Nuclear Structure – Current
Directions
A Thematic Overview
R. F. Casten
Early Universe
Temperature Tc
Quarks and Gluons
Critical Point?
Hadrons
Color SuperConductor ?
Nuclei
Neutron stars
Net Baryon Density
Nucleon
100
Mean Field Models
Collective models
Shell Model(s)
Proton Number
10
Effective
Interactions
Microscopic
Ab Initio
(GFMC...)
QCD
Bare Nucleon-Nucleon
Interactions
1
QCD Vacuum
Quark-Gluon
Interactions
QCD
Vacuum
1
5
Neutron Number
10
50
100
The Nuclear Many-Body Problem
Energy, Distance, Complexity
few
body
heavy
nuclei
quarks
gluons
vacuum
quark-gluon
soup
QCD
nucleon
QCD
few body systems many body systems
free NN force
effective NN force
The Nucleus: an integral part of nuclear science
The study of nuclei is a forefront area of science that links the Standard
Model, QCD phenomena, many-body systems, and the cosmos.
Goal: a comprehensive description of nuclei and their reactions
Nuclear structure and reactions go beyond nuclei per se:
–Understanding the quantum many-body problem at
variousdistance/energy scales
–Testing the fundamental laws of nature
–Understanding stellar evolution and the origin of the elements
–Society (national security, energy, medicine…)
Both theory and experiment are needed.
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
Nuclear Structure Theory
Overarching goal:
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
• This has been a lofty and ambitious goal 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 threenucleon components
– We seek to describe the properties of “nuclei” ranging from the deuteron
to neutron stars
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
A new era in Nuclear Structure Physics
The New Frontiers
of Physics with Exotic Nuclei
Terra incognita — huge
gene pool of nuclei
Four Frontiers
1. Proton Rich Nuclei
2. Neutron Rich Nuclei
3. Heaviest Nuclei
4. Evolution of structure within
these boundaries
We can customize our system – fabricate “any” nucleus
(designer nuclei) controlling the number of constituent
protons and neutrons to isolate and amplify specific
physics or interactions
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
4U1728-34
331
Masses and drip lines
Nuclear reaction rates
Weak decay rates
Electron capture rates
Neutrino interactions
Equation of State
Fission processes
330
329
328
327
Nuclear Input
(experiment and theory)
10
15
Time (s)
Supernova
20
Nova
neutron-Star
T Pyxidis
protons
KS 1731-260
neutrons
E0102-72.3
Themes and challenges of Modern Science
•Complexity out of simplicity
How the world, with all its apparent complexity and diversity can be
constructed out of a few elementary building blocks and their interactions
•Simplicity out of complexity
How the world of complex systems can display such remarkable regularity
and simplicity
•Understanding the nature of the physical universe
•Manipulating nature for the benefit of mankind
Nuclei: Two-fluid, many-body, strongly-interacting, quantal systems provide
wonderful laboratories for frontier research in all four areas
Nuclear collective motion
200000
counts
150000
100000
50000
0
0
1000
energy (keV)
What is the origin of
ordered motion of complex
nuclei?
Complex systems often display
astonishing simplicities. Nuclei are
no exception. How is it that a
heavy nucleus, with hundreds of
rapidly moving nucleons, can
exhibit collective motion.
Two views of nuclear structure
Single-particle motion
Single-particle excitations
with residual interactions
Bulk collective motion
Macroscopic shape
of nuclear matter
Phonons — bosons
Protons, neutrons — fermions
j = half-integer (orbital + intrinsic)
Pauli Principle: At most 2j + 1
particles in a given orbit
Microscopy, mean field, shell structure
Ui
Vij
r = |ri - rj|

 = nl , E = Enl
H.O.
Clusters of levels
 shell structure
r
E = ħ (2n+l)
E (n,l) = E (n-1, l+2)
E (2s) = E (1d)
Pauli Principle (≤ 2j+1 nucleons in orbit with ang. mom.
j)  magic numbers, inert cores, valence nucleons
Many-body  few-body: each body counts. Addition of 2
neutrons in a nucleus with 150 can drastically alter
structure
Independent Particle Motion
(particles in a box)
• Mottleson
Importance of shell gaps, magic numbers, and shell
structure is not just a matter of details but fundamental to
our understanding of one of the most basic features of
nuclei– independent particle motion. If we don’t
understand the basic quantum levels of nucleons in the
nucleus, we don’t understand nuclei.
Many aspects: Changing magic numbers, intruder
orbits, residual interactions, correlations, collectivity,
binding (e.g., drip lines, superheavies), and regularities.
Perhaps counter-intuitively, the emergence of specific
forms of nuclear collectivity depends on independent
particle motion (and the Pauli Principle).
