Multigroup transport equations with nondiagonal cross section matrices

It is shown that multigroup transport equations with nondiagonal cross section matrices arise when the modal approximation is applied to energy dependent transport equations. This work is a study of such equations for the case that the cross section matrix is nondiagonalizable. For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions.