Some applications of functional analysis to problems of neutron transport

Ritz method is used to obtain an approximate solution of the stationary neutron transport Boltzmann equation in its integral form in plane and spherical symmetry. Such a method is based on the maximum property of the quadratic form corresponding to a symmetric transformation in a finite dimensional subspace spanned by the first n functions of a complete orthonormal set. In order to justify some numerical results, we also show that the transport operators are compact as acting both on the space C and on the space L2. Moreover, we investigate some properties of the solution and we prove that the neutron distribution is not increasing as a function of the spatial coordinate. Finally, a series of calculations have been performed for various values of the system-dimensions measured in mean-free-paths and the number of secondaries per conllision to maintain the system critical has been found.