Perspektywy Teorii Struktury Jądra Atomowego
Witold Nazarewicz (Tennessee/Warszawa)
Kraków, Maj 2006
•
•
•
•
Wstęp
Pytania i zadania dla teorii
Modele struktury: dziś i jutro
Podsumowanie
The Nuclear Many-Body Problem
relativistic
heavy ions
electron
scattering
radioactive
beams
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
Energy Scales in Nuclear Physics
u
g
g g
g
g
g
g
g
g
g
g
_
d
_
ud
_
u d_
ud
QCD scale
1000 MeV
pion p+
~140 MeV
_ _
u d u_d
d
u
u u
u
_d_
d ud ud d
Effective Field Theory tells us that:
pion-mass
• Short-range (high-k) physics
can bescale
integrated out
• No need to worry about explicit inclusion of hard coredeuteron
• Low-energy phenomena can be described with low-k ~3 MeV
100 MeV
forces
N-binding scale
10 MeV
collective ~1 MeV
J. Dobaczewski, RIA Summer School, 2004
Questions that Drive the Field
of Nuclear Physics with Nucleons
•
•
•
•
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?
Physics
of nuclei
•
•
•
When and how did the elements from iron to uranium originate?
How do stars explode?
What is the nature of neutron star matter?
Nuclear
astrophysics
•
•
Why is there more matter than antimatter?
What are the weak interactions among hadrons, and how are
they affected by the nucleus?
What are the masses of neutrinos and how have they shaped
the evolution of the universe?
Fundamental
interactions
& neutrinos
•
•
How can our knowledge of nuclei and our ability to produce them
benefit the humankind?
–
–
–
–
Life Sciences
Material Sciences
Nuclear Energy
Security
Applications
of nuclei
Nuclear Structure Theory
Overarching goal:
To arrive at a comprehensive and unified microscopic description of all
nuclei and there low-energy reactions from the the basic interactions
between the constituent protons and neutrons
• This is a lofty and ambitious goal that has been a “Holy Grail” in
physics 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
Theory roadmap
Nuclear Structure: the interaction
• Effective-field theory potentials
Parameters for EFT three-nucleon interaction
Best EFT threenucleon potential
N3LO: Entem et al.,
PRC68, 041001 (2003)
•Quality two- and three-nucleon
interactions exist
•The challenge is to understanding
how to use them in nuclei
Bottom-up approaches to nuclear structure
Roadmap
Ab initio
Configuration
interaction
Density
Functional
Theory
Collective and
Algebraic Models
(top-down)
Theoretical
approaches
overlap and
need to be
bridged
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)
No-Core Shell Model
Coupled-Cluster Techniques
Unitary Model Operator Approach
Faddeev-Yakubovsky
Bloch-Horowitz
…
12C
13C
16O
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!)
1024 is not an option!!!!
Smarter solutions are needed
Challenges:
Martinez-Pinedo
ENAM’04
Configuration space
Effective Interactions
Open channels
Nuclear DFT
From Qualitative to Quantitative!
Deformed Mass Table in one day!
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
Shell Energy (MeV)
10
Shells
experiment
experiment
0
-10
Nuclei
theory
theory
0
-10
20 28
discrepancy
50
82
126
0
diff.
20
60
100
Number of Neutrons
Sodium Clusters
1 experiment
Shell Energy (eV)
-10
0
-1
58
1 theory
92
138
198
spherical
clusters
0
deformed
clusters
-1
50
100
150
200
Number of Electrons
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 missing pieces?
Ab Initio
Shell Model
Density Functional Theory
What are the limits of atoms and nuclei?
Do very long-lived superheavy nuclei exist?
What are their physical and chemical properties?
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
What are the limits of nuclear
mean field?
lifetimes > 1y
Towards the Nuclear Energy Density Functional
(Equation of State)
Challenges:
•density dependence of the symmetry energy
•neutron radii
•clustering at low densities
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.
Skins and Skin Modes
n
n
p
p
p
n
LAND-FRS
Collective or single-particle?
Skin effect? Threshold effect?
Energy differential electromagnetic
dissociation cross section
Deduced photo-neutron
cross section.
E
fission/fusion
exotic decay
heavy ion coll.
Q0
E
Q
shape
coexistence
Q1 Q2 Q
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
Shape coexistence
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
•coupling to continuum in weakly bound
systems
•dynamical corrections; fundamental
theoretical problems.
•rotational, vibrational, translational
•particle number
•isospin
GCM
M. Bender et al., PRC 69, 064303 (2004)
Nuclear Structure
and Reactions
Nuclear Theory
forces
methods
extrapolations
low-energy
experiments
Nuclear Astrophysics
Tests of the Standard Model
Parity violation
studies in francium
82
protons
Weak interaction
studies in N=Z nuclei
EDM search
in radium
50
Specific
nuclei offer new opportunities
82
for precision tests of:
28
20
50
8
28
2
20
2 8
126
neutrons



CP and P violation
Unitarity of the CKM matrix
…
How will we turn experimental signals into precise
information on physics beyond the standard
model?
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…
Physics
of Nuclei
•In-medium interactions
•Symmetry breaking
•Collective dynamics
•Phases and phase transitions
•Chaos and order
•Dynamical symmetries
•Structural evolution
Giga…
How do nuclei shape the physical
universe?
•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 forefront area of science. It is this research that
makes the connection between the Standard Model, QCD phenomena, manybody systems, and the cosmos.
A comprehensive and unified theory for nuclei and their reactions is needed
Nuclear structure and reactions are important for not just nuclei:
• Understanding the quantum many-body problem
• 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
• Theory gives the mathematical formulation of our understanding and
predictive ability
• Experiment provides verification
END
How does the physics of nuclei impact the physical universe?
RIA intensities (nuc/s)
2
> 1012Mass
10known
1010 Half-life
10-2 known
10-6 known
106 nothing
• 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
n-Star
T Pyxidis
protons
KS 1731-260
neutrons
E0102-72.3