= Nuclear chain reaction
{title2=$N_{g+1}=k_{\rm eff}N_g$}
{wiki}
A <nuclear chain reaction> is a sequence in which <particles> released by one <nuclear reaction> induce further <nuclear reactions>. In a neutron-driven <nuclear fission> chain, emitted <neutrons> can cause new <nuclear fission>, be absorbed without causing <nuclear fission>, or leave the material.
In a simple generation model, let $N_g$ be the mean number of chain-carrying <neutrons> in generation $g$, and let $k_{\rm eff}$ be their effective reproduction ratio. Then $N_{g+1}=k_{\rm eff}N_g$. For $k_{\rm eff}<1$ the mean chain dies away; $k_{\rm eff}=1$ gives a steady mean population; and $k_{\rm eff}>1$ gives growth in this fixed-coefficient model. Thus a steady chain has reproduction ratio one, while a growing chain is also self-sustaining in the mean. This elementary generation model does not describe every timescale or spatial change.
Whether material is <fissile material> depends on reaction probabilities, neutron production and losses in a specified setting. A positive <nuclear fission> <Q value> establishes that the final products can release <energy>, but does not by itself establish the neutron balance.
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