Small Angle Scattering of Neutrons

Abstract

The differential and total scattering cross sections have been calculated for slow neutrons impinging on crystalline spheres whose radii are very much greater than the neutron wavelength. The results for the differential cross section show that when the difference, $\rho$, between the neutron phase shift in traversing the particle diameter and the phase shift in traversing the same distance in vacuum is small, the result agrees with the Born approximation, while if $\rho$ is large, the result agrees with that obtained by geometrical optics. Also, the total cross section for $\rho$ small is $\frac{\pi R^2{\rho }^2}{2}$ and for $\rho$ large is $2\pi R^2$, where $R$ is the particle radius.