The Ben-Gurion University measurements of neutron energy spectra in a graphite stack, resulting from the scattering of 14.7-MeV neutrons streaming through a 6-cm-diam collimator in a 121-cm-thick paraffin wall, have been used as a benchmark for the compatibility and accuracy of discrete ordinates, Pn, and transport calculations and as a tool for fusion reactor neutronics. The transport analysis has been carried out with the DOT 4.2 discrete ordinates code and with cross sections processed with the NJOY code. Most of the parameters affecting the accuracy of the calculations have been investigated: the density of the spatial mesh, the order of expansion of the flux and L system scattering cross sections in the Pn approximation, the quadrature set employed, and the energy multigroup structure., First, a spectrum calculated with DOT 4.2, with a detector located on the axis of the system, was compared with a spectrum calculated with the MCNP Monte Carlo code, which was a preliminary verification of the DOT 4.2 results. Both calculated spectra were in good agreement., Next, the DOT 4.2 calculations were compared with the measured spectra. The comparison showed that the discrepancies between the measurements and the calculations increase as the distance between the detector and the system axis increases. This trend indicates that when the flux is determined mainly by multiple scatterings, a more divided multigroup structure should be employed., Nevertheless, the agreement between the measurement and the calculation for a detector located on the axis is good. The slight discrepancy in this case is attributed to an inadequacy in the ENDF/B-V elastic scattering data of carbon, as well as to an erroneous unfolding of the neutron energy spectra with the FORIST code from proton-recoil spectra measured by an NE-213 scintillator., A P7 (or even P6) order of scattering is sufficient for most of the neutron transport problems associated with a high degree of anisotropy because the Legendre expansion of the flux converges much faster than that of the L system Legendre components of the scattering cross sections. The P7 order of scattering is needed only for treatment of elastic scattering, while lower orders of scattering are needed for discrete-level inelastic scatterings.