1. 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

2. 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

3. 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

4. Theory roadmap

5. Energy Scales in Nuclear Physicsd _ 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

6. (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

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

17. 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

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

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

22. 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

23. 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

24. 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?

25. Superheavy Elements

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

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

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

31. (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

32. 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

33. Nuclear collective motion
Rotational Transitions ~ MeV
Vibrational Transitions ~ 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. Q1 Q E Q2 Q0 fission/fusion exotic decay heavy ion coll. shape
coexistence Q2 Q0
fission/fusion
exotic decay
heavy ion coll.

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

36. 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

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

40. 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.

41. EXTRAS

42. 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?

43. (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, (2004)
Navratil, Ormand, et al.

44. 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