PU-304 · Nuclear & Particle Physics
The unit builds from the empirical structure of nuclei — binding, size, stability, and decay — up to the relativistic quantum framework that governs the subatomic world, establishing how cross-sections, decay rates, and scattering encode the underlying interactions. It culminates in the gauge and symmetry principles of the Standard Model, showing how conservation laws, spontaneous symmetry breaking, and quark structure emerge from a small set of rigorously derivable results.
Lectures
| L01 | The Nuclear Landscape: Scales, Units and the Chart of Nuclides — |
| L02 | Nuclear Sizes and Charge Distributions from Electron Scattering |
| L03 | Binding Energy and the Liquid-Drop Model |
| L04 | The Fermi Gas and the Origin of the Asymmetry Term |
| L05 | Nuclear Stability, Mass Parabolas and the Valley of Beta Stability |
| L06 | The Radioactive Decay Law and Decay Chains |
| L07 | Quantum Tunnelling and Alpha Decay |
| L08 | The Geiger-Nuttall Law and Systematics of Alpha Emission |
| L09 | Fermi's Golden Rule: Transition Rates from First Principles |
| L10 | Beta Decay: The Fermi Theory and the Continuous Spectrum |
| L11 | Kurie Plots, Sargent's Rule and the Neutrino Mass |
| L12 | Gamma Decay, Selection Rules and the Mossbauer Effect |
| L13 | The Nuclear Shell Model and Magic Numbers — |
| L14 | Fission, Fusion and Nuclear Energy |
| L15 | Scattering Theory: Cross-Sections and the Optical Picture — |
| L16 | Rutherford Scattering: Classical and Quantum |
| L17 | The Born Approximation and Form Factors |
| L18 | Relativistic Kinematics: Mandelstam Variables and Thresholds |
| L19 | Cross-Sections, Decay Widths and Lorentz-Invariant Phase Space |
| L20 | Relativistic Wave Equations I: Klein-Gordon and the Yukawa Force |
| L21 | Relativistic Wave Equations II: The Dirac Equation and Antimatter |
| L22 | Spin, Magnetic Moments and the Prediction g=2 |
| L23 | Symmetries and Conservation Laws: Noether's Theorem |
| L24 | Discrete Symmetries: Parity, Charge Conjugation and CP Violation |
| L25 | Gauge Invariance and the Origin of QED |
| L26 | Feynman Diagrams and Perturbative Amplitudes |
| L27 | Isospin, Strangeness and the Eightfold Way |
| L28 | The Quark Model and Hadron Multiplets |
| L29 | Deep Inelastic Scattering and Evidence for Partons |
| L30 | The Weak Interaction, Parity Violation and the W and Z |
| L31 | Spontaneous Symmetry Breaking and the Higgs Mechanism |
| L32 | The Standard Model Assembled and Its Open Questions |
Derivations homed in this unit
Semi-Empirical Mass Formula from the Liquid-Drop Model
Derives the nuclear binding energy B(A,Z) as a sum of volume, surface, Coulomb, asymmetry and pairing terms from the liquid-drop picture.
Coulomb Energy of a Uniformly Charged Nucleus
Derives the self-energy (3/5)(Z^2 e^2)/(4 pi eps0 R) that becomes the Coulomb term of the mass formula.
Asymmetry Term from the Fermi-Gas Model
Derives the (N-Z)^2/A symmetry energy by summing neutron and proton kinetic energies in a degenerate Fermi gas.
The Valley of Beta Stability
Derives the most stable Z for fixed A by minimising the mass formula, yielding the parabolic mass isobars and the stability line.
Gamow Factor and the Geiger-Nuttall Law
Derives the exponential tunnelling suppression through the Coulomb barrier and the linear log(t_half) vs 1/sqrt(Q) relation for alpha decay.
Fermi's Golden Rule
Derives the transition rate 2 pi/hbar |M|^2 rho(E) from first-order time-dependent perturbation theory.
Fermi Theory of Beta Decay and the Kurie Plot
Derives the electron energy spectrum and Sargent's rule from the four-fermion contact interaction and phase-space factors.
Radioactive Decay and Bateman Equations
Derives the exponential decay law and the multi-species Bateman solution for sequential decay chains and secular equilibrium.
Rutherford Scattering Cross-Section
Derives dsigma/dOmega for Coulomb scattering from classical orbit mechanics, recovered identically in the Born approximation.
Born Approximation and the Form Factor
Derives the scattering amplitude as the Fourier transform of the potential and defines the nuclear/charge form factor.
Mandelstam Invariants and Relativistic Two-Body Kinematics
Derives s, t, u, the threshold energy, and the centre-of-mass momentum for relativistic collisions and decays.
Lorentz-Invariant Phase Space and the Decay/Cross-Section Master Formulae
Derives the invariant phase-space measure and the general formulae relating |M|^2 to decay widths and cross-sections.
Klein-Gordon Equation and the Yukawa Potential
Derives the Klein-Gordon equation from E^2=p^2+m^2 and its static Green's function, giving the range h/mc Yukawa force.
Dirac Equation, Antiparticles and the g=2 Prediction
Derives the Dirac equation by linearising the relativistic dispersion, predicting spin-1/2, the magnetic moment g=2, and antiparticles.
Noether's Theorem for Conserved Currents
Derives the conserved current and charge associated with any continuous symmetry of the action.
Local U(1) Gauge Invariance Fixes the QED Coupling
Derives the minimal coupling and the photon field by demanding local U(1) invariance of the Dirac Lagrangian.
Isospin, Hypercharge and the Gell-Mann-Nishijima Relation
Derives Q = I_3 + Y/2 from SU(2) isospin and hypercharge assignments, organising the hadron multiplets.
Spontaneous Symmetry Breaking and the Higgs Mechanism
Derives how a spontaneously broken gauge symmetry gives mass to gauge bosons while a Goldstone mode is absorbed.