Macroscopic Representation of the Anisotropic Neutron Flux Spectrum and a New Greuling-Goertzel Approximation

The macroscopic representation of complicated moderating processes has been investigated to describe the collision integral in the Legendre polynomial expansion of the neutron transport equation in terms of the macroscopic moderating parameter, defined as the ratio of the l'th-order Legendre component of the slowing-down density to the corresponding collision integral. This approach is similar in form to the Wigner-type continuous slowing-down theory, but the present moderating parameter is a function of lethargy, space, and time. For practical applications a new Greuling-Goertzel approximation is proposed based on the factorization of the angular flux. The present parameter, γ_l(u), is defined so as to compensate the difference between the lethargy spectrum of the space- and time-independent flux and the exact spectrum.