Three-Body Problem and Resonant Photoemission in Insulators and Semiconductors

Three-body problem involving two valence holes and a single conduction electron, which appears in the study of the final state of the resonant photoemission in insulators and semiconductors, is formulated to be solved exactly in a two-band Hubbard model by use of Faddeev's scattering theory. The wave functions and energy eigenvalues are calculated numerically in a one-dimensional model. By use of this exact solution of the three-body problem, resonance photoemission spectra are studied from a weak correlation resion to a strong one. It is shown that the approximation used in the past analysis, in which two valence holes are assumed to be localized, deviates from the present results even in the strong correlation region U v v ∼2 W v with U v v and W v denoting the Coulomb integral and the band width of valence holes, respectively.