nuclear physics

• The production of the first nuclei began 13.7 billion years ago in the Big Bang by nuclear reactions between protons and neutrons.
• 10-3 seconds after the Big Bang, the universe was at a temperature T~10^12 K.
• Deuterons, the isotope 2 H, were created and rapidly destroyed by high energy photons known as gamma/γ-rays, achieving a state of equilibrium.
• Following expansion of the universe, it cooled to T~10^9 K.
• Gamma-ray energies associated with lower temperature/ thermal energy distribution fell below the deuteron binding energy of 2.22 MeV, causing deuterium to no longer be destroyed by photons.
• Following the production of deuterium, 3 He, 4 He, and some 6 Li and 7 Li were also synthesised in the big bang.
• Gamow thought all elements were produced in the Big Bang, but he was wrong.
• The solution to the equation n(t) = n(0) exp ( υ q – 1)t/ τ is an exponential increase in neutron density and energy release for masses exceeding a critical mass, such as 52kg for a spherical sample of pure 235 U material, with a value τ ~ 10 - 8 s.
• For υ q > 1, a steady source of energy is required corresponding to υ q – 1 = 0.
• For a typical thermal reactor, τ ~ 10 - 3 s, making it a short time-scale to control fluctuations in energy production.
• The fission reaction products themselves are a source of delayed neutrons.
• The radioactive β - - decay process sometimes produces an excited state in the intermediate system 87 Kr that is above the neutron separation energy and a neutron is emitted.
• The 87 Br lifetime is ~ 80s, allowing time to control the total neutron density (from prompt and delayed neutrons) in the reactor core by moving in and retracting control rods, which are made of B or Cd, strong neutron absorbers.
• The abundances of these light elements are the earliest observational evidence we have relating to the big-bang.
• Big-bang nucleosynthesis ended after ~3 minutes.
• Cosmic microwave background radiation originates from ~300,000 years later by comparison.
• The strong force binds the deuteron and nuclei in general.
• Nuclei typically have a similar average binding energy per nucleon: B(N, Z)/A ~ 8 MeV.
• The total volume binding energy is associated with binding energy in the bulk of the nuclear interior.
• There is a gradual reduction in B (N, Z)/A beyond A>60.
• The nucleus can be considered analogous to a spherical charged liquid drop with a total Coulomb potential energy α Q 2 / R (radius) α Z 2 / A 1/3.
• The Z 2 dependence of the total volume binding energy is proportional to the total number of pairs of protons interacting with one another electrostatically.
• The total volume binding energy only scales with the number of nucleons A, due to the short range nature of the strong force.
• The line of nuclear stability represents the locus of nuclear stability as a function of N and Z.
• There are 262 stable nuclei in nature but in total ~7000 isotopes, including unstable ones, are expected to exist.
• Stable isotopes, corresponding to the most tightly bound configurations, have N=Z up to Z~20 and then a gradual excess of neutrons with increasing A.
• N=Z represents the most bound configuration since nucleons will occupy the lowest energy levels in the ground-state configuration.
• The energy of the highest occupied level is known as the Fermi Energy, E F, which can be estimated by considering the nucleus to be a Fermi gas of freely moving fermionic particles confined within a box of volume.
• For neutrons, N/V = 1/3 π 2 * (2 m n E F / 2 ħ 2 ) 3/2, giving E F ~ 38 MeV.
• Nucleons are typically moving at relatively low speeds (compared to c), and non-relativistic methods, such as the Schroedinger equation, can be applied.
• The uncertainty in the energy of a quantum system, Δ E, is related to the time interval over which the system changes appreciably, Δ t, by Δ E Δ t ~ ħ.
• All unstable quantum states have a finite (>0) energy uncertainty.
• The nuclear potential can be modelled by the nucleon density distribution ρ(r).
• The Woods-Saxon potential is a square well with rounded edges.
• The constant density ρ0 inside all nuclei results in a constant nuclear potential V0 ~ 50 MeV.
• Bound nucleons have KE<50 MeV (<<m p,n ~1 GeV/c 2 ).
• The non-relativistic Schrödinger equation with the Woods-Saxon potential can be used to predict quantised energy levels.
• The spin-orbit term in the nuclear potential is essential to understand the major shell structure of heavier nuclei.
• The spin-orbit interaction in nuclei is associated with the strong interaction and is not electromagnetic in origin.
• Spin-orbit splitting is much greater in magnitude in nuclei than in atoms.