Criticality of bare and reflected spheres by PN method

The criticality problem of the one-speed transport equation with isotropic scattering for bare and reflected spheres is studied by PN method. The divergence of the PN method for sufficiently small radius in high order of approximation are discussed. A robust numerical method to overcome the difficulty in accurately finding the roots of the determinantal equation has been proposed. A range of critical radii have been obtained for bare and different reflected coefficient by the PN method. Results are compared with published data where possible.