A nucleus is a self-bound quantum many-body system of protons and neutrons interacting through the strong interaction. At low energies the relevant degrees of freedom are nucleons, not quarks and gluons, so nuclear structure is often described using effective Hamiltonians of the form $$H = \sum_i T_i + \sum_{i<j} V_{ij} + \sum_{i<j<k} V_{ijk} + \cdots$$ where two- and three-nucleon forces dominate the structure of light and medium-mass nuclei.

Important conserved quantities include baryon number, electric charge, total angular momentum $J$, parity $\pi$, and isospin $T$ as an approximate symmetry. Nuclear states are classified by $J^\pi T$ and often by additional shell-model quantum numbers when a mean-field approximation is valid.

The nucleon-nucleon force contains a short-range repulsive core, an intermediate-range attractive component, tensor forces, spin-orbit terms, and strong dependence on spin and isospin channels. These features explain deuteron binding, saturation trends, and the nontrivial shell structure of nuclei.