Neutron moderation in the Oklo natural reactor and the time variation of $\alpha$

In previous analyses of the Oklo (Gabon) natural reactor to test for a possible time variation of the fine-structure constant $\alpha ,$ a Maxwell-Boltzmann low energy neutron spectrum was assumed. We present here an analysis where a more realistic spectrum is employed and show that the most recent isotopic analysis of samples implies a decrease in $\alpha ,$ over the last $2\times {10}^9$ years since the reactor was operating, of $\left({\alpha }_{\mathrm{past}}-{\alpha }_{\mathrm{now}}\right)/\alpha >~4.5\times {10}^{-8}$ $(6\mathrm{}\sigma$ confidence). Issues regarding the interpretation of the shifts of the low energy neutron absorption resonances are discussed.