Neutron transport through semi-infinite continuous stochastic media using Gaussian statistics

The stationary solution of the one-speed neutron transport equation in a semi-infinite stochastic medium with linear anisotropic scattering is considered. The cross-section function of the medium is assumed to be a continuous random function of position with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as radiant neutron energy and net neutron flux, for an arbitrary correlation function. The problem is solved at first in the deterministic case, then the solution is averaged using Gaussian joint probability distribution function. A modified Gaussian probability distribution function is also used to average the solution. Numerical results are given for the sake of comparison