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Structure of Exotic Nuclei
Witold Nazarewicz (UT/ORNL)
NSCL User Workshop 2005
• Introduction
• Roadmap
• Why Exotic Nuclei?
• Examples
• Summary
Theory roadmap
What are the missing pieces?
Ab Initio
Shell Model
Density Functional Theory
asymptotic
freedom…
Nuclear Landscape
126
stable nuclei
82
known nuclei
protons
terra incognita
50
82
Precision measurements on light nuclei
28
20
50
8
28
2
20
2 8
neutrons
Changes in shell structure for very
neutron-rich nuclei
Nuclear structure below
100Sn
Isospin physics: EOS, masses, moments,
reaction mechanism, Astro…
Diagonalization Shell Model
(medium-mass nuclei reached;dimensions 109!)
Challenges:
Configuration space
1024 is not an option!!!!
Smarter solutions are 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!
Interactions: Shell Model on the interface…
Intruder states
in the sdpf nuclei
Gergana Stoitcheva et al.
Zdunczuk et al.,
Phys.Rev. C71 (2005) 024305
different behavior
for N=Z and N>Z
nuclei
Competition between
and
Surprisingly strong
B(E2)’s !!!
M. Lach et al., E. Phys. J. A, in press
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
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
Michel, Rotureau, Nazarewicz, Ploszajczak
scattering
continuum
essential
bound-state
structure
dominates
non-perturbative
behavior
•25 points in p1/2 and p3/2 contours, DMRG treatment
•Two-body interaction fitted to g.s. of 6He and 7He
Meister et al. (2002)
Towards the Universal Nuclear Energy Density Functional
Walter Kohn: Nobel Prize in Chemistry in 1998
0 r   0 r ,r    r  ;r  
isoscalar (T=0) density 0  n   p 
1r   1 r ,r    r  ;r  
isovector (T=1) density 1  n   p 





s0 r    r  ;r  '   '
s1r  
isoscalar spin density
 ' 
 r ;r  '    
'
 '





i
'  T r ,r ' r ' r
2
i
JT r   '   sT r ,r ' r ' r
2

 T r    ' T r,r ' r ' r
kinetic density

TT r    ' sT r,r ' r ' r
kinetic spin density



jT r  
current density
spin-current tensor density
H T r   CT T2  CTs sT2  CT T T  CTssT sT


+CT T  T  j  C sT  TT  J  C

2
T
Local densities
and currents
+ pairing…

isovector spin density
T
T
2
T
J
T
See Bertsch et al.
PRC71, 054311 (2005)
  J
T
T

 sT   jT
 2
 3
E tot     0 + H0 r   H1r d r
2m


Total groundstate HF energy
Example: Skyrme
Functional
Nuclear DFT
From Qualitative to Quantitative!
Deformed Mass Table in one day!
Towards the Nuclear Energy Density Functional
(Equation of State)
Challenges:
•density dependence of the symmetry energy
•neutron radii
•clustering at low densities
From Finite Nuclei to the Nuclear Liquid Drop
Leptodermous Expansion Based on the Self-consistent Theory
P.G. Reinhard, M. Bender, W.N., T. Vertse
The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature
constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density
functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained
self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of
A-1/3 (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to
perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei
with huge numbers of nucleons, of the order of 106.
The limitations of applying the leptodermous expansion for finite nuclei are discussed. While the
leading terms in the macroscopic energy expansion can be extracted very precisely, the higherorder, isospin-dependent terms are prone to large uncertainties due to finite-size effects.
From HF
or RMF
Shell corr. estimated using
Green’s function method
Liquid-Drop Expansion
O(0)
O(1)
Droplet Model Expansion
Myers, Swiatecki 1974
O(2)
asurf
avol
residual
shell effects
8000
1000
300
125
LDM and Droplet Model Coefficients
Skins and Skin Modes
n
n
p
p
p
n
Beyond Mean Field
examples
GCM
M. Bender et al., PRC 69, 064303 (2004)
Shape coexistence
HFB+QRPA
J. Terasaki et al., Phys. Rev. C71, 034310 (2005)
Soft modes in drip-line nuclei
Isoscalar 1- Strength Function in the Sn Isotopes
(Jun Terasaki, QRPA+HFB)
What is the nature of
the low-energy strength?
•Skin effect
•Threshold effect?
•Both?
Old paradigms, universal ideas, are not correct
Near the drip lines nuclear structure may be
dramatically different.
First experimental indications
demonstrate significant changes
Sn  F  
S2n  2F

No shell closure for N=8 and 20
for drip-line nuclei; new shells at
14, 16, 32…
What are the limits of s.p. motion?
Excitation energy
Isospin
Mass and charge
Nuclear Structure
and Reactions
Nuclear Theory
forces
methods
extrapolations
low-energy
experiments
Nuclear Astrophysics
subfemto…
• How does complexity emerge from
simple constituents?
• How can complex systems display
astonishing simplicities?
nano…
•Origin of NN interaction
•Many-nucleon forces
•Effective fields
femto…
Giga…
Physics
of Nuclei
How do nuclei shape the physical
universe?
•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
The study of nuclei is a
of science. It is this
makes the connection
phenomena, many-body
the cosmos.
END
forefront area
research that
between QCD
systems, and
Instead of summary….
Robert B. Laughlin, Nobel Prize Lecture, December 8, 1998