Bogner Nuclear Theory
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Transcript of Bogner Nuclear Theory
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An Introduction to TheoreticalNuclear Physics
Scott Bogner (NSCL/MSU)July 23, 2008
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Different Length Scales 1026 m universe
1024 m cluster of galaxies 1022m milky way
1014 m solar system/star
107m earth
100
m human beings 10-2 m insects
10-5 m cells
10-8 m DNA
10-10m atom
10-14 m nucleus
10-15 m nucleons
10-16 m quarks/gluons
10-22m strings?
Many aspects governedby laws of Classical
Physics
Purely QuantumPhenomena
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Nuclei are REALLY small
Atoms are really small Typical atomic size: ~10-10m 10,000,000 atoms in a row: thickness of your
fingernail Best (scanning tunneling) microscopes are just good
enough to resolve individual atoms
Nuclei are another factor100,000 smaller Typical nuclear size:
~10-15m
Nucleus inside an atom islike a golf ball in a footballstadium (but containsalmost all of the mass )
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How do we learn about nuclei?
We hit the nuclei (with other nuclei or elementaryparticles or gamma rays) and watch what happens.
Nuclear processes require high energy (> 1 MeV)
More than 100,000 times the energy of chemical processes
Nuclear processes last a very short time (
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Nuclei: From Simplicity to Complexity
vacuumvacuum
RHICRHIC
CEBAFCEBAF
RIARIA
nucleonnucleonQCDQCD
few-body systemsfew-body systemsfree NN forcefree NN force
many-body systemsmany-body systems
effective NN forceeffective NN force
fewfewnucleonsnucleons
heavyheavynucleinuclei
quarksquarksgluonsgluons
quark-gluonquark-gluonplasmaplasmaQCDQCD
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The Challenge for Nuclear Theorists Starting from the forces between nucleons, can we solve the
equations of Quantum Mechanics to predict allobservableproperties of allnuclei?Analogous to what is done intheoretical chemistry given the Coulomb force betweenelectronsexcept our problem is much harder!
1)
2)
3)
4)
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1) What binds protons and neutrons into stable/rare nuclei?
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2)
e.g., collective rotations and vibrations involving all of thenucleons in a nucleus moving in concert w/each other.
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1. What is dark matter?
2. What is dark energy?3. How were the heavy elements
from iron to uranium made?
4. ..
3) How were the heavy elements made?
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Atoms, Nuclei, and Nucleons
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Quantum Mechanics in 5 Minutes
The Heisenberg Uncertainty Principle
h = Plancks Constant = 6.63 x 10-34Joule-Second
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Quantum Mechanics in 5 Minutes
Alternative form of Uncertainty Principle:
(I.e., Energy)
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Quantum Mechanics in 5 Minutes
Atoms, Nuclei, etc. can only exist in certain
allowable discrete (quantum) states
e.g., Boron-10 nucleus hasstates with different discreteenergies and angular momentum
Only certain quantum numbers(I.e., values of energy andangular momentum) appear inNature.
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Feynman Diagrams
virtual particles can do weird things like violate the Conservationof Energy (!!) by an amount !E provided we pay it back in !t = h/(4"!E)
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The Strong Force at WorkThe strong-force between 2 nucleons is due to the exchange of
virtual pairs of quarks (called mesons).
Unfortunately, only the longest range part of the nuclear force(due to pion-exchange) is well-known and understood.
= several fermi( 1 fermi = 10-15m)
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Three-Body Forces Between Nucleons
A three-body force is a force that does not exist in a systemof two particles but appears in a system of three particles.
A Corny Analogy:People particlesEmotions forces
Then jealousy islike a three-bodyforce!!
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Three-Body Forces Between Nucleons
A three-body force is a force that does not exist in a systemof two particles but appears in a system of three particles.
Ex: Gravitational force between Earth, Moon, and a satellite
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Three-Body Forces Between Nucleons
A three-body force is a force that does not exist in a systemof two particles but appears in a system of three particles.
