Note on the Spherical Harmonic Method As Applied to the Milne Problem for a Sphere

The spherical analog of the Milne problem for the half-plane is treated by an approximate method based on expanding the neutron distribution function in a finite number of spherical harmonics. The results are improved markedly in going from the first to the second approximation and more slowly in higher approximations. The neutron distribution is calculated in the first two approximations. Values of the "extrapolated endpoint"---as predicted by the first three approximations---are tabulated in Table I as a function of the radius of the sphere.