Diffusion of Neutrons

Abstract

It is the object of the present investigation to include the thermal motion of the medium in the treatment of neutron diffusion, under the simplifying assumption that the collisions are such as between hard elastic spheres. The methods used are those previously established by the author in radiative and gas-kinetic transfer. They only have to be adapted to the present purpose. This is done in Sec. II. Boltzmann's original equation which is quadratic in the distribution functions is linearized by the assumption that the velocity distribution of the molecules is Maxwellian. The treatment of the resultant transport equation is different for "thermal" and for "fast" neutrons. Section III deals with thermal neutrons by the method of "moments." The distribution function is assumed to be of the form: Maxwellian factor times arbitrary function of direction, the latter written as a series of general spherical harmonics. Thereby, and by the use of a theorem due to Maxwell, the fundamental equation may be reduced to an infinite system of linear differential equations which have been previously treated. The case of arbitrary geometry is treated to second-order moments (inclusive). For the case of cylindrical symmetry a recurrence relation for the moments, to any order, is derived. In Sec. IV the case of fast neutrons is treated by the method of iterated integrations. In order to make them straightforward the kernel of the integral equation is transformed into the standard form. This is achieved by characterizing the collisions in a way which is different from that usually applied. A simple example for the working of the method is given and the results are discussed.