Lesson 5

Fundamental Aspects of Nuclear Structure

Fundamental Forces of Nature

Force

Range (m)

Relative Strength

Force Carrier Gravitational

∞

10-38

Graviton

W eak

10-18

10-5

W ±, Z0

Electrom agnetic

∞

=1/137

Photon

Strong

10-15

1

Gluon

Exchange Particles and Force Carriers

Forces occur through the notion of the virtual exchange of bosons that are force carriers

€

Δt = hΔE

“Virtual” means we can “violate” conservation of energy by an amount ΔE for a time Δtgiven by the Heisenberg Uncertainty Principle by emitting a photon (boson)

The distance travelled by this photon is R where R=cΔt

For particles with mass

€

Δt ≤ h /mc 2

€

R ≤ h /mc

Electromagnetic force• Virtual exchange of photons

€

ΔE • Δt ≥ h

Δt ≈ hΔE

R = cΔt ≈ hcΔE

= hcmc 2 = ∞

Nuclear Force• Virtual exchange of particles of mass m

2

2

/1404.1 cMeVmfmRmc

R

mct

≥⇒=

≤

≤Δ

h

h

What does this mean?

Force Exchange Particle

Mass Range

Electromagnetic

photon 0 infinite

Gravity graviton 0 infinite

Weak W boson 90 GeV/c2 10-3 fm

Strong gluon > 140 MeV/c2 < 1.4 fm

Let’s focus on the strong or nuclear force.

What are the properties of the “strong” force?

1. It is “short” range, R < 1.4 fmEvidence for this

a. Saturation of forces, nearest neighbor interaction, B.E.(avA)

2. It is attractive with a repulsive core (quark volume)

Nuclear Force• Not spherically symmetric (deuteron

quadrupole moment), has symmetric central component and asymmetric tensor component.

• Spin dependent (deuteron ground state is triplet, singlet state is unbound)

Nuclear potential (simple square well model)

Woods-Saxon Potential

€

V = − V0

1+ exp r − Ra

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Woods-Saxon Potential

€

V = − V0

1+ exp r − Ra

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Other potentials of note

Other potentials of note

Charge independence of nuclear forces

The nuclear force between a neutron and a proton is the same as the force betweentwo protons or two neutrons.

A

Nucleus Total Binding Energy (MeV)

Coulomb Energy (MeV)

Net nuclear binding energy (MeV)

3 3H -8.486 0 -8.4863He -7.723 0.829 -8.552

13 13C -97.10 7.631 -104.73413N -94.10 10.683 -104.770

23 23Na -186.54 23.13 -209.6723Ne -181.67 27.75 -209.42

41 41Ca -350.53 65.91 -416.4441Sc -343.79 72.84 -416.63

Table 5-1

Isospin

Consider that the neutron and the proton are just two states of the nucleon. Consider further that these two states are labeled by a quantum number, T, called isospin.

For the nucleon, T=1/2. There are two projections of T in isospace, T3=+1/2 (proton) and T3=-1/2 (neutron)

For a nucleus containing Z protons and N neutrons, T3=(Z-N)/2.

ExampleConsider the A=10 isobars, 10Be, 10B and 10C. 10Be and 10C have T3=±1.Thus they must be part of an isospin multiplet, T=1. In 10B, T3=0, but there must be a state with T=1. This state is called the isobaric analog of the ground states of 10Be and 10C.

QuarksProperties of QuarksSpin ½Charge ±1/3, ±2/36 types (flavors)Size < 10-18 m

The protonThe neutron

Back to “Fundamental Particles”“Classification of Particles”

Using Spin For Classification

Fermions(e,p,n) ½ integer spin No two particles may occupy the same quantum state.

Bosons(photon) Integer spin Do not obey Pauli exclusion principle

(Animation)

Types of Fermions

Fermionic Hadronsinteract via the strong interaction—p,n

LeptonsDo not interact via the strong interaction--e

Types of Hadrons

Baryons (Fermionic Hadrons)Composed of three quarks like the proton or neutron

They are fermionsStrongly interacting

Mesons (Bosonic Hadrons)Composed of quark/anti-quark pairs.They are bosonsStrongly interacting

Examples of Fermions

Lepton conservation

The number of leptons is conserved in nuclear processes

L=1 for each particle, L=-1 for each antiparticle

Examples of Bosons