UNCLASSIFIED CRLR - 479 - SOME USEFUL INTEGRAL FORMULAS FOR THE INITIAL REDUCTION OF THE TRANSPORT EQUATION (U). Richard L. Liboff, 31 March 1955. UNCLASSIFIED, Special Report (u) The procedure for expanding the corresponding differential eross sections for light, gamma, and neutron scattering in convergent series of spherical harmonics is outlined and the related integrals are reduced through the appropriate formas. The formulas which are presented are a good expedient in overcoming the difficulties involved in reducing the integral term of the transport equation. These formulas are useful in the application of the transport equation to problems of shielding (neutrons and gamma rays) or to the investigation of the scattering of electromagnetic radiation in aerosol clouds. CRLR - 502 - BEST AVAILARPLE “OPY APPLICATIONS OF INFINITE PLANE THEORY OF GAMMA SCATTERING.» Ralph Fullwood, Sam Holland, Richard Liboff, and Paul Grant, 8 May 1956. UNCLASSIFIED, Special Report (u) Work is reported on the following problems in the theory of gamma scattering from an infinite plane source: function of energy at 3 ft above the plane; (1) the dose rate as a (2) the dose rate as a function of height above the plane for source energies of 1 and 2.76 Mev; (3) the dose rate as a function of the radius of contamination for three source energies (1, 2, and 3 Mev); and (4) the dose rate received 3 ft below the surface in a hole 3 ft in diameter for a source energy of 1 Mev. Wizthin the accuracy of the infinite plane theory, the four problems have been adequately and validly treated with the possible exception of problem 4. The theory gives for this case results which may be high oy a factor of about 2. UNCLASSIFIED 48