VARIATIONAL APPROACH TO THE MILNE PROBLEM WITH A SPECULAR AND DIFFUSEREFLECTING BOUNDARY

An approximate solution of the Milne integral equation for specular an d diffuse reflecting boundary is deduced by using variational calculus . An approximate, (four variable parameters) expression, for the parti cle density and emergent angular distribution has been proposed. Numer ical results for extrapolated endpoint, particle density and angular d istribution in a region close to the boundary are calculated. The perc entage difference for extrapolated endpoint, taking the exact values a s a reference, is approximately 1.4 x 10(-10) for a non-reflecting med ium and does not exceed 0.01% for all degrees of blackness in the diff usion reflection. The results for a combination of specular and diffus e reflections are also given. (C) 1998 Elsevier Science Ltd.