rev. C71 (2005) 024305

7. Competition between and Surprisingly strong B(E2)’s !!! M. Lach et al., E. Phys. J. A, in press

9. Coupling of nuclear structure and reaction theory (microscopic treatment of open channels) Nuclei are open quantum systems • ab-initio description • continuum shell model • Real-energy CSM (Hilbert space formalism) • Gamow Shell Model (Rigged Hilbert space) • cluster models • Challenges: • Treatment of continuum in ab initio • How to optimize CSM configurations spaces? • Effective forces in CSM • Multi- channel reaction theory • Halo nuclei: an ultimate challenge! • virtual state • center of mass • cross-shell effects

11. scattering continuum essential non-perturbative behavior bound-state structure dominates Michel, Rotureau, Nazarewicz, Ploszajczak • 25 points in p1/2 and p3/2 contours, DMRG treatment • Two-body interaction fitted to g.s. of 6He and 7He

12. Meister et al. (2002)

13. Towards the Universal Nuclear Energy Density Functional 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 spin-current tensor density See Bertsch et al. PRC71, 054311 (2005) kinetic density kinetic spin density Example: Skyrme Functional Total ground-state HF energy

14. Nuclear DFT From Qualitative to Quantitative! Deformed Mass Table in one day!

15. Towards the Nuclear Energy Density Functional (Equation of State) • Challenges: • density dependence of the symmetry energy • neutron radii • clustering at low densities

16. From Finite Nuclei to the Nuclear Liquid Drop Leptodermous Expansion Based on the Self-consistent Theory P.G. Reinhard, M. Bender, W.N., T. Vertse The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A-1/3 (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 106. The limitations of applying the leptodermous expansion for finite nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects. From HF or RMF Shell corr. estimated using Green’s function method

17. Liquid-Drop Expansion O(0) O(1) O(2) Droplet Model Expansion Myers, Swiatecki 1974

18. asurf avol

19. residual shell effects 8000 1000 300 125

20. LDM and Droplet Model Coefficients

21. n n p p p n Skins and Skin Modes

22. Beyond Mean Field examples M. Bender et al., PRC 69, 064303 (2004) GCM Shape coexistence HFB+QRPA J. Terasaki et al., Phys. Rev. C71, 034310 (2005) Soft modes in drip-line nuclei

23. Isoscalar 1- Strength Function in the Sn Isotopes (Jun Terasaki, QRPA+HFB) • What is the nature of • the low-energy strength? • Skin effect • Threshold effect? • Both?

24. 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.

25. Excitation energy Isospin Mass and charge What are the limits of s.p. motion?

26. Nuclear Structure and Reactions Nuclear Theory forces methods extrapolations low-energy experiments Nuclear Astrophysics

27. QCD • Origin of NN interaction • Many-nucleon forces • Effective fields subfemto… nano… Complex Systems Giga… Cosmos femto… Physics of Nuclei Quantum many-body physics Nuclear Astrophysics • In-medium interactions • Symmetry breaking • Collective dynamics • Phases and phase transitions • Chaos and order • Dynamical symmetries • Structural evolution • Origin of the elements • Energy generation in stars • Stellar evolution • Cataclysmic stellar events • Neutron-rich nucleonic matter • Electroweak processes • Nuclear matter equation of state • How does complexity emerge from simple constituents? • How can complex systems display astonishing simplicities? How do nuclei shape the physical universe?

28. END The study of nuclei is a forefront area of science. It is this research that makes the connection between QCD phenomena, many-body systems, and the cosmos.

29. Instead of summary…. Robert B. Laughlin, Nobel Prize Lecture, December 8, 1998