core), one can write a modified evolution equation: where is the rate at which the external source injects neutrons into the core. In equilibrium, the core is not changing and dN/dt is zero, so the equilibrium number of neutrons is given by: If the core is subcritical, then is negative so there is an equilibrium with a positive number of neutrons. If the core is close to criticality, then is very small and thus the final number of neutrons can be made arbitrarily large. Neutron moderators To improve and enable a chain reaction, natural or low enrichment uranium-fueled reactors must include a neutron moderator that interacts with newly produced fast neutrons from fission events to reduce their kinetic energy from several MeV to thermal energies of less than one eV, making them more likely to induce fission. This is because 235U has a larger cross section for slow neutrons, and also because 238U is much less likely to absorb a thermal neutron than a freshly produced neutron from fission. Neutron moderators are thus materials that slow down neutrons. Neutrons are most effectively slowed by colliding with the nucleus of a light atom, hydrogen being the lightest of all. To be effective, moderator materials must thus contain light elements with atomic nuclei that tend to scatter neutrons on impact rather than absorb them. In addition to hydrogen, beryllium and carbon atoms are also suited to the job of moderating or slowing down neutrons. Hydrogen moderators include water (H2O), heavy water (D2O), and zirconium hydride (ZrH2), all of which work because a hydrogen nucleus has nearly the same mass as a free neutron: neutron-H2O or neutron-ZrH2 impacts excite rotational modes of the molecules (spinning them around). Deuterium nuclei (in heavy water) absorb kinetic energy less well than do light hydrogen nuclei, but they are much less likely to absorb the impacting neutron. Water or heavy water have the advantage of being transparent liquids, so that, in addition to shielding and moderating a reactor core, they permit direct viewing of the core in operation and can also serve as a working fluid for heat transfer. Carbon in the form of graphite has been widely used as a moderator. It was used in Chicago Pile-1, the world's first man-made critical assembly, and was commonplace in early reactor designs including the Soviet RBMK nuclear power plants such as the Chernobyl plant. Moderators and reactor design