A NOTE ON THE SPECTRUM OF NEUTRON TRANSPORT OPERATOR IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α(v,μ),γ(v,μ)and the scattering-fission kernel k(x,v,v′,μ,μ′)are boundedmeasurable,and the total collision frequency v∑(x,v)is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i(?)|β(?)β(?)β},where β>β>-λ~*,with λ~* the essential infimum of v∑(x,v).Fi-nally,the asymptotic expansion of the solution for the time-dependent equation(dN)/(dt)=AN,N(0)=Nis given as a corollary.