The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium.
The symbols are defined as:
ν {\displaystyle \nu } , ν f {\displaystyle \nu _{f}} and ν t {\displaystyle \nu _{t}} are the average number of neutrons produced per fission in the medium (2.43 for uranium-235).
σ f F {\displaystyle \sigma _{f}^{F}} and σ a F {\displaystyle \sigma _{a}^{F}} are the microscopic fission and absorption cross sections for fuel, respectively.
Σ a F {\displaystyle \Sigma _{a}^{F}} and Σ a {\displaystyle \Sigma _{a}} are the macroscopic absorption cross sections in fuel and in total, respectively.
Σ f F {\displaystyle \Sigma _{f}^{F}} is the macroscopic fission cross-section.
N i {\displaystyle N_{i}} is the number density of atoms of a specific nuclide.
I r , A , i {\displaystyle 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 ′ {\displaystyle I_{r,A,i}=\int _{E_{th}}^{E_{0}}dE'{\frac {\Sigma _{p}^{mod}}{\Sigma _{t}(E')}}{\frac {\sigma _{a}^{i}(E')}{E'}}}
ξ ¯ {\displaystyle {\overline {\xi }}} is the average lethargy gain per scattering event. Lethargy is defined as decrease in neutron energy.
u f {\displaystyle u_{f}} (fast utilization) is the probability that a fast neutron is absorbed in fuel.
P F A F {\displaystyle P_{FAF}} is the probability that a fast neutron absorption in fuel causes fission.
P T A F {\displaystyle P_{TAF}} is the probability that a thermal neutron absorption in fuel causes fission.
B g 2 {\displaystyle {B_{g}}^{2}} is the geometric buckling.
L t h 2 {\displaystyle {L_{th}}^{2}} is the diffusion length of thermal neutrons.
L t h 2 = D Σ a , t h , {\displaystyle {L_{th}}^{2}={\frac {D}{\Sigma _{a,th}}},} where D {\displaystyle D} is the diffusion coefficient.
τ t h {\displaystyle \tau _{th}} is the age to thermal.
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