Boundary conditions in dynamical neutron diffraction

Difficulties can arise when one attempts to analyze the diffraction of thermal neutrons from complicated arrangements of perfect crystals using standard dynamical diffraction theory. The theory is traditionally developed either so as to satisfy the boundary conditions produced by a plane incident wave or so as to satisfy point-source boundary conditions, and convenient techniques for satisfying the boundary conditions presented by more complicated incident waveforms have hitherto received little attention. This paper presents a development of dynamical diffraction theory, using coupled differential equations, in which the boundary-value problem is separated from the dynamical diffraction formalism and can be treated explicitly. The theory is applied to the case of symmetric Laue diffraction where familiar plane-wave-source and point-source solutions emerge under the appropriate boundary conditions. These two solutions are shown to be connected by a form of uncertainty relation