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.
*$\Sigma_f^F$ is the macroscopic fission cross-section.
*$N_i$ is the number density of atoms of a specific nuclide.
*$I_$ is the resonance integral for absorption of a specific nuclide.
**$I_ = \int_^ dE' \frac \frac$
*$\overline$ 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.
*$P_$ is the probability that a fast neutron absorption in fuel causes fission.
*$P_$ is the probability that a thermal neutron absorption in fuel causes fission.
*$^2$ is the geometric buckling.
*$^2$ is the diffusion length of thermal neutrons.
**$^2 = \frac$
*$\tau_$ is the age to thermal.
**$\tau = \int_^ dE'' \frac \frac$
**$\tau_$ is the evaluation of $\tau$ where $E'$ 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

{{reflist

Nuclear technology
Radioactivity