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

摘要

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（?）|β1（?）β（?）β2},where β2β1-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）=N0 is given as a corollary.