Gravitational and magnetic field effects on the dynamical diffraction of neutrons

This paper examines in detail the effect of an external force field on the diffraction of neutrons by a perfect crystal. The theoretical connection of this problem with the propagation of x rays in a strained crystal, and with the motion of band electrons in a crystal under the influence of an applied electric field is described. Two methods of solution are utilized: (a) an eikonal (WKB) approach which is analogous to the method used by Kato in discussing the x-ray strain problem, and (b) a coupled-partial-differential-equation approach, which is analogous to the Takagi-Taupin method of solving the x-ray strain problem. Extensive numerical examples are given.