DISSIPATION OF CORE-HOLE MOMENTUM BY PHONONS IN SOFT-X-RAY RADIATION PROCESSES FROM VALENCE-BAND TO CORE-LEVEL OF WIDE-GAP INSULATORS

The role of phonons in the soft-x-ray radiation process from a valence band to a core level in an insulator is studied theoretically. A thre e-band system composed of a dispersionless core band, a conduction ban d, and a valence band, with wide energy gaps between them, is taken as a typical example. Phonons with a finite dispersion are assumed to co uple weakly only with a hole in the core band (core hole). Using this model, we calculate the resonant second-order optical process composed of an excitation of an electron from the core band to the conduction band by an incident x ray, and a subsequent transition from the valenc e band to the core band by radiating another x ray. Without the phonon s, the momentum of the core hole is expected to be well defined by the resonance condition of the incident x ray. However, this momentum is dissipated by the phonons. If the radiation occurs completely after th is dissipation, we obtain a so-called luminescence, which is independe nt of the incident x ray. In this case, the spectral shape fully refle cts the density of states (DOS) of the valence band. However, if the r adiation occurs long before this dissipation effect, we obtain a reson ant Raman scattering that depends on the incident x ray. The spectral shape of this Raman scattering has a sharp peak, quite different from the DOS. The relative intensity between these two components is determ ined by the phonon dispersion, the lifetime of the core hole, and the core-hole-phonon coupling constant. From this theoretical framework, w e have concluded that there are various cases, i.e., Raman-dominant ca ses and luminescence-dominant cases, as well as intermediate cases, in good agreement with various experimental observations. The B 1s<->2p transitions of cubic BN are concluded to correspond to a luminescence- dominant case. [S0163-1829(98)02619-8].