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

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

Nuclear Landscape protons neutrons stable nuclei proton drip line superheavy nuclei Nuclear Landscape 126 stable nuclei 82 r-process known nuclei proton drip line terra incognita 50 protons rp-process 82 neutron stars neutron drip line 28 20 50 8 28 neutrons 2 20 2 8

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

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

(can be unified at low-k) 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

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

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

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

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

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!

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

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

Microscopic Mass Formula (can we go below 500 keV?) Goriely, ENAM’04 Reinhard 2004 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

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

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

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

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

Shells Nuclei Sodium Clusters 28 50 82 126 58 92 138 198 experiment theory discrepancy 20 60 100 -10 10 Nuclei Number of Neutrons Shell Energy (MeV) 28 50 82 126 diff. -1 1 50 100 150 200 Number of Electrons Shell Energy (eV) 58 92 138 198 experiment theory deformed clusters spherical Sodium Clusters

Old paradigms, universal ideas, are not correct Near the drip lines nuclear structure may be dramatically different. No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32… First experimental indications demonstrate significant changes

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

Superheavy Elements

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

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

Skins and Skin Modes p n p n p n

(in nuclei and nuclear matter) 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

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

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.

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

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

nuclear collective dynamics 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

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

Summary 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.

EXTRAS

QCD Complex Systems Cosmos subfemto… nano… Giga… femto… Physics Origin of NN interaction Many-nucleon forces Effective fields femto… Physics of Nuclei How does complexity emerge from simple constituents? How can complex systems display astonishing simplicities? Complex Systems nano… Quantum many-body physics In-medium interactions Symmetry breaking Collective dynamics Phases and phase transitions Chaos and order Dynamical symmetries Structural evolution Cosmos Giga… Nuclear Astrophysics 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 do nuclei shape the physical universe?

(with realistic effective forces and effective operators) 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.

Coupled Cluster Method (with microscopic effective forces) 16O with Idaho-A ORNL, Oslo, MSU, UT 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 Challenges & GOALS: Implementation of NNN Open-shell, A=20-50 nuclei Nuclear matter