Editing Nuclear chain reaction (section)

==== Six-factor formula ====
The effective neutron multiplication factor <math>k_{\mathrm{eff}}</math> can be described using the product of six probability factors that describe a nuclear system. These factors, traditionally arranged chronologically with regards to the life of a neutron in a [[Thermal-neutron reactor|thermal reactor]], include the probability of fast non-leakage <math>P_{\mathrm{FNL}}</math>, the fast fission factor <math>\varepsilon</math>, the resonance escape probability <math>p</math>, the probability of thermal non-leakage <math>P_{\mathrm{TNL}}</math>, the thermal utilization factor <math>f</math>, and the neutron reproduction factor <math>\eta</math> (also called the neutron efficiency factor). The six-factor formula is traditionally written as follows:

<math>k_{\mathrm{eff}} = P_{\mathrm{FNL}} \varepsilon p P_{\mathrm{TNL}} f \eta</math>

Where:

* <math>P_{\mathrm{FNL}}</math> describes the probability that a [[Neutron temperature|fast neutron]] will not escape the system without interacting. 
** The bounds of this factor are 0 and 1, with a value of 1 describing a system for which fast neutrons will never escape without interacting, i.e. an infinite system.
** Also written as <math>L_f</math>
* <math>\varepsilon</math> is the ratio of total fissions to fissions caused only by thermal neutrons
** Fast neutrons have a small probability to cause fissions in uranium, specifically uranium-238.
** The fast fission factor describes the contribution of fast fissions to the effective neutron multiplication factor
** The bounds of this factor are 1 and infinity, with a value of 1 describing a system for which only thermal neutrons are causing fissions. A value of 2 would denote a system in which thermal and fast neutrons are causing equal amounts of fissions.
* <math>p</math> is the ratio of the number of neutrons that begin thermalization to the number of neutrons that reach thermal energies.
** Many isotopes have "resonances" in their capture [[Neutron cross section|cross-section]] curves that occur in energies between fast and thermal.
** If a neutron begins thermalization (i.e. begins to slow down), there is a possibility it will be absorbed by a non-multiplying material before it reaches thermal energy.
** The bounds of this factor are 0 and 1, with a value of 1 describing a system for which all fast neutrons that do not leak out and do not cause fast fissions eventually reach thermal energies.
* <math>P_{\mathrm{TNL}}</math> describes the probability that a thermal neutron will not escape the system without interacting.
** The bounds of this factor are 0 and 1, with a value of 1 describing a system for which thermal neutrons will never escape without interacting, i.e. an infinite system.
** Also written as <math>L_{th}</math>
* <math>f</math> is the ratio of number of thermal neutrons absorbed in by [[Fissile material|fissile]] nuclei versus the number of neutrons absorbed in all materials in the system.
** This factor describes the efficiency of thermal neutron utilization in the system, hence the name thermal utilization factor.
** The bounds of this factor are 0 and 1, with a value of 1 describing a system for which the entire system is made of fissile nuclei (i.e. thermal neutrons can only react with fissile materials). Similarly, a value of 0.5 describes a system for which reactions with fissile and non-fissile nuclei are equal.
** For a conventional nuclear power reactor, this factor is the only one that can be directly controlled by the operator. With manipulations to the [[control rod]]s, you can increase the amount of neutrons being absorbed in non-fissile nuclei while simultaneously decreasing the amount of neutrons absorbed in fissile nuclei.
* <math>\eta</math> describes the probability that a neutron absorbed will cause a fission reaction.
** This factor describes the behavior of the fissile material, specifically if a neutron is absorbed, how likely is it to cause a fission, and how many neutrons does the fission produce.

The multiplication factor is sometimes calculated with a simplified [[four factor formula|four-factor formula]], which is the same as described above with <math>P_{\mathrm{FNL}}</math> and <math>P_{\mathrm{TNL}}</math> both equal to 1, and is used when an assumption is made that the reactor is "infinite" in that neutrons are very unlikely to leak out of the system. This value <math>k_\infty</math> is often used in safety evaluations of reactor designs.