On the PN Method in Spherical Geometry: A Stable Solution for the Exterior of a Sphere

A numerically stable version of the P-N method for solving the one-speed problem of neutron transport in the exterior of a sphere is developed. A transformation is used to obtain a plane-geometry-like neutron transport equation, where the angular derivative part of the streaming term in spherical geometry is considered as a source. In this way, conventional P-N solutions developed for plane geometry can be used to solve the problem and avoid having to deal with ill-conditioned solutions expressed in terms of the modified spherical Bessel functions of the third kind.