The Oklo bound on the time variation of the fine-structure constant revisited

It has been pointed out by Shlyakhter that data from the natural fission reactors which operated about two billion years ago at Oklo (Gabon) had the potential of providing an extremely tight bound on the variability of the fine-structure constant alpha. We revisit the derivation of such a bound by: (i) reanalyzing a large selection of published rare-earth data from Oklo, (ii) critically taking into account the very large uncertainty of the temperature at which the reactors operated, and (iii) connecting in a new way (using isotope shift measurements) the Oklo-derived constraint on a possible shift of thermal neutron-capture resonances with a bound on the time variation of alpha. Our final (95% C.L.) results are: -0.9 \times 10^{-7} <(alpha^{Oklo} - alpha^{now})/alpha <1.2\times 10^{-7} and -6.7 \times 10^{-17} {yr}^{-1} < {\dot alpha}^{averaged}/alpha <5.0\times10^{-17} {yr}^{-1}$.