Nuclear Physics: the Shell Model - PowerPoint Presentation

Slide1

Nuclear Physics: the Shell Model

Maria

Goppert-Mayer with the King of Sweden in 1963. 2nd female Nobelist after Marie Curie.

Nuclear spin-orbit

Magic Numbers (especially stable)

The nuclear shell model is a model of the atomic nucleus that uses the Pauli exclusion principle to describe the structure of nuclear states in terms of energy levels. (May remind you of the shells in atomic physics but is different).

What is the multiplicity of the 1S and 1P states ?Slide2

BTW what is the parity of the nuclear states in the 1P level of the shell model ?

P=(-1)

l

O

17

8 (oxygen 17) example: 8 protons filling the first three shells and 8 neutrons filling the three shells and one extra neutron. The extra neutron is in a d-shell l=2, s=1/2 so the j value for O17 is 5/2 and P=(-1)l =+1, JP=5/2+Slide3

Today’s Plan

More QCD:

1) Quick review of nucleon substructure and the parton model2) Evolution of αS versus Q23) OZI rule4) Color singlet bound states

Pick a notable paper for a 15 minute presentation in April from Experimental Foundations of Particle Physics or other source.Slide4

What is an example of experimental evidence that quarks have spin ½ ?

What is an example of experimental evidence that

partons (quarks) in the nucleon are fractionally charged ?What is an example of experimental evidence for the existence of gluons ?What is an example of experimental evidence for the existence of a quark-antiquark sea in the nucleon ?

deviation of ratio of νN to anti-

ν N from 35. Give some examples of experimental evidence for the existence of the color quantum number.

6. Why does Bjorken scaling breakdown ?Review questions Angular distribution of e+

e-q qbar

;

Callan

-Gross relation in deep inelastic scattering,

Ratio of

eP

to

νN

cross-section (5/18); ratio of

νN

to anti-

ν

N (also steps in R)

Three jet events

Cross-section ratio R; pi-zero width;

Δ++ and Pauli exclusion principle

Gluon bremsstrahlung

.Slide5

QCD: The strong interaction coupling is not constant

Running of α

S

is a large effect (note the contrast to QED).

The width of the yellow band is the theoretical uncertainty.Slide6

QCD versus QED I

In QED, there are only fermion loops e.g. virtual

e+e- contributions. In QCD there are also boson loops.

Field Theory Question:

What are these boson loops ?

Ans: Gluon loops involving the three-gluon coupling. These contribute with the opposite sign compared to fermion loops.QCD

QEDSlide7

QCD versus QED II

QCD

QED

Here

n

f

is the number of active quark flavors and μ is the renormalization scale.

Question:

How does the running of the coupling compare ? What is the same and different ?Slide8

Note log scale for Q

QCD coupling is weak at high Q

2Slide9

Major sources include deviations from scaling in deep inelastic scattering, ratio of three jets to two jet events, measurements of R etc.Slide10

QCD

asymptotic freedom and confinement

QCD

Here

n

f is the number of active quark flavors and μ is the renormalization scale.

2004 Nobel Prize in Physics.Both Politzer and

Wilczek

were graduate students at the time of their 1973 work.

David

Politzer

David Gross

Frank

WilczekSlide11

Outtakes from a Jefferson Lab movie on quark confinement in hadrons.

Quark being struck in a) and re-

hadronizing. Note the gluonic strings !Slide12

QCD Coupling is weaker at shorter distances and individual quarks are confined.Slide13

In Quantum Field Theory, introduce a β function that describes the dependence of the coupling on the renormalization scale μ.

QED

QCD

Can also do this for the electroweak theory and

supersymmetry

.Not covered in BettiniSlide14

Introduce the QCD mass scale Λ

QCD

With this definition,

Note that the coupling constant

diverges

at Λ

QCD (In QED divergence at the Landau pole, very high energies chap 5.)QCD diverges at low energy !! Slide15

Masses in QCD are also running

In QED masses of leptons are observable and can identified in the theory without ambiguity.

In QCD, masses are like coupling constants and depend on the energy scale due to the effect shown above.

Effects are clear for the b quark mass.Slide16

OZI(Okubo Zweig

Iizuka) Suppression

Radiative charmonium decay

Strong decays with disconnected quark lines are highly suppressed.

Question:

Draw the Feynman diagram for ϕπ+ π- π0 explicitly showing the gluons.Slide17

Question:

Draw the Feynman diagram for

ϕπ+ π- π0 explicitly showing the gluons.

How many powers of α

S

are needed in the diagram on the right ?The diagram on the left has very little phase space (Q value is tiny) compared to the one on the right. Calculate. Yet it is dominant. Why ?BF=84%Slide18

OZI(Okubo-Zweig-

Iizuka) Suppression

Radiative

charmonium decay(a good way to find “

glueballs”)Slide19

Notice the narrow resonances in this log-log plot !!Slide20

Question:

Why

is the J/

ψ so narrow (factor of 50) ?

Hint if needed.

Ans: OZI

suppression and running of αS