Six factor formula
The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium.
| Symbol | Name | Meaning | Formula | Typical Thermal Reactor Value |
| Thermal Fission Factor | The number of fission neutrons produced per absorption in the fuel. | 1.65 | ||
| The thermal utilization factor | Probability that a neutron that gets absorbed does so in the fuel material. | 0.71 | ||
| The resonance escape probability | Fraction of fission neutrons that manage to slow down from fission to thermal energies without being absorbed. | 0.87 | ||
| The fast fission factor | 1.02 | |||
| The fast non-leakage probability | The probability that a fast neutron will not leak out of the system. | 0.97 | ||
| The thermal non-leakage probability | The probability that a thermal neutron will not leak out of the system. | 0.99 |
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 cross sections for fuel, respectively.
- and are the macroscopic absorption cross sections in fuel and in total, respectively.
- 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 geometric buckling.
- is the diffusion length of thermal neutrons.
- *.
- is the age to thermal.
- *.
- * is the evaluation of where is the energy of the neutron at birth.
Multiplication
- 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.