Nuclear reactor physics
Modern deposits of uranium contain only up to ~0.7% U (and ~99.3% U), which is not enough to sustain a chain reaction moderated by ordinary water. But U has a much shorter half-life (700 million years) than U (4.5 billion years), so in the distant past the percentage of U was much higher. About two billion years ago, a water-saturated uranium deposit (in what is now the Oklo mine in Gabon, West Africa) underwent a naturally occurring chain reaction that was moderated by groundwater and, presumably, controlled by the negative void coefficient as the water boiled from the heat of the reaction. Uranium from the Oklo mine is about 50% depleted compared to other locations: it is only about 0.3% to 0.7% U; and the ore contains traces of stable daughters of long-decayed fission products.Fermi age theory
Isotopes of protactinium
Protactinium-231 is the longest-lived isotope of protactinium, with a half-life of 32,760 years. In nature, it is found in trace amounts as part of the actinium series, which starts with the primordial isotope uranium-235; the equilibrium concentration in uranium ore is 46.55 Pa per million U. In nuclear reactors, it is one of the few long-lived radioactive actinides produced as a byproduct of the projected thorium fuel cycle, as a result of (n,2n) reactions where a fast neutron removes a neutron from Th or U, and can also be destroyed by neutron capture though the cross section for this reaction is also low.