3DHZETRN: Neutron leakage in finite objects

The 3DHZETRN formalism was recently developed as an extension to HZETRN with an emphasis on 3D corrections for neutrons and light ions. Comparisons to Monte Carlo (MC) simulations were used to verify the 3DHZETRN methodology in slab and spherical geometry, and it was shown that 3DHZETRN agrees with MC codes to the degree that various MC codes agree among themselves. One limitation of such comparisons is that all of the codes (3DHZETRN and three MC codes) utilize different nuclear models/databases; additionally, using a common nuclear model is impractical due to the complexity of the software. It is therefore difficult to ascertain if observed discrepancies are caused by transport code approximations or nuclear model differences. In particular, an important simplification in the 3DHZETRN formalism assumes that neutron production cross sections can be represented as the sum of forward and isotropic components, where the forward component is subsequently solved within the straight-ahead approximation. In the present report, previous transport model results in specific geometries are combined with additional results in related geometries to study neutron leakage using the Webber 1956 solar particle event as a source boundary condition. A ratio is defined to quantify the fractional neutron leakage at a point in a finite object relative to a semi-infinite slab geometry. Using the leakage ratio removes some of the dependence on the magnitude of the neutron production and clarifies the effects of angular scattering and absorption with regard to differences between the models. Discussion is given regarding observed differences between the MC codes and conclusions drawn about the need for further code development. Although the current version of 3DHZETRN is reasonably accurate compared to MC simulations, this study shows that improved leakage estimates can be obtained by replacing the isotropic/straight-ahead approximation with more detailed descriptions.