Four factor formula
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.
| Symbol | Name | Meaning | Formula | Typical thermal reactor value |
| Reproduction factor | 1.65 | |||
| Thermal utilization factor | 0.71 | |||
| Resonance escape probability | 0.87 | |||
| Fast fission factor | 1.02 |
The symbols are defined as:
- , and are the average number of neutrons produced per fission in the medium.
- and are the microscopic fission and absorption thermal cross sections for fuel, respectively.
- and 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.
- 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 :- 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.