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One could interpret the relaxation rate as the effective hybridization strength in the core-hole state renormalized by taking into account the many-body interactions of the fully relaxed core-hole state in terms of the core-hole spectral function. From this viewpoint there is no difference between the relaxation rate and the effective hybridization strength. In the present work the hybridization strength means the unrenormalized hybridization strength to emphasize the importance of the many-body effects of the core-hole state.
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