Solution of the finite slab criticality problem using an alternative phase function with the second kind of Chebyshev polynomials

The critical size of a finite homogenous slab is investigated for one-speed neutrons using the alternative phase function (AG, Anlı–Güngör) in place of the scattering function of the transport equation. First of all, the neutron angular flux expanded in terms of the Chebyshev polynomials of second kind (U_N approximation) together with the AG phase function is applied to the transport equation to obtain a criticality condition for the system. Then, using various values of the scattering parameters, the numerical results for the critical half-thickness of the slab are calculated and they are tabulated in the tables together with the ones obtained from the conventional spherical harmonic (P_N) method for comparison. They can be said to be in good accordance with each other.