U1 approximation to the neutron transport equation and calculation of the asymptotic relaxation length

The U1 approximation is used to determine the asymptotic relaxation length (diffusion length) for one-speed neutrons in a homogeneous slab. The method is based on the series expansion of the neutron angular flux in terms of the Chebyshev polynomials of second kind and then calculating the diffusion length by applying the first order approximation to transport equation. Analytic and numerical results are obtained for the diffusion length and compared with the ones obtained from the method of separation of variables and simple diffusion theory (P1 approximation). (orig.)