Editing Nuclear chain reaction (section)

==== Special reactivity cases ====
Not all neutrons are emitted as a direct product of fission; some are instead due to the [[radioactive decay]] of some of the fission fragments. The neutrons that occur directly from fission are called "prompt neutrons", and the ones that are a result of radioactive decay of fission fragments are called "delayed neutrons". The fraction of neutrons that are delayed is called <math>\beta</math>, as discussed before, and this fraction is typically less than 1% of all the neutrons in the chain reaction.<ref name="Duderstadt" />

As the delayed neutron precursors (the radionuclides that decay via neutron emission) have decay constants on the order of seconds and milliseconds, the delayed neutrons born from them allow the neutron population in a system to respond to small reactivity changes several orders of magnitude more slowly than just prompt neutrons would alone, as these delayed neutrons effectively increase the mean neutron lifetime <math>l</math>.<ref name="Lamarsh" /> Without delayed neutrons, changes in reaction rates in nuclear systems would occur at speeds that are too fast for humans to control.

When <math>\beta_{\mathrm{eff}}>0</math> and <math>\rho = 0</math>, a nuclear system is called '''[[Delayed criticality|delayed critical.]]''' The region of supercriticality where <math>0 < \rho < \beta_{\mathrm{eff}}</math> is known as '''delayed supercriticality.''' It is in this region that all nuclear power reactors operate. When <math>\rho = \beta_{\mathrm{eff}}</math>, the system is described as '''prompt critical'''. The region of supercriticality for <math>\rho > \beta_ {\mathrm{eff}}</math> is known as '''prompt supercriticality.''' This is the region in which nuclear weapons operate, alongside some pulsing nuclear research reactors, like the [[TRIGA]] reactor.
[[File:Criticality Diagram.png|alt=A graph with a horizontal line denoting the point at which k_effective equals 1 and five sets of bars composed of two sections stacked on each other labeled "prompt" (bottom) and "delayed" (top). The five categories moving left to right are "Subcritical," "Delayed Critical," "Delayed Supercritical," "Prompt Critical," and "Prompt Supercritical." The bars are lengthening from left to right. For subcriticality the bar is below the line. For delayed critical, the bar is just touching the line. For delayed supercritical, the delayed section of the bar is above the line. For prompt critical, the delayed section is completely above the line and the prompt section is just touching the bar. For prompt supercritical, the delayed section is completely above the line, and the prompt section extends partially above the line.|center|thumb|400x400px|Graphical representation of delayed and prompt criticality and supercriticality]]