Exact P-N method solutions

The spherical harmonics (PN) solution at the surface of a source-free half- space is investigated to determine conditions for which exact results can. be obtained with art approximation of any odd order N. For isotropic scatte ring, an exact solution for the net current cart be obtained if the inciden t illumination comes from an isotropic plane source, which extends the obse rvation of Garcia and Siewert that an exact solution for the scalar flux ca n be obtained if the incident illumination is constant with the cosine of t he polar angle. An exact solution for the scalar flux at the interface betw een two isotropic scattering, halfspace media also can be obtained with a f inite N for a spatially uniform source in one half-space.