Extension to quadratic anisotropic scattering in one-speed neutron transport equation for critical thickness calculations

The effect for different types of scattering on the critical half thickness in slab geometry for one speed neutron transport equation is studied for isotropic, linearly anisotropic and quadratic anisotropic scatterings. An extensive numerical survey is carried out for the critical thickness in order to provide the effect of the different scattering types. The numerical results are obtained by P${}_N$, T${}_N$ and U${}_N$ methods. The P${}_N$ method is the Legendre polynomial solution that is accepted as the exact result for the neutron transport theory calculations and the U${}_N$ and T${}_N$ methods are the types of Chebyshev polynomials. Critical thickness values are calculated by using Mark boundary condition. Results are compared with the literature.