On the possibility of investigating the dispersion of the energy bands of a crystal using resonant x-ray emission spectra

It is shown that, when the dispersion of the energy bands of crystals is investigated by resonant x-ray emission (RXE), an ambiguity can arise in the determination of k _tr — the transition point in k space — as a result of the characteristic features of the band structure and the value of the matrix elements. It is proposed that calculations of the distribution of partial contributions to interband optical transitions in the Brillouin zone (BZ) be used as a means of obtaining a simplified estimate of k _tr. The basic properties of this distribution are examined for lithium hydride, which is a convenient model object having a simple band structure and interband transitions which have been studied in detail. It is shown that the k points of the general position, which form a complex figure in the BZ, make the main contribution to the interband transitions. The contribution of high-symmetry points is much smaller mainly because of their small representativeness. This make it easier to understand the reason for the possible nonmonotonic variation of k _tr in RXE measurements of the dispersion of the energy bands of crystals or the sharp changes in the resonance-fluorescence intensity. Fiz. Tverd. Tela (St. Petersburg) 41, 1597–1601 (September 1999)