On Computing Neutron Transmission from the Responses of a Void Fraction Evaluation Scheme with Mixed Beams

In this technical note we report on a slight but important modification in a recently developed backscattered neutron-based void fraction evaluation scheme for slab materials, and we describe an add-on numerical scheme for computing total (direct plus diffuse) neutron transmission through a test slab. In the void fraction evaluation scheme, the broad neutron beam consists of a monodirectional (singular), normally incident component and a smooth (regular), angularly continuous component, i.e., a mixed neutron beam. Once the void fraction of the test slab has been evaluated, the diffuse component of the angular flux of transmitted neutrons can be computed from an accurate spherical harmonics-discrete ordinates solution of the neutron beam transport problem defined in a reduced slab domain (the direct component is rather straightforward to compute). The add-on scheme described here can be used to evaluate the amount of neutrons that escape from the slab through the back side. Numerical results are given to illustrate the usefulness of our add-on scheme in neutron shielding studies.