Toward a Unified Theory of Nucleonic Matter: Perspectives on Nuclear Structure

1. The ultimate goal of the physics of nuclei is to develop a unified, predictive theory of nucleonic matter Perspectives on nuclear structure: Understanding complex systems Witold Nazarewicz (UT/ORNL) 2005 Gordon Conference on Nuclear Physics • Introduction • Landscape/Playground • Why Exotic Nuclei? • Nuclear Many-Body Problem • Summary

2. heavy nuclei few body quarks gluons vacuum quark-gluon soup QCD nucleon QCD few body systems bare NN force many body systems effective NN force The Nuclear Many-Body Problem radioactive beams electron scattering relativistic heavy ions

3. superheavy nuclei proton drip line neutron stars neutron drip line 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

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

5. pion p+ ~140 MeV QCD scale 1000 MeV g g g g g g g g g g g deuteron ~3 MeV N-binding scale pion-mass scale _ _ _ _ _ _ _ _ _ d d d d d d d d d d d 10 MeV 100 MeV u u u u u u u u u u u u d collective ~1 MeV Energy Scales in Nuclear Physics J. Dobaczewski, RIA Summer School, 2004

6. NN and NNN forces (can be unified at low-k) • Many different NN interactions provide excellent fit to scattering data below 350 MeV • Details not resolved for relative momenta larger than L~2.1 fm-1. Different modeling of short-distance part. • High-momentum physics can be integrated out (renormalization; EFT; RGM) • If nucleus is probed at low energies, short distance details are not resolved! • Low-energy interaction is not determined uniquely; depends on the energy region • Replace short-distance structure by something simple! • Chiral forces; Vlow-k

7. Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003)

9. Ab initio: GFMC, NCSM, CCM (nuclei, neutron droplets, nuclear matter) S. Pieper, ENAM’04 1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed

10. 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 • … Input: Excellent forces based on the phase shift analysis (can be unified through Vlow k) Realistic NNN interactions EFT based nonlocal chiral NN and NNN potentials Challenges: Interaction: NNN (How important is NNNN?) How to extend calculations to heavier systems? Treatment of weakly-bound and unbound states, and cluster correlations

11. Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!) Honma, Otsuka et al., PRC69, 034335 (2004) and ENAM’04 Martinez-Pinedo ENAM’04

12. Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!) • Challenges: • Configuration space 1024 is not an option!!!! More intelligent solution is 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!

14. 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 open channels • 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

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

17. Microscopic Mass Formula (can we go below 500 keV?) Reinhard 2004 Goriely, ENAM’04 • Challenges: • need for error and covariance analysis (theoretical error bars in unknown regions) • a number of observables need to be considered (masses, radii, collective modes) • only data for selected nuclei used

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

19. Towards Nuclear Energy Density Functional (unified description of nuclei and nuclear matter) • Self-consistent mean-field theory (HF, HFB, RMF) • Nuclear density functional theory • Symmetry breaking crucial • Symmetry restoration essential (projection techniques, GCM, QRPA) • Pairing channel extremely important but poorly know • Challenges: • better understanding of isovector and density dependence • of p-h and p-p interaction • how to extrapolate in isospin and mass? • time-odd fields • spin and isospin pieces • improved treatment of many-body correlations • microscopic treatment • nuclear matter equation of state at low and high temperatures • low density limit and clustering • isovector dependence of the symmetry energy

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

21. Neutron Drip line nuclei 6He 4He 8He HUGE D i f f u s e d PA IR ED 5He 7He 9He 10He

22. 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

23. 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.

24. Do very long-lived superheavy nuclei exist? What are their physical and chemical properties? Three frontiers, relating to the determination of the proton and neutron drip lines far beyond present knowledge, and to the synthesis of the heaviest elements What are the limits of atoms and nuclei?

25. Superheavy Elements

26. lifetimes > 1y Superheavy Elements S. Cwiok, P.H. Heenen, W. Nazarewicz Nature, 433, 705 (2005)

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

28. n n p p p n Skins and Skin Modes

31. Pairing (in nuclei and nuclear matter) • Unique nuclear features: surface effects/finite size, 4 kinds of Cooper pairs, anisotropic fields • Essential for existence of weakly-bound nuclei • Various regimes of strength • Crucial for many-body dynamics (both LACM and vibrations/rotations) • Connection to other fields (BECs, CSC) Questions • role of range • density dependence • bare vs. induced (in bulk and finite) • continuum scattering, change in asymptotics • pair localization, skin modes • clustering in the skin • response to spin, seniority

32. r excited 1Su and1Pu states + N N Diabatic potential energy surfaces for excited electronic configurations of N2 Excitation spectrum of N2 molecule Rotational Transitions ~ 10 meV Vibrational Transitions ~ 100 meV Electronic Transitions ~ 1 eV

33. Nuclear collective motion Rotational Transitions ~ 0.2-2 MeV Vibrational Transitions ~ 0.5-12 MeV Nucleonic Transitions ~ 7 MeV What is the origin of ordered motion of complex nuclei? Complex systems often display astonishing simplicities. Nuclei are no exception. It is astonishing that a heavy nucleus, consisting of hundreds of rapidly moving protons and neutrons can exhibit collective motion, where all particles slowly dance in unison.

34. E fission/fusion exotic decay heavy ion coll. Q0 Q E shape coexistence Q1 Q2 Q

35. Beyond Mean Field examples M. Bender et al., PRC 69, 064303 (2004) Shape coexistence Soft modes in drip-line nuclei

36. Beyond Mean Field nuclear collective dynamics • Variety of phenomena: • symmetry breaking and quantum corrections • LACM: fission, fusion, coexistence • phase transitional behavior • new kinds of deformations • Significant computational resources required: • Generator Coordinate Method • Projection techniques • Imaginary time method (instanton techniques) • QRPA and related methods • TDHFB, ATDHF, and related methods • Challenges: • selection of appropriate degrees of freedom • simultaneous treatment of symmetry breaking in p-h and p-p channel • coupling to continuum in weakly bound systems • dynamical corrections; fundamental theoretical problems. • rotational, vibrational, translational • particle number • isospin

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

40. 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. Summary

41. EXTRAS

42. 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?

43. No Core Shell Model (with realistic effective forces and effective operators) • Challenges: • How to optimize enormous configurations spaces? • Extrapolation methods • Higher-order clusters in long-range effective operators Goals: On-the-fly computations to do Lanczos (~100 processors) All p-shell nuclei with NN +NNN in 6 shells within 2005 NNNN potentials (alpha clustering) Navratil and Caurier, PRC69, 014311 (2004) Navratil, Ormand, et al.

44. Coupled Cluster Method (with microscopic effective forces) Triples add 1 MeV of binding to the ground-state energy. Expt: 128 MeV. (Leaves room for Coulomb,V3N) 3- is a 1p-1h excited state. Well described by EOMCCSD and CR-EOMCCSD(T) Expt: 7.0 MeV 0+ is a 4p-4h state; Requires higher order theory for description. Expt: 6.8 MeV 16O with Idaho-A ORNL, Oslo, MSU, UT Challenges & GOALS: Implementation of NNN Open-shell, A=20-50 nuclei Nuclear matter