Reappraisal of the limit on the variation in $\alpha$ implied by Oklo
  We reconsider the analysis of the sensitivity of neutron resonance energies
$E_i$ to changes in $\alpha$ with a view to resolving uncertainties that plague
earlier treatments. We point out that, with more appropriate choices of nuclear
parameters, the standard estimate (due to Damour and Dyson) of the sensitivity
for resonances in ${}^{150}$Sm is increased by a factor of 2.5. We go on to
identify and compute excitation, Coulomb and deformation corrections. To this
end, we use deformed Fermi density distributions fitted to the output of
Hartree-Fock (HF) + BCS calculations (with both the SLy4 and SkM$^*$ Skyrme
functionals), the energetics of the surface diffuseness of nuclei, and thermal
properties of their deformation. We also invoke the eigenstate thermalization
hypothesis, performing the requisite microcanonical averages with two
phenomenological level densities which, via the leptodermous expansion of the
level density parameter, include the effect of increased surface diffuseness.
Theoretical uncertainties are assessed with the \emph{inter-model} prescription
of Dobaczewski et al. [J. Phys. G: Nucl. Part. Phys. {\bf 41}, 074001 (2014)].
The corrections diminish the revised ${}^{150}$Sm sensitivity but not by more
than 25\%. Subject to a weak and testable restriction on the change in
$m_q/\Lambda$ (relative to the change in $\alpha$) since the time when the Oklo
reactors were active ($m_q$ is the average of the $\text{u}$ and $\text{d}$
current quark masses, and $\Lambda$ is the mass scale of quantum
chromodynamics), we deduce that
$|\alpha_{\text{Oklo}}-\alpha_{\text{now}}|<1.1\times
10^{-8}\alpha_{\text{now}}$ (95\% confidence level). The corresponding bound on
the present-day time variation of $\alpha$ is tighter than the best limit to
date from atomic clock experiments.
