The Passage of Neutrons Through Crystals and Polycrystals

We investigate in this paper phenomena, occurring in the passage of neutrons through matter, which originate from the crystalline or polycrystalline constitution. While the procedure is in many respects closely similar to that followed in the theory of x-rays, important and quantitatively decisive differences arise from the complicated coherence properties of the atomic scattering. The theoretical formulae developed in the first two paragraphs permit us to interpret in a quantitative manner a series of experiments which show deviations from the so far almost always assumed additivity of nuclear cross sections. We also obtain information concerning the relative phases of the scattering amplitudes of nuclear isotopes. We next show for illustrative purposes how the Larmor precession of the spin of the neutron passing through the magnetized medium, and the well-known differentiation between the action of the vectors "B" and "H" can be explained as a simple dispersion phenomenon. The preceding formulae permit us to determine quantitatively the transmission and polarization of neutron beams passing through ferromagnetic bodies. The main uncertainties which enter into attempts to evaluate experiments, arise from our incomplete knowledge of the velocity distribution of the incident beam and of the form factor which enters into the formulae for magnetic scattering. We present a detailed discussion of these uncertainties. Even neglecting depolarization effects which are due to incomplete saturation and which would still further diminish the theoretical value for transmission effects, we find that the observed values are considerably higher than those theoretically predicted and are not in good agreement with each other.