The Oklo Natural Reactor Bound on the Fine-Structure Constant, Expressed as a Frame Coupling Limit

Two billion years ago a uranium deposit in present-day Gabon sustained fission reactions, and the isotopic abundances it left behind record the energy of a neutron-capture resonance in samarium-149 at that epoch. Because the resonance energy is exquisitely sensitive to the fine-structure constant, the record bounds any change in alpha since then to between -9.00e-08 and 1.20e-07 (Damour and Dyson 1996). Averaged over the 1.8 billion year interval the upper edge corresponds to a mean rate of 6.67e-17 per year. Expressed against logarithmic accumulation with expansion, the bound limits the coupling to 8.86e-07. The reactor bound and the laboratory-clock bound are consistent, and each disciplines the other: the reactor integrates over deep time, the clocks measure the present slope. Computed from published inputs, not measured.