The Nucleus: a quantum open many-body system Witold Nazarewicz (Tennessee)

1. The ultimate goal of the physics of nuclei is to develop a unified, predictive theory of nucleonic matter The Nucleus: a quantum open many-body system Witold Nazarewicz (Tennessee) Yale University, Physics Club, September 8, 2006 • Introduction • Challenges and questions • Microscopic Nuclear Structure theory • Recent examples • Future: exotic beams • Summary

2. 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

3. Energy-dependent resolution (use different microscopes to probe different degrees of freedom) 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 J. Dobaczewski, RIA Summer School, 2004

4. 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

5. 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

6. Nuclear Structure Theory Overarching goal: • This is a lofty and ambitious goal that has been a “Holy Grail” in nuclear science 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 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

7. Nuclear Structure: the interaction Vlow-k (cutoff in momentum; renormalization group) can it describe low-energy observables? Effective-field theory (χPT) potentials • 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.

8. 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

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

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

11. 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

12. Diagonalization Shell Model (medium-mass nuclei reached;dimensions 109!) N=0 CI works great, but… 1024 is not an option!!! Smarter solutions are needed Challenges: Configuration space Effective Interactions Open channels Martinez-Pinedo ENAM’04

13. Nuclear DFT From Qualitative to Quantitative! • Deformed Mass Table in one day! • HFB mass formula: m~700keV • Good agreement for mass differences

14. theory (DFT) experiment Er Pb deformed systems spherical systems Shell closure Ra U deformed systems octupole collectivity Stoitsov, Nazarewicz + Cakirli, Casten

15. What are the missing pieces? Density Functional Theory

16. 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

17. Old paradigms, universal ideas, are not correct Near the drip lines nuclear structure may be dramatically different. Experimental indications from RNB facilities (ISOLDE, NSCL, RIKEN, SPIRAL,…) demonstrate significant changes No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32…

18. Why is the shell structure changing at extreme N/Z ? Interactions Many-body Correlations Open Channels

19. Coupling of nuclear structure and reaction theory (microscopic treatment of open channels) • ab-initio description • continuum shell model • Real-energy CSM (Hilbert space formalism) • Gamow Shell Model (Rigged Hilbert space) • cluster models • N. Michel et al., Phys. Rev. Lett. 89, • 042502 (2002); Phys. Rev. C67, 054311 (2003); Phys. Rev. C70, 064311 (2004) • G. Hagen et al, Phys. Rev. C71, 044314 (2005)

20. One-body basis Contour is discretized GSM Hamiltonian matrix is complex symmetric J. Rotureau et al., DMRG Phys. Rev. Lett., in press nucl-th/0603021 Recent work: Wigner cusp!

21. Soon: implementation to molecular and hadron spectroscopy

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

24. 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

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

26. Superheavy Elements

27. Crazy topologies of superheavy nuclei…

28. r excited 1Su and1Pu states + N N Rotational Transitions ~ 10 meV Vibrational Transitions ~ 100 meV Electronic Transitions ~ 1 eV Excitation spectrum of N2 molecule

29. 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.

30. n p Skins and Skin Modes

31. Vibrator Rotor Soft Transitional Deformed Spherical Energy Deformation

32. RARE ISOTOPE ACCELERATOR EXOTIC BEAM FACILITY

33. Future major facilities Existing major dedicated facilities NSCL GSI GANIL TRIUMF HRIBF RIKEN ISOLDE RIF Radioactive Ion Beam Facilities Worldwide

34. 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?

35. 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 description of nuclei and their reactions is needed Nuclear structure and reactions are important not just for nuclei: Understanding the quantum many-body problem at various distance/energy scales 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 THE END The Nucleus: an integral part of nuclear science

36. 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 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 HF energy

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

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

39. S1n Brown & Sherrill, MSU

40. non-perturbative behavior scattering continuum essential WS potential depth decreased to bind 7He. Monopole SGI strength varied

41. WS potential depth varied

42. Why is the shell structure changing at extreme isospins? • Many-body correlations • Pairing • Deformation (islands of inversion) • Coexistence phenomena • Is the shell model (HF) picture valid in the limit of very strong • configuration interaction? • Dripline systems • Superheavies • Low-lying open channels • The nucleus is an open quantum system • Exotic nuclei unify structure and reaction aspects • Continuum coupling can influence bulk properties (such as binding and sizes) and spectroscopy (shell effects)

43. Nuclear Input (experiment and theory) Masses and drip lines Nuclear reaction rates Weak decay rates Electron capture rates Neutrino interactions Equation of State Fission processes Supernova neutron-Star E0102-72.3 KS 1731-260 How does the physics of nuclei impact the physical universe? • What is the origin of elements heavier than iron? • How do stars burn and explode? • What is the nucleonic structure of neutron stars? X-ray burst p process s-process 4U1728-34 331 330 Frequency (Hz) r process 329 328 327 10 15 20 Time (s) rp process Nova Crust processes T Pyxidis stellar burning protons neutrons

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

45. Radioactive Ion Beam Facilities Timeline ISOLDE 2000 2005 2010 2015 2020 NSCL HRIBF CARIBU@ATLAS In Flight ISOL Fission+Gas Stopping Beam on target ISAC-II ISAC-I SPIRAL2 SPIRAL FAIR SIS RIBF RARF RIF