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The diffusion lengths for one-speed neutrons are calculated by solving transport equation in one-dimensional spherical geometry. The pseudo-slab transport equation is obtained using a reasonable approach. The neutron angular flux is expanded in a series of both the Chebyshev polynomials of first and second kinds. Then analytic and numerical results for asymptotic relaxation length are obtained by applying first order approximations to the transport equation and they are compared with each other.

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The UN method is used to solve the critical slab problem for reflecting boundary conditions in one-speed neutron transport theory. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. It is shown that the method converges rapidly with easily executable equations. The presented numerical results are compared with the results available in the literature.