
The frequency at which a specific nuclear reaction occurs, often estimated from cross-section data.The reaction rate is the frequency at which a specific nuclear reaction occurs, typically estimated from cross-section data. It is a central quantity in nuclear physics, astrophysics, and nuclear engineering, determining how quickly nuclei transform under given conditions. In stellar nucleosynthesis, for example, the rate of reactions like carbon fusion or neutron capture dictates the abundance of elements produced in stars and supernovae.
The concept was formalized in the early 20th century with the development of nuclear physics, particularly through the work of George Gamow and others on stellar energy generation in the 1930s.
The rate depends on the cross-section (a measure of probability for a reaction at a given energy), the number densities of the interacting particles, and their relative velocity distribution. In practice, it is computed by integrating the cross-section over the energy spectrum of the particles, often using the Gamow peak for thermonuclear reactions. For neutron-induced reactions, the rate is proportional to the neutron flux and the cross-section at the relevant energies.
Reaction rates are used to model stellar evolution, design nuclear reactors, and plan medical isotope production, such as in the creation of radionuclides for cancer therapy.
In stars, the reaction rate for proton-proton fusion is so low that a single proton would wait on average about a billion years before fusing, yet the Sun still shines because of the immense number of protons.
| \Gamma | variable | Reaction rate — reaction rate per second |
| E_a | variable | Activation energy — energy joule |
| T | variable | Absolute temperature — temperature kelvin |
| A | constant | Frequency factor, related to collision frequency and steric effects — pre exponential factor = material-dependent per second |
| k_B | constant | Relates temperature to energy — boltzmann constant = 1.380649e-23 joule per kelvin |
| e^{-E_a/k_B T} | operator | Exponential decay with inverse temperature — exponential |















