Nuclear resonant inelastic absorption of synchrotron radiation in an anisotropic single crystal

The Singwi and Sjölander theory of nuclear resonant inelastic absorption of x rays is extended to the general case of an anisotropic single crystal. The energy dependence of nuclear inelastic absorption for the specific direction of the x-ray quantum relative to the crystal lattice is described using the density of phonon states, weighted by the projection of the phonon polarization vectors to the wave vector of the x-ray quantum. An applicability of the sum rules in the case of the anisotropic crystal is analyzed. The method of calculation of the phonon projected density of states from experimental data is proposed, where deconvolution of the data with the instrumental function of the monochromator and the subtraction of the multiphonon absorption is handled using the Fourier transformation. The results are illustrated by processing the experimental data of nuclear inelastic absorption of x rays in the anisotropic ferric borate ${\mathrm{FeBO}}_3$ single crystal.