Lesson 5 Fundamental Aspects of Nuclear Structure

Fundamental Forces of Nature

Exchange Particles and Force Carriers Forces occur through the notion of the virtual exchange of bosons that are force carriers “Virtual” means we can “violate” conservation of energy by an amount ΔE for a time Δt given 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

Electromagnetic force Virtual exchange of photons

Nuclear Force Virtual exchange of particles of mass m

What does this mean? ForceExchange Particle MassRange Electromagneti c photon0infinite Gravitygraviton0infinite WeakW boson90 GeV/c fm Stronggluon> 140 MeV/c 2 < 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 fm Evidence for this a.Saturation of forces, nearest neighbor interaction, B.E.(a v A) 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

Other potentials of note

Charge independence of nuclear forces The nuclear force between a neutron and a proton is the same as the force between two protons or two neutrons. A NucleusTotal Binding Energy (MeV) Coulomb Energy (MeV) Net nuclear binding energy (MeV) 3 3H3H He C N Na Ne Ca Sc 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, T 3 =+1/2 (proton) and T 3 =-1/2 (neutron) For a nucleus containing Z protons and N neutrons, T 3 =(Z-N)/2.

Example Consider the A=10 isobars, 10 Be, 10 B and 10 C. 10 Be and 10 C have T 3 =±1. Thus they must be part of an isospin multiplet, T=1. In 10 B, T 3 =0, but there must be a state with T=1. This state is called the isobaric analog of the ground states of 10 Be and 10 C.

Quarks Properties of Quarks Spin ½ Charge ±1/3, ±2/3 6 types (flavors) Size < m

The proton The 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 Hadrons interact via the strong interaction—p,n Leptons Do not interact via the strong interaction--e

Types of Hadrons Baryons (Fermionic Hadrons) Composed of three quarks like the proton or neutron They are fermions Strongly interacting Mesons (Bosonic Hadrons) Composed of quark/anti-quark pairs. They are bosons Strongly 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