Multiple Scattering of Thermal Neutrons by a Perfect Crystal. I. General Foundations

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Abstract
The wave function of a neutron in a regular crystal is built up as a superposition of a primary plane wave and outgoing spherical waves. The elastic scattering properties of the nuclei are given exactly by their complex scattering amplitude f. It is carefully distinguish‐ed between the total wave field and the arriving field at any scattering centre. This results in a correct and consistent description of absorption effects. In the case of an infinite crystal slab the construction of the wave field is simplified by a lattice plane method: all the spherical waves coming out from such an infinite lattice plane add to plane waves, most of them are strongly damped with increasing distance from the plane. The undamped waves give the far‐field, which contains all the interesting informations about the collective interference effects. Neglect of the damped waves gives a good starting point for the approach given in the following two parts of this paper.