The criticality of the transport system in a slab geometry with partially reflecting boundary conditions

In this paper we investigate the critical solution of transport System in a slab geometry with partially reflecting boundary conditions. We shed the p roperties of the principal eigenvalue (i.e. the critical parameter) of the corresponding Boltzmann integral operator, by using the functional analysis , especially the operator theory in LP spaces. WE) prove that the correspon ding transport system is in the subcritical state if k<1, and the critical stab exists if k<1, where c(x). Sigma (x) is the total cross section, scatt ering-fission cross section, respectively and k = varisup {c (x) [Sigma (x) ](-1)}.