A study on the solution of the extrapolation distance for monoenergetic neutrons using U1 method in neutron transport theory

In this study, the extrapolation distance problem for mono-energetic (one-speed) neutrons has been investigated by using the U1 approximation in which the neutron angular flux is expanded in terms of the Chebyshev polynomials of second kind in one-dimensional neutron transport theory. To do this, first the problem was solved by the traditional P1 approximation in which the neutron angular flux is expanded in terms of the Legendre polynomials and then it was solved with the present method. The slab is assumed to be homogeneous and the neutrons are scattered as isotropic. Finally, numerical results for the extrapolation distances were calculated using both methods and they were given in the tables together with the literature results for comparison. More convenient results with the literature may be obtained in case applying higher-order approximations. However, it is important to underline that the U1 method was first applied to this problem and an analytical expression for the extrapolation distance was derived explicitly.