Solution of the transport equation in slab geometry for extrapolation distance problem with T1 method

In this study, the time-independent, one-speed neutron transport equation in slab geometry is solved for the extrapolated distance problem using Mark and Marshak boundary conditions. For this purpose, first the T1 approximation which adds original value to this study, is used in which the angular neutron flux is expanded into a series in terms of the first kind of Chebyshev polynomials, and then the traditional P1 approximation, in which the angular neutron flux is expanded in terms of the Legendre polynomials is used. It is assumed that the neutrons are scattered isotropically in a homogeneous slab. As a result, the calculated extrapolation distances obtained numerically by both methods are given in the tables together with the results in the literature for comparison. The T1 approximation is applied to this problem for the first time and an explicit analytical expression for the extrapolation distance is obtained.