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The first order approximations of the Legendre and Chebyshev polynomials are applied to neutron transport equation to calculate the diffusion length for one-speed neutrons in a uniform homogeneous slab. The Anli-Güngör (AG) phase function is used for the scattering kernel. Analytic and numerical results are obtained for the diffusion length of the neutrons in terms of scattering parameters of AG phase function and cross-section parameters. The numerical results for certain scattering parameters of AG phase function and selected values of cross-section parameter from first order approximations of both Legendre and Chebyshev polynomials are tabulated in the tables for comparison.

Diffusion approximation for certain scattering parameters of the Anli-Güngör phase function