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A first-principles calculation of a surface-binding-energy shift has been done for the $3s$ orbital of Cu(100). Both initial- and final-state effects are found to be important to the binding-energy shift. Surface and bulk screening lengths around the core holes are small relative to the near-neighbor distance. The surface-binding-energy shift is 0.36 eV, which is consistent with experimental data on noble metals. The relaxation shift is -0.30 eV.
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Smith et al. (1982) studied this question.
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