The four-factor formula, also known as Fermi's four factor formula, is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in an infinite medium.The symbols are defined as:

• are the average number of neutrons produced per fission in the medium (2.43 for uranium-235).

• are the microscopic fission and absorption thermal cross sections for fuel, respectively.

• are the macroscopic absorption thermal cross sections in fuel and in total, respectively.

• is the macroscopic fission cross-section.

• is the number density of atoms of a specific nuclide.

is the resonance integral for absorption of a specific nuclide.

is the average lethargy gain per scattering event.

• Lethargy is defined as decrease in neutron energy.

• (fast utilization) is the probability that a fast neutron is absorbed in fuel.

• is the probability that a fast neutron absorption in fuel causes fission.

• is the probability that a thermal neutron absorption in fuel causes fission.

• is the thermal non-leakage probability

Multiplication

The multiplication factor, , is defined as (see Nuclear chain reaction):

• If is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.

• If is less than 1, the chain reaction is subcritical, and the neutron population will exponentially decay.

• If , the chain reaction is critical and the neutron population will remain constant.

, which is approximated by the four-factor formula.

See also

• Six factor formula

• Critical mass

• Nuclear chain reaction

• Nuclear reactor

References