On Multiple Scattering of Neutrons I. Theory of the Albedo of a Plane Boundary

Abstract

The paper contains the rigorous solution of the following problem in multiple scattering: a beam of particles impinges with arbitrary velocity distribution upon the plane boundary surface of a body which extends towards infinity on the other side ot the boundary. In this body the particles have a finite probability of being either captured or scattered without loss of energy. The probability of scattering shall be spherically symmetrical in the laboratory frame of reference. Number and velocity distribution of the returning particles are given explicitly; density as well as velocity distribution of the particles inside the body are determined by the formulae but not worked out in detail since they lack direct physical interest. The result is found to depend on the ratio of the capture to the scattering cross section and on the velocity distribution of the incident particles. Applying the theory to the diffuse reflection of slow neutrons at paraffin surfaces it is found that agreement with observations and previous determinations of the capture cross section can exclusively be obtained, if the active level of the "deuteron with spin zero" is virtual. The connection of these results with some other experiments on the velocity and magnetic moment of the neutrons is discussed.