From Atoms, to Nucleons, to Quarks Why we call quarks and leptons the “building blocks” of nature. The only quarks needed to build up protons and neutrons are u and d. u has charge 2e/3, and d has charge minus e/3. What quarks do neutrons contain? Helium Who ordered this one? What else can we make from the six quarks? Thousands of other not-so-stable particles! The only particles needed to build the periodic table of the elements are protons, neutrons, and electrons! (Plus photons and gluons!)

Particle “multiplets”: “periodic tables” of the strongly interacting particles. Spin1/2 Proton Neutron Spin 3/2

Distances: Atoms, to Nucleons, to Quarks

The fundamental building blocks in nature, and the interactions among them. Electromagnetic Force Strong (Nuclear) Force Weak Force (Changes particle types) Gravity (Gravitons?)

Easy way to picture particle masses? 2/22/2019 5

Approximate Representations of the Nuclear Potential

The nucleus can be thought of as a spherical finite potential well that is created and filled by the nucleons themselves. Even though closely packed, the nucleons are quasi-free and they will occupy the energy levels within this well from the lowest energies upward, constrained by the Pauli Exclusion principle. Like electrons filling orbital states in atoms, there are quantum numbers nlm associated with these levels, which nucleons can fill partially or completely. When a given “shell” is filled (see below) the corresponding nucleus will be much more stable than its “nearby” isotopes. This is the basis of the “shell model” of nuclei.

Alpha decay is a quantum tunneling process The illustration represents an attempt to model the alpha decay characteristics of polonium-212, which emits an 8.78 MeV alpha particle with a half-life of 0.3 microseconds. The Coulomb barrier faced by an alpha particle with this energy is about 26 MeV, so by classical physics it cannot escape at all. Quantum mechanical tunneling gives a small probability that the alpha can penetrate the barrier. To evaluate this probability, the alpha particle inside the nucleus is represented by a free-particle wavefunction subject to the nuclear potential. Inside the barrier, the solution to the Schrodinger equation becomes a decaying exponential. Calculating the ratio of the wavefunction outside the barrier and inside and squaring that ratio gives the probability of alpha emission. The half-lives of heavy elements which emit alpha particles varies over 20 orders of magnitude, from about a tenth of a microsecond to 10 billion years. This half-life range depends strongly on the observed alpha kinetic energy which varies only about a factor of two; from about 4 to 9 MeV. This extraordinary dependence upon kinetic energy suggests an exponential process, and is modeled by quantum mechanical tunneling through the Coulomb barrier.