The influence of some rare earth elements as neutron absorbers on the inception of Oklo natural nuclear reactors

A totally reflected core model was built to estimate the infinite multiplication factor ${{k}}_{{\infty}}$ as a parametric function using MCNP code. Thus, it was possible to evaluate the influence of a specific physical parameter on the criticality occurrence of the Oklo phenomenon, namely initial Poisons (IP: Gd, Sm and Nd). In fact, these rare earth elements, prior to criticality occurrence in Oklo reaction zones (RZs), are considered as a key parameter in the present study. Thus, it was possible to construct isocritical lines, ${{k}}_{{\infty}}\left({{V}}_{{UO}{2}},{{\varPhi}}_{{C}}\ \right)\cong{1}$, over a significant range of Uraninite volume fraction: ${{V}}_{{UO}{2}}\left[\%\right]{\in}\left[{0};{40}\right]$. The corresponding critical porosity ${{\varPhi}}_{{C}}$ is obtained for a given value of ${{V}}_{{UO}{2}}$ by Python-driven MCNP5 calculations. By including realistic measurements of IP for different RZs, it was possible to distinguish the corresponding inception circumstances for the natural RZs considered here.