Ex: Gravitational force between Earth, Moon, and a satellite
Tidal bulge changes mass distribution (and hence gravitational force)
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Three-Body Forces Between Nucleons
The 3-body nuclear force arises from the squishiness ofnucleons since they are composite objects made up of quarks.
Quarks Earths Oceans in the previous example
N
N
N
!
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Complexity in Many-Body Systems
2 !
Np
102 !105
logC
VERY Schematically
Complexity
# of particles
mesoscopic systems are the hardest!
few-body systems are easy in that the quantum mechanical equations can often be solved exactly, sometimes just with pencil and paper!
paradoxically, systems with millions (or even #) of
particles are often easy to describe since statistical trends and regularities emerge independent of details Nuclear theorists are unlucky as nuclei consist of 10s or 100s of particles and fall in between (mesoscopic)
Computers are essential to solve these problems!
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Moores Law
Computer speed doubles every 18 months (Moores Law) Data storage doubles every 12 months Network speed doubles every 9 months Improvement 1988 to 2005
Computers: x 2,500 Storage: x 130,000 Networks: x 6,600,000
Physics limits not to bereached for another decade
or moreMoores Law vs. storage improvements vs. optical
improvements. Graph from Scientific American (Jan-
2001) by Cleo Vilett, source Vined, Khoslan, Kleiner,
Caufield and Perkins.
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Computer Speeds and Moores Law
Earth Simulator
BlueGene
ASCI White
ASCI Red
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Visualization using Computers
Type IA supernova explosion
(BIG SPLASH)
Fusion Stellarator
Acceleratordesign
Atmospheric models
Multi-scale
model of
HIV
Materials: Quantum Corral
Collection: D. Dean, ORNL
Nuclear Physics: STAR event (G.D. Westfall)
Insight
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Huge national effort to bring theoretical physicistsand computer scientists together to attack cuttingedge problems using supercomputers.
Scientific Discovery throughAdvanced Computing
Project Building a Universal NuclearEnergy Density Functional
(SciDAC)
MSU is a member multi-million $ project Funded in 5 year intervals
Paradigm shift of how science is done (open source codes, etc.) SciDAC funds several other big science collaborations, see http://www.scidac.gov
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An example : Mass
0.5115.486x1
0-4
9.11x10
-31
Electron
939.571.008665
1.675x10-27
Neutron
938.281.007276
1.673x10-27
Proton
MeV/c2
ukgParticle
1 unified mass unit: mass(12C)/12Einstein: E=mc2 so: m=E/c2
1eV=1.60217733x10-19 J1MeV=1.60217733x10-13 J
1u=931.494 MeV/c2
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Binding energy and MassThe total energy (mass) of a bound system is lessthan the combined energy (mass) of the separatednucleons!!
Example: deuteron 2H (1 proton + 1 neutron)
mp =1.007825 umn =1.008665 u
mp+n =2.016490 u m2H=2.014102 u
The deuteron is 0.002338 u lighter than the sum ofthe proton and the neutron. This is thebindingenergy and is the energy needed to break thatnucleus apart
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Binding energy
MeV perNucleon
Atomic mass
M(A)=M(Z)+M(N)-B(N,Z)
Most stable
MeasuredBinding energy
Can we (theorists) calculate these
from first principles?
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To give a taste of the types of calculations we can now do:
Calculate the binding energies of > 2000 nuclei in a matter of hours
RMS error ~ 1-2 MeV(out of 100s of MeV)
Many of these sophisticated computerprograms are freely available thanks toSciDAC. ==> More science gets donein this open source model.
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Summary The Big Questions in nuclear theory are often intimately
related to the Big Questions in other fields of science, most
notably Astrophysics.
Nuclear theorists must contend with complications that ourfriends in other areas of physics and chemistry never have toworry about.
Three-body forces exist Incomplete knowledge of the nuclear forces
The nuclear force is a strong force
Nuclei are mesoscopic systems
As a consequence, advanced supercomputing resources areessential to our field. Indeed, one can even say a newdiscipline of Computational Physics has arisen in the lasttwo decades. Thanks to SciDAC, our community is slowlyembracing the open source model, which will hopefully resultin more physics getting done!