Effect of Short Wavelength Interference on Neuteron Scattering by Dense Systems of Heavy Nuclei

Abstract

The interference term in the expression for the total cross section for scattering of neutrons by dense systems of heavy nuclei is investigated in the region of small wavelength. Asymptotically, this term has the form $\frac{\delta \sigma }{\sigma }=-\left(\frac{{\lambda }^2{\rho }^{\frac{2}{3}}}{8\pi }\right)I$, where $\lambda$ is the neutron wavelength and $\rho$ the number of particles per unit volume. The discussion of the coefficient, $I$, and its evaluation for various systems is the main object of the paper. It is based on an extension to general systems of particles of Ewald's method for the calculation of lattice sums. For any system, $I$ is found to be smaller than 3. It remains very near to this value for all systems not too far removed from conditions of close packing. The cases of ideal lattices, real crystals with thermal disorder, and liquids are treated in detail.