Proof and implementation of the stochastic formula for ideal gas, energy dependent scattering kernel

The ideal gas, scattering kernel for heavy nuclei with pronounced resonances was developed [Rothenstein, W., Dagan, R., 1998. Ann. Nucl. Energy 25, 209–222], proved and implemented [Rothenstein, W., 2004 Ann. Nucl. Energy 31, 9–23] in the data processing code NJOY [Macfarlane, R.E., Muir, D.W., 1994. The NJOY Nuclear Data Processing System Version 91, LA-12740-M] from which the scattering probability tables were prepared [Dagan, R., 2005. Ann. Nucl. Energy 32, 367–377]. Those tables were introduced to the well known MCNP code [X-5 Monte Carlo Team. MCNP – A General Monte Carlo N-Particle Transport Code version 5 LA-UR-03-1987 code] via the “mt” input cards in the same manner as it is done for light nuclei in the thermal energy range. In this study we present an alternative methodology for solving the double differential energy dependent scattering kernel which is based solely on stochastic consideration as far as the scattering probabilities are concerned. The solution scheme is based on an alternative rejection scheme suggested by Rothenstein [Rothenstein, W. ENS conference 1994 Tel Aviv]. Based on comparison with the above mentioned analytical (probability S(α,β)-tables) approach it is confirmed that the suggested rejection scheme provides accurate results. The uncertainty concerning the magnitude of the bias due to the enhanced multiple rejections during the sampling procedure are proved to lie within 1–2 standard deviations for all practical cases that were analysed.