bogner nuclear theory

8/13/2019 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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Alternative form of Uncertainty Principle:

(I.e., Energy)


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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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Ex: Gravitational force between Earth, Moon, and a satellite


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Ex: Gravitational force between Earth, Moon, and a satellite

Tidal bulge changes mass distribution (and hence gravitational force)


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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!

bogner nuclear theory

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