Proof of the formula for the ideal gas scattering kernel for nuclides with strongly energy dependent scattering cross sections

The current study is a sequel to a paper by Rothenstein and Dagan [Ann. Nucl. Energy 25 (1998) 209] where the ideal gas based kernel for scatterers with internal structure was introduced. This double differential kernel includes the neutron energy after scattering as well as the cosine of the scattering angle for isotopes with strong scattering resonances. A new mathematical formalism enables the inclusion of the new kernel in NJOY [MacFarlane, R.E., Muir, D.W., 1994. The NJOY Nuclear Data Processing System Version 91 (LA-12740-m)]. Moreover the computational time of the new kernel is reduced significantly, feasible for practical application. The completeness of the new kernel is proven mathematically and demonstrated numerically. Modifications necessary to remove the existing inconsistency of the secondary energy distribution in NJOY are presented.