Introduction Theory Roadmap Highlights Summary

1. The ultimate goal of the physics of nuclei is to develop a unified, predictive theory of nucleonic matter Perspectives on Nuclear Structure Theory Witold Nazarewicz (Tennessee) ACS National Meeting Atlanta March 2006 • Introduction • Theory Roadmap • Highlights • 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? Why is there more matter than antimatter? What are the weak interactions among hadrons, and how are they affected by the nucleus? What are the masses of neutrinos and how have they shaped the evolution of the universe? 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(see RIA Brochure) Physics of nuclei • Theory plays crucial role • complements experiment • provides vision • provides deeper understanding • provides intellectual motivation Nuclear astrophysics Fundamental interactions & neutrinos Applications of nuclei

3. Nuclear Structure Theory Overarching goal: • This is a lofty and ambitious goal that has been a “Holy Grail” in physics for over fifty years • “Unified” does not mean that there is a single theoretical method that will work in all cases • Self-bound, two-component quantum many-fermion system • Complicated interaction based on QCD with at least two- and three-nucleon components • We seek to describe the properties of “nuclei” ranging from the deuteron to neutron stars To arrive at a comprehensive and unified microscopic description of all nuclei and there low-energy reactions from the the basic interactions between the constituent protons and neutrons There is no “one size fits all” theory for nuclei, but all our theoretical approaches need to be linked by an underlying use of the constituents and the interactions between them E. Ormand, RISAC, Irvine 2006

4. Best EFT three-nucleon potential Nuclear Structure: the interaction • Effective-field theory potentials Parameters for EFT three-nucleon interaction N3LO: Entem et al., PRC68, 041001 (2003) • Quality two- and three-nucleon interactions exist • The challenge is to understanding how to use them in nuclei

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: 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

7. 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

8. Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!) 1024 is not an option!!!! Smarter solutions are needed Challenges: Configuration space Effective Interactions Open channels Martinez-Pinedo ENAM’04

9. Coupling of nuclear structure and reaction theory (microscopic treatment of open channels)

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

11. 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.

12. Shell Model Ab Initio Density Functional Theory What are the missing pieces?

13. What are the limits of atoms and nuclei? Do very long-lived superheavy nuclei exist? What are their physical and chemical properties?

14. lifetimes > 1y 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? What are the limits of nuclear mean field?

15. n n p p p n Skins and Skin Modes

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

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

18. Beyond Mean Field nuclear collective dynamics Shape coexistence GCM M. Bender et al., PRC 69, 064303 (2004) • 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 • coupling to continuum in weakly bound systems • dynamical corrections; fundamental theoretical problems. • rotational, vibrational, translational • particle number • isospin

19. (3He,p) N=Z line Measure the np transfer cross section to T=1 and T=0 states Both absolute s(T=0) and s(T=1) and relative s(T=0) / s(T=1) tell us about the character and strength of the correlations

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

21. The study of nuclei is a forefront area of science. It is this research that makes the connection between the Standard Model, QCD phenomena, many-body systems, and the cosmos. A comprehensive and unified theory for nuclei and their reactions is needed Nuclear structure and reactions are important for not just nuclei: Understanding the quantum many-body problem Testing the fundamental laws of nature Understanding stellar evolution and how the elements were made Society (national security, energy, medicine…) Theory and experiment are both needed to achieve this goal Theory gives the mathematical formulation of our understanding and predictive ability Experiment provides verification END