Virginia TechLarsen, E. W.Zweifel, Paul F.2014-04-092014-04-091974-11Larsen, E. W., Zweifel, P. F., "On the spectrum of linear transport operator," J. Math. Phys. 15, 1987 (1974); http://dx.doi.org/10.1063/1.16665700022-2488http://hdl.handle.net/10919/47086In this paper, spectral properties of the time_independent linear transport operator A are studied. This operator is defined in its natural Banach space L 1(D _ V), where D is the bounded space domain and V is the velocity domain. The collision operator K accounts for elastic and inelastic slowing down, fission, and low energy elastic and inelastic scattering. The various cross sections in K and the total cross section are piecewise continuous functions of position and speed. The two cases _0>0 and _0=0 are treated, where _0 is the minimum neutron speed. For _0=0, it is shown that _(A) consists of a full half_plane plus, in an adjoining strip, point eigenvalues and curves. For _0>0, _(A) consists just of point eigenvalues and curves in a certain half_space. In both cases, the curves are due to purely elastic ``Bragg'' scattering and are absent if this scattering does not occur. Finally the spectral differences between the two cases _0>0 and _0=0 are discussed briefly, and it is proved that A is the infinitesimal generator of a strongly continuous semigroup of operators.en-USIn Copyrightelasticityeigenvaluestransport propertieselastic collisionsinelastic scatteringneutronsspectral propertiesArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/15/11/10.1063/1.1666570https://doi.org/10.1063/1.1666570