The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium.
+ Six-factor formula: Symbol Name Meaning Formula Typical thermal reactor value Thermal fission factor (eta) 1.65 Thermal utilization factor 0.71 Resonance escape probability 0.87 Fast fission factor (epsilon) 1.02 Fast non-leakage probability 0.97 Thermal non-leakage probability 0.99
The symbols are defined as: , and are the average number of neutrons produced per fission in the medium (2.43 for uranium-235). 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 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 geometric buckling. is the diffusion length of thermal neutrons. where is the diffusion coefficient. is the age to thermal.
is the evaluation of where is the energy of the neutron at birth.
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.
See also Critical mass Nuclear chain reaction Nuclear reactor Four factor formula
References