Nuclear resonant forward scattering of x rays: Time and space picture

Abstract

The problem of forward resonant scattering of x rays by an ensemble of nuclei is being solved directly in time and space. The wave equation describing the propagation of the radiation through the nuclear ensemble is derived. It is a first-order integrodifferential equation. Its kernel is a double time function $K(t,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t})$ that represents a coherent single scattering response of the nuclear system at time t to excitation at $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}.$ The explicit form of the kernel is defined by the character of interactions, the nuclei experience with the environment and by the character of their spatial motion. A general procedure of the solution of the wave equation is introduced that is independent of the type of the kernel. Examples for various kernels are presented and discussed for some particular cases: collective or diffusive motion of nuclei in space, thermal lattice vibrations, time-independent hyperfine interactions, and time-dependent hyperfine interactions due to atomic spin fluctuations or external magnetic-field switching.