A reaction cross section measures interaction probability and is defined by $$\sigma = \frac{\text{reaction rate}}{\text{incident flux}}$$. Differential cross sections resolve angular or energy dependence and are central observables in scattering experiments.

At low energies, scattering is naturally expanded in partial waves labeled by orbital angular momentum $\ell$. Resonances arise when the scattering phase shift passes rapidly through $\pi/2$, often indicating quasi-bound states or strong channel coupling.

Direct reactions occur on short timescales and often probe single-particle structure, while compound-nucleus reactions proceed through an equilibrated intermediate system. The statistical Hauser-Feshbach framework is widely used for compound reactions in nuclear astrophysics and reactor modeling.