Time variability of α from realistic models of Oklo reactors

We reanalyze Oklo ${}^{149}\mathrm{Sm}$ data using realistic models of the natural nuclear reactors. Disagreements among recent Oklo determinations of the time evolution of α, the electromagnetic fine structure constant, are shown to be due to different reactor models, which led to different neutron spectra used in the calculations. We use known Oklo reactor epithermal spectral indices as criteria for selecting realistic reactor models. Two Oklo reactors, RZ2 and RZ10, were modeled with MCNP. The resulting neutron spectra were used to calculate the change in the ${}^{149}\mathrm{Sm}$ effective neutron capture cross section as a function of a possible shift in the energy of the 97.3-meV resonance. We independently deduce ancient ${}^{149}\mathrm{Sm}$ effective cross sections and use these values to set limits on the time variation of α. Our study resolves a contradictory situation with previous Oklo α results. Our suggested $2\sigma$ bound on a possible time variation of α over 2 billion years is stringent: $-0.11\le \Delta \alpha /\alpha \le 0.24$, in units of ${10}^{-7}$, but model dependent in that it assumes only α has varied over time.

Figure 1

Reactor zone RZ10 MCNP neutron fluxes and neutron densities for temperatures 20, 100, 200, 300, 420, ${500}^{°}C$. The neutron fluxes are plotted as $\varphi E$ and are the family of curves starting from a temperature of ${20}^{°}C$ at the lower left. The neutron densities (normalized to one neutron per unit volume) are the families of curves starting upper left.

Figure 2

Reactor zone RZ2 MCNP neutron fluxes and neutron densities for temperatures 20, 100, 200, 300, 420, ${500}^{°}C$. The neutron fluxes are plotted as $\varphi E$ and are the family of curves starting from a temperature of ${20}^{°}C$ at the lower left. The neutron densities (normalized to one neutron per unit volume) are the families of curves starting upper left.

Figure 3

Calculations of the ${}^{149}\mathrm{Sm}$ effective capture cross section ${\stackrel{\wedge }{\sigma }}_{149}$ as a function of a possible resonance energy shift ${\Delta }_r$ from −200 meV to +200 meV. The results shown are for RZ2 (dotted lines) and RZ10 (solid lines), and for temperatures $T$ = 20, 100, 200, 300, 420, ${500}^{°}C$ starting from the top.

Figure 4

Expanded version of the RZ10 cross section plot of Fig. 3 for temperatures 200 and ${300}^{°}C$ and the bounds on ${\Delta }_r$ obtained from our $\pm 2\sigma$ limits on the ${\stackrel{\wedge }{\sigma }}_{149}$.