In discrete ordinates (S_n) discontinuous finite element (DFEM) radiation transport calculations, the current standard is to assume cell-wise constant radiation interaction cross-sections or opacities for all problems. However, interaction cross sections are functions of spatially varying quantities such as temperature, density, burn-up history, etc., and thus are not in reality cell-wise constants. We show that assuming cell-wise constant cross sections for problems with spatially varying cross sections limits solution accuracy and introduces non-physical interaction rate behavior in neutronics problems. We then show that this behavior also occurs in the temperature solution of coupled radiative transfer solutions. Finally, we introduce a family of DFEM schemes for problems with spatially varying cross section that alleviate the non-physical interaction rates and are not limited in order of accuracy or convergence.