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.

The symbols are defined as:
 * $$\nu$$, $$\nu_f$$ and $$\nu_t$$ are the average number of neutrons produced per fission in the medium (2.43 for uranium-235).
 * $$\sigma_f^F$$ and $$\sigma_a^F$$ are the microscopic fission and absorption cross sections for fuel, respectively.
 * $$\Sigma_a^F$$ and $$\Sigma_a$$ 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.
 * $$I_{r,A,i} = \int_{E_{th}}^{E_0} dE' \frac{\Sigma_p^{mod}}{\Sigma_t(E')} \frac{\sigma_a^i(E')}{E'}$$.
 * $$\overline{\xi}$$ 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.
 * $$P_{FAF}$$ is the probability that a fast neutron absorption in fuel causes fission.
 * $$P_{TAF}$$ is the probability that a thermal neutron absorption in fuel causes fission.
 * $${B_g}^2$$ is the geometric buckling.
 * $${L_{th}}^2$$ is the diffusion length of thermal neutrons.
 * $${L_{th}}^2 = \frac{D}{\Sigma_{a,th}}$$.
 * $$\tau_{th}$$ is the age to thermal.
 * $$\tau = \int_{E_{th}}^{E'} dE \frac{1}{E} \frac{D(E)}{\overline{\xi} \left[ D(E) {B_g}^2 + \Sigma_t(E') \right]}$$.
 * $$\tau_{th}$$ is the evaluation of $$\tau$$ where $$E'$$ is the energy of the neutron at birth.

Multiplication
The multiplication factor, $neutrons produced from fission⁄absorption in fuel isotope$, is defined as (see nuclear chain reaction):


 * If $neutrons absorbed by the fuel isotope⁄neutrons absorbed anywhere$ is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.
 * If $fission neutrons slowed to thermal energies without absorption⁄total fission neutrons$ is less than 1, the chain reaction is subcritical, and the neutron population will exponentially decay.
 * If $k = number of neutrons in one generation⁄number of neutrons in preceding generation$, the chain reaction is critical and the neutron population will remain constant.