Using modern methods of reactor physics we have performed full-scale calculations of the natural reactor Oklo. For reliability we have used recent version of two Monte Carlo codes: Russian code MCU REA and world wide known code MCNP (USA). Both codes produce similar results. We have constructed a computer model of the reactor Oklo zone RZ2 which takes into account all details of design and composition. The calculations were performed for three fresh cores with different uranium contents. Multiplication factors, reactivities and neutron fluxes were calculated. We have estimated also the temperature and void effects for the fresh core. As would be expected, we have found for the fresh core a significant difference between reactor and Maxwell spectra, which was used before for averaging cross sections in the Oklo reactor. The averaged cross section of Sm-149 and its dependence on the shift of resonance position (due to variation of fundamental constants) are significantly different from previous results. Contrary to results of some previous papers we find no evidence for the change of the fine structure constant in the past and obtain new, most accurate limits on its variation with time: -4 10^{-17}year^{-1} < d alpha/dt/alpha < 3 10^{-17} year^{-1} A further improvement in the accuracy of the limits can be achieved by taking account of the core burnup. These calculations are in progress.
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