Solution of the transport equation for critical thickness problem with alternative phase function and second kind of the chebyshev polynomials

In this study, Anlı-Güngör (AG) phase function as an alternative phase function is used instead of the scattering function placed in neutron transport equation to calculate the critical half thicknesses. The neutron transport equation is solved for the critical thickness problem by using first the traditional Legendre polynomials approximation (PN method) and then the second of the Chebyshev polynomials approximation (UN method) in a homogeneous source free slab extending from x = -a to a. Since the effect of the scattering function on the criticality of the system is very important, the critical thicknesses of the system are calculated as functions of the parameters of this function. Thus, the critical thicknesses of the system are calculated for various values of the c and t parameters using both PN and UN methods. In order to investigate the consistency of the results obtained from UN method, the numerical results are given in the tables and the results obtained from both polynomial approximations are compared with each other.