Neutron calculations in the neutron shielding of fast neutron reactors are a complex problem as deterministic schemes are usually not suited for such calculations while Monte-Carlo codes have poor computational performance due to the very low flux levels in neutron shields. In this article, both methods are studied, as well as a hybrid scheme on the neutron shielding of the ASTRID fast reactor benchmark. This hybrid scheme uses a fission source calculated by a deterministic code in order to precisely calculate neutron fluxes in the shielding with a Monte-Carlo code using variance reduction techniques. This provides reference results in order to validate deterministic calculations. Comparisons between deterministic codes and this hybrid reference show that large biases are obtained, up to 50%. Further studies are made to reduce the biases, showing that many physical phenomena should be treated, including anisotropy of the scattering law at high energies and spatial self-shielding inside the boron carbide shielding. These improvements reduce the biases to less than 10%. Finally, some applications to designing criteria for the neutron shielding are presented, such as gas production in the neutron shielding and activation of secondary sodium at the intermediate heat exchanger (IHX).
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