A Potential Issue Involving the Application of the Unit Base Transformation to the Interpolation of Secondary Energy Distributions

Secondary neutron energy spectra used by Monte Carlo codes are often provided in tabular format. Examples are the spectra obtained from ENDF/B-VI File 5 when the LF parameter has the value 1. These secondary spectra are tabulated on an incident energy mesh, and in a Monte Carlo calculation the tabulated spectra are generally interpolated to the energy of the incident neutron. A common method of interpolation involves the use of the unit base transformation. The details of the implementation vary from code to code, so here we will simply focus on the mathematics of the method. Given an incident neutron with energy E, the bracketing points Ei and Ei+1 on the incident energy mesh are determined. The corresponding secondary energy spectra are transformed to a dimensionless energy coordinate system in which the secondary energies lie between zero and one. A dimensionless secondary energy is then sampled from a spectrum obtained by linearly interpolating the transformed spectra--often using the method of statistical interpolation. Finally, the sampled secondary energy is transformed back into the normal energy coordinate system. For this inverse transformation, the minimum and maximum energies are linearly interpolated from the values given in the non-transformed secondary spectra. The purpose of the unit base transformation is to preserve (as nearly as possible) the physics of the secondary distribution--in particular the minimum and maximum energies possible for the secondary neutron. This method is used by several codes including MCNP and the new MC21 code that is the subject of this paper. In comparing MC21 results to those of MCNP, it was discovered that the nuclear data supplied to MCNP is structured in such a way that the code may not be doing the best possible job of preserving the physics of certain nuclear interactions. In this paper, we describe the problem and explain how it may be avoided