Nuclear Physics

A rigorous graduate-level treatment of nuclear physics -- from nuclear forces and binding energies through radioactive decay, nuclear reactions, and models of nuclear structure -- with full derivations, numerical simulations, and Fortran/Python examples.

Course Overview

Nuclear physics explores the structure, stability, and transformations of atomic nuclei. From the discovery of radioactivity by Becquerel in 1896 to the modern understanding of nuclear forces via meson exchange and QCD, this field connects quantum mechanics, electromagnetism, and the strong interaction. This course follows the graduate-level treatment in the tradition of Krane, Wong, and Heyde, covering the full mathematical structure from first principles.

What You will Learn

  • - Nuclear forces: Yukawa potential, deuteron
  • - Binding energy and the semi-empirical mass formula
  • - Radioactive decay: alpha, beta, gamma processes
  • - Nuclear reaction kinematics and cross sections
  • - Fission and fusion physics
  • - Shell model and collective nuclear models
  • - Nuclear reactor physics
  • - Nucleosynthesis in stars and the Big Bang

Prerequisites

  • - Quantum mechanics (Schrodinger equation, angular momentum)
  • - Classical electromagnetism
  • - Special relativity basics
  • - Multivariable calculus
  • - Ordinary differential equations
  • - Linear algebra

References

  • - K. S. Krane, Introductory Nuclear Physics
  • - S. S. M. Wong, Introductory Nuclear Physics (2nd ed.)
  • - K. Heyde, Basic Ideas and Concepts in Nuclear Physics
  • - P. Ring & P. Schuck, The Nuclear Many-Body Problem

Key Equations of Nuclear Physics

Semi-Empirical Mass Formula:

$$B(A,Z) = a_V A - a_S A^{2/3} - a_C \frac{Z(Z-1)}{A^{1/3}} - a_A \frac{(A-2Z)^2}{A} + \delta(A,Z)$$

Yukawa Potential:

$$V(r) = -g^2 \frac{e^{-m_\pi r / \hbar c}}{4\pi r}$$

Course Structure

Part I: Nuclear Structure

Nuclear forces, binding energy, semi-empirical mass formula, and introduction to nuclear models.

Part II: Radioactivity & Decay

Alpha decay and tunneling, beta decay and Fermi theory, gamma transitions and selection rules.

Part III: Nuclear Reactions

Cross sections, Breit-Wigner resonances, fission chain reactions, and fusion in stars and laboratories.

Part IV: Nuclear Models

Shell model with spin-orbit coupling, magic numbers, collective models, rotational and vibrational spectra.

Part V: Applications

Nuclear reactor physics, stellar nucleosynthesis (s-process, r-process), and connections to astrophysics.

Key Results at a Glance

Nuclear Radius

$$R = r_0 A^{1/3}, \quad r_0 \approx 1.2 \text{ fm}$$

Empirical formula relating nuclear radius to mass number

Q-Value

$$Q = (M_{\text{initial}} - M_{\text{final}})c^2$$

Energy released or absorbed in a nuclear reaction

Gamow Tunneling Factor

$$G = \frac{2\pi \eta}{e^{2\pi\eta} - 1}, \quad \eta = \frac{Z_1 Z_2 e^2}{\hbar v}$$

Coulomb barrier penetration probability

Breit-Wigner Resonance

$$\sigma(E) = \pi \lambdabar^2 \frac{\Gamma_a \Gamma_b}{(E - E_0)^2 + (\Gamma/2)^2}$$

Cross section near an isolated resonance

Geiger-Nuttall Law

$$\log_{10} t_{1/2} = a + \frac{b}{\sqrt{Q_\alpha}}$$

Relationship between alpha-decay half-life and energy

Lawson Criterion

$$n \tau_E > \frac{12 k_B T}{E_\alpha \langle\sigma v\rangle}$$

Condition for self-sustaining thermonuclear fusion