Gamma-ray fluxes in Oklo natural reactors

Uncertainty in the operating temperatures of Oklo reactor zones impacts the precision of bounds derived for time variation of the fine structure constant $\alpha$. Improved $^{176}$Lu/$^{175}$Lu thermometry has been discussed but its usefulness may be complicated by photo excitation of the isomeric state $^{176m}$Lu by $^{176}$Lu($\gamma,\gamma^\prime$) fluorescence. We calculate prompt, delayed and equilibrium $\gamma$-ray fluxes due to fission of $^{235}$U in pulsed mode operation of Oklo zone RZ10. We use Monte Carlo modeling to calculate the prompt flux. We use improved data libraries to estimate delayed and equilibrium spectra and fluxes. We find $\gamma$-ray fluxes as a function of energy and derive values for the coefficients $\lambda_{\gamma,\gamma^\prime}$ that describe burn-up of $^{176}$Lu through the isomeric $^{176m}$Lu state. The contribution of the ($\gamma,\gamma^\prime$) channel to the $^{176}$Lu/$^{175}$Lu isotopic ratio is negligible in comparison to the neutron burn-up channels. Lutetium thermometry is fully applicable to analyses of Oklo reactor data.