Using certain well-known properties of chebyshev polynomials, a simple and highly efficient approach to evaluate eigenvalue in radiation transport is presented. The spectrum of eigenvalues has been studied for slabs with isotropic scattering of different magnitudes of the cross section parameter c (i.e., the mean number of neutrons emitted per collision). It is shown that in the presence of the chebyshev polynomial approximation (T-N) there are both discrete and continuum of eigenvalues. It is found that the T-N method gives very good agreement with conventional spherical harmonies approximation (PN). (c) 2005 Elsevier Ltd. All rights reserved.