Calculation of Partial Differential Scattering Cross Sections for Slow Neutrons

Abstract

As an approach to developing methods for calculating differential scattering cross sections of materials for neutrons with energy below 1 ev five approximations to the exact formalism of Zemach and Glauber have been applied to treat the scattering by gases composed of semirigid molecules. This paper outlines the theory for the methods which are the following (1) A quite rigorous method valid when the neutron energy and kBT are both much less than the characteristic vibrational energies of the molecules. (2) A method which treats vibrations harmonically rotations classically, and neglects rotation-vibration coupling. Within these limitations the method is valid at all neutron energies. (3) A method like (2) except that averages over orientation are approximated by the Krieger-Nelkin method of introducing average values of functions of the Eulerian angles wherever they appear. (4) A method which treats vibrations with characteristic energies much less than the neutron energy by a short collision time approximation. (5) A method which treats such low energy vibrations classically.Method (5) has the feature that when all normal modes are treated classically the equation for the differential scattering cross section reduces to that for scattering by unbound particles. If some, but not all, vibrations are treated classically and averages over orientation are approximated as in method (3) the effective mass for a scattering atom attached to the molecule is intermediate between the mass of the atom and the Sachs-Teller mass which applies when all vibrations are treated exactly by quantum mechanics. Method (5) has the advantage of being easily adapted to treating simple models for liquids and amorphous solids.These methods are evaluated in the accompanying paper.