The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium. The formula is
k = η f p ε P F N L P T N L The symbols are defined as:
ν , ν f and ν t are the average number of neutrons produced per fission in the medium (2.43 for Uranium-235). σ f F and σ a F are the microscopic fission and absorption cross sections for fuel, respectively. Σ a F and Σ a are the macroscopic absorption cross sections in fuel and in total, respectively. N i is the number density of atoms of a specific nuclide. I r , A , i is the resonance integral for absorption of a specific nuclide. I r , A , i = ∫ E t h E 0 d E ′ Σ p m o d Σ t ( E ′ ) σ a i ( E ′ ) E ′ . ξ ¯ is the average lethargy gain per scattering event.Lethargy is defined as decrease in neutron energy. u f (fast utilization) is the probability that a fast neutron is absorbed in fuel. P F A F is the probability that a fast neutron absorption in fuel causes fission. P T A F is the probability that a thermal neutron absorption in fuel causes fission. B g 2 is the geometric buckling. L t h 2 is the diffusion length of thermal neutrons. L t h 2 = D Σ a , t h . τ t h is the age to thermal. τ = ∫ E t h E ′ d E ″ 1 E ″ D ( E ″ ) ξ ¯ [ D ( E ″ ) B g 2 + Σ t ( E ′ ) ] . τ t h is the evaluation of τ where E ′ is the energy of the neutron at birth.The multiplication factor, k, is defined as (see Nuclear chain reaction):
k = number of neutrons in one generation number of neutrons in preceding generation If k is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.
If k is less than 1, the chain reaction is subcritical, and the neutron population will exponentially decay.
If k = 1, the chain reaction is critical and the neutron population will remain constant.
