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The Fe metal takes a bcc structure. Figures 2 and 3 show DOS’s projected onto the states with d symmetry ( d -DOS) at the core-hole site for Ni and Co, respectively. The corresponding DOS’s for Fe are shown in Fig. 3 in Ref. 19. In these calculations, six k -points are picked up in the irreducible Brillouin zone for super-cell sys- tems. The DOS’s calculated with no core-hole are essen- tially the same as those reported by Moruzzi, Janak and Williams. 25 Table I lists the screening electron number Δ n$_{dσ}$ in the d -symmetric states with spin σ , that is, the difference of the occupied electron number between in the presence and in the absence of the core hole inside the muffin-tin sphere. 

On the basis of these one-electron states, we calcu- late the 3 s XPS spectra, by following the procedure de- scribe in Sec. II. Figures 4, 5 and 6 are the spectra thus calculated as a function of the binding energy ω$_{q}$ − ϵ for Ni, Co, and Fe, respectively, in comparison with the experiments. 10,11,13 The spectral shape in Fig. 6 for Fe is slightly different from our previous result (Fig. 4 in Ref. 19), since the present calculation takes full account of ex- citations up to three e-h pairs in comparison with only up to two e-h pairs in Ref. 19. The spectra are strikingly different between the up-spin channel and the down-spin channel and strongly depend on elements, in good agree- ment with the experiments. In the following, we explain the origin of these behaviors in relation to one-electron states screening the core hole. 

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