SEPARATION DYNAMICS OF THE RESONANT SOFT-X-RAY RADIATION INTO LUMINESCENCE AND COHERENT RAMAN-SCATTERING IN WIDE-GAP INSULATORS

We study theoretically the roles of phonons in spectral shapes of soft X-ray radiation from a valence band to a core level in an insulator, and clarify how this radiation separates into luminescence and Raman s cattering. We take a three-band system composed of a dispersionless co re band, a conduction band, and a valence band, with wide energy gaps between them. Phonons with finite dispersion are assumed to couple wea kly with a hole in the core band (core hole). Using this model, we cal culate the resonant second order optical process composed of an excita tion of an electron from the core band to the conduction band by an in cident X-ray, and subsequent transition from the valence band to the c ore band by radiating another X-ray. Without phonons, the momentum of the core hole is expected to be well defined by the resonance conditio n of the incident X-ray. However, this momentum is dissipated by the p honons. If the radiation occurs after this dissipation, we get so-call ed luminescence which is independent of the incident X-ray. In this ca se, the spectral shape fully reflects the density of states (DOS) of t he valence band. If the radiation occurs before the dissipation, we ge t resonant Raman scattering which depends on the incident X-ray. The s pectral shape of this Raman scattering has a sharp peak, being quite d ifferent from the DOS. The relative intensity between these two compon ents is determined by phonon dispersion, the life time of the core hol e, and the core-hole-phonon coupling constant. From this theoretical f ramework, we have concluded that various cases exist-Raman dominant, l uminescence dominant and intermediate-which is in good agreement with observations in recent experiments. (C) 1998 Elsevier Science B.V. All rights reserved.