Pairing
(in nuclei and nuclear matter)
Manifestations:
Energy gaps in even-even nuclei; Compression of levels in odd-A nuclei
Odd-even mass differences
Moments of inertia and rotational motion
Quenching of Coriolis coupling
Structural evolution in an Ising context; H = Hsph + HColl : Sph.-Def. Competition
Structural singularities in N = Z nuclei
 Unique nuclear features: surface effects/finite size, kinds
of Cooper pairs,
 Essential for existence of weakly-bound nuclei; continuum
scattering
 Various density regimes of strength
 Crucial for many-body dynamics, skin modes, pair localization
 Connection to other fields (BECs, CSC)
p-n interactions
Strongest along
diagonal where
highest p-n
overlaps occur
Empirical
R4/2
First direct
correlation of
empirical p-n
interaction
strengths with
empirical
growth rates
of collectivity
Approaches to nuclear structure
Roadmap
Ab initio
Configuration
interaction
Density
Functional
Theory
Collective and
Algebraic Models
Theoretical
approaches
overlap and
need to be
bridged
Approaches to Nuclear Structure
Microscopic – Approximate solutions to real nuclei
•
Effective Interactions
• Ab initio, No core, Monte Carlo
• Density Functional Theory
Enormously complex, numerically intensive. However,
revolutionary advances, greatly enhanced ability to predict wide variety
of nuclei  promise of a comprehensive theory
Macroscopic – Exact solutions to ideal nuclei
Geometric symmetries. Simple patterns, quantum nos., Selection rules
•
•
Analytic, Intuitive understanding -- WHAT symmetries?
Challenge to microscopy – Why THESE symmetries, which
nuclei, why in THESE nuclei?
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
Asymptotic Freedom (for theorists)
Density Functional Theory
New Features in Weakly Bound Nuclei
Spatially extended
wave functions
V (r)
Halo Nuclei
Normal
nuclear
density
11Li
p-n
core
Density
(log)
r
n-skin
0
r
10
20
Radius (fm)
Diffuse
V (r)
Normal potential
Altered shell structure
New form of matter – low density,
diffuse, spatially extended, nearly
pure neutron matter
Possible Changes in
Structure for Skin Nuclei
J. Dobaczewski and
W. Nazarewicz
h9/2
f5/2
p1/2
p3/2
f7/2
h11/2
g7/2
d3/2
s1/2
d5/2
g9/2
N=5
126
3p
2f
1h
N=4
82
3s
2d
1g
p1/2
f5/2
i13/
p23/2
h9/2
f7/2
d3/2
h11/2
s1/2
g7/2
d5/2
50
g9/2
very diffuse
surface
neutron drip line
harmonic
oscillator
no spin
orbit
exotic nuclei/
hypernuclei
around the
valley of
b-stability
SUPERHEAVIES
Classifying Structure -- The Symmetry Triangle of
Collective Behavior
Dynamical Symmetries, Phase Transitions, Critical Point Symmetries, Order and Chaos
E(5)
Deformed
Sph.
X(5)
Landau Theory
Complementarity of macroscopic and microscopic approaches.
Why do certain nuclei exhibit specific symmetries and not others?
Why these specific evolutionary trajectories? What unknown regularities appear
along the Arc?
What will happen far from stability?
Neutron “skins” near the neutron drip line
Outer regions of low density nearly pure neutron matter
Skins and Skin Modes
n
p
Production and use of Exotic Isotopes
High Energy
Heavy Ion
Driver
Intense Stable
Ion Beam
Fragmentation
Target and Ion
Separator
Exotic Ion Beam
Gas
Stopping
High Energy
Proton Driver
Intense
Proton Beam
ISOL Target/Ion
Extraction
Exotic Ions
Fast Beam
Experiments
Stopped Beam
Experiments
(Traps)
Second
Accelerator
Exotic Ion
Beam
Reaccelerated
Beam
Experiments
Radioactive Ion Beam Facilities Timeline
ISOLDE
ISAC-II
ISAC-I
SPIRAL2
SPIRAL
FAIR
SIS
RIBF
RARF
2000
2005
2010
2015
NSCL
HRIBF
In Flight
ISOL
Fission+Gas Stopping
Beam on target
CARIBU@ATLAS
RIF
2020
Exotic Nuclei
Paradigm-Changing Discovery Potential
Complexity – Simplicity
Comprehensive Understanding of Atomic
Nuclei
Links to nano-science, high energy
physics, and the cosmos
Applications
Jargon

• Key to conference is communication
• Biggest bottleneck to communication is jargon.
• Examples (some may shock you):
– Jlab: Partons, generalized parton distributions, the
sea, quantitative relation of Q2 to size, Bjorken x…
– RIA: island of inversion, yrast states, gamma
vibrations, intruder states, K quantum number, B(E2)
values, density functional theory…
Thanks to many from whom I have
stolen slides, especially Witek
Have a great Workshop !!!