## Abstract

An approach is summarized for developing a full analytical method for the generation of laboratory (lab) coordinate system multigroup transfer cross sections of elastic and discrete-level inelastic scatterings of neutrons, where the angular distribution data of the scattered neutrons are given as coefficients of truncated Legendre polynomial expansions in the center-of-mass (c.m.) coordinate system. In the ``kernel form'' of the multigroup approximation, fluxes, cross sections, and angular data are left outside the integration signs of the transfer cross-section expression. Then, the integrand is a four-index kernel - the source and sink energy groups and the Legendre polynomials in the c.m. and lab systems each contributing one index - integrated over the source and sink groups. In the method introduced, the double integration on the neutron pre- and postscattering energies, in these two groups, is carried out analytically. This is done by decomposing the Legendre polynomials in the integrand into their representations as polynomials of their arguments - the cosines of the angle of scattering in the lab and the c.m. systems. It is assumed that the flux is presented as a simple function of the neutron prescattering energy. The first integration takes place between the cosines of scattering in the c.m. system related by the kinematics of scattering to the energy boundaries of the sink group, while the second integration takes place between the energy boundaries of the source group. Transfer cross sections of discrete-level inelastic scatterings are evaluated quite similarly to those of elastic scatterings. The only difference is in the integration over the prescattering energies, which stems from the replacement of the mass number of the scattering nucleus, appearing in the expression for the cosine of scattering in the lab system, by an energy-dependent ``effective mass number'' in the case of inelastic scattering. The method of evaluation described seems to be fast and accurate and is valid theoretically up to any order of Legendre expansions desired. Some evaluations made with this method, for both elastic and discrete-level inelastic scatterings, are compared with numerical computations carried out by other methods: the NJOY cross-section processing code and the method outlined by Hong and Shultis. The flux used as a weighting function is either energy independent or of a 1/E′ form (where E′ is the prescattering energy of the neutron). The results are in good agreement.

Original language | English |
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Pages (from-to) | 319-344 |

Number of pages | 26 |

Journal | Nuclear Science and Engineering |

Volume | 111 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jan 1992 |

## ASJC Scopus subject areas

- Nuclear Energy and Engineering