Behaviour of criticality eigenvalues of one-speed transport operator with linearly anisotropic scattering

The c--eigenvalue problem of the one-speed transport equation with linearly anisotropic scattering and vacuum boundary conditions is considered. The variation of the full c-spectrum with the system parameters is studied numerically and explained theoretically. It is noted that the c--eigenvalues are complex only for a finite interval of hiʹ the strength of anisotropic scattering. Finally. it is shown that the simple buckling approximation is valid for large systems. irrespective of the form or positivity of the scattering function.