HauserFeshbach

Hauser-Feshbach, also known as Hauser-Feshbach theory, is a statistical model used to calculate cross sections for nuclear reactions that proceed via a compound nucleus. Developed by Hartland S. Hauser and Fred Feshbach in 1952, it provides a framework for understanding reactions in which the intermediate nucleus reaches statistical equilibrium before decaying.

The core idea is that when a reaction forms a highly excited intermediate nucleus, the decay probabilities into various exit channels depend on the density of available final states and the probability for emitted particles to penetrate potential barriers. The theory relies on Bohr’s independence hypothesis, which states that the formation and decay of the compound nucleus are independent processes and that the decay does not remember how the nucleus was formed. In practice, cross sections are obtained by averaging over many resonances, treating the compound-nucleus stage statistically.

Formally, the cross section for a reaction a + A → c + C is described by a sum over compound-nucleus states of products of transmission coefficients for the entrance and exit channels, weighted by level densities. Transmission coefficients are computed from optical-model potentials, while level densities describe the number of available final states at a given excitation energy. Gamma and particle emission channels compete, and width fluctuation corrections account for statistical correlations between partial widths.

Computationally, Hauser-Feshbach is embedded in reaction-model codes such as TALYS, EMPIRE, and CoH, and is used in various nuclear data libraries. Required inputs include optical-model potentials, nuclear level densities, gamma-ray strength functions, and fission properties. The model is often combined with pre-equilibrium or direct-reaction components for a complete description.

Applications span nuclear astrophysics, reactor design, activation cross sections, and isotope production. Its validity hinges on a high level density in the compound nucleus; it is less reliable for light nuclei, near reaction thresholds, or environments where direct reactions dominate.