7 total screening electron numbers are almost unity, 0 . 91 , 0 . 99 , and 0 . 95 for Ni, Co, and Fe, respectively. The local magnetic moments at the core-hole site are not signifi- cantly changed from those in the ground states. The | A$_{↑}$ | $^{2}$’s are not far from unity as listed in Table II, by the same reason as in the up-spin channel. Note that | A$_{↓}$ | $^{2}$’s are larger than in the up-spin channel, indicating that one-electron wave functions for down-spin conduc- tion electrons are less modified in the down-spin channel than in the up spin-channel. Figure 4(b) shows the calculated spectra for Ni, in comparison with the experiment. The final states | f$_{1}$ 〉 ’s containing one e-h pair with down-spin give rise to con- siderable intensities in a wide energy region 110 ∼ 115 eV, while the final states | f$_{2}$ 〉 ’s containing two e-h pairs give rise to small intensities in a wide energy region with the maximum around ω$_{q}$ − ϵ = 115 eV. We obtain a asymmetric shape with a tail in the high-energy region in agreement with the experiment. Figure 5(b) shows the calculated spectra for Co. The lowest-energy final states | f$_{0}$ 〉 gives rise to a peak at the threshold around ω$_{q}$ − ϵ = 100 eV. Different from Ni, final states | f$_{1}$ 〉 ’s and | f$_{2}$ 〉 ’s give rise to intensities on a limited region near the threshold. This suggests that one- electron wave functions are modified only for levels in the vicinity of the Fermi level. Contributions of final states | f$_{3}$ 〉 ’s (three e-h pairs) are found negligible. Figure 6(b) shows the calculated spectra for Fe. The final state | f$_{0}$ 〉 gives rise to a main peak at the thresh- old ω$_{q}$ − ϵ = 91 eV with the largest contribution in the three metals. Final states | f$_{1}$ 〉 ’s with one down-spin e-h pair give rise to a broad peak around 94 eV, which is quite small in comparison with the main peak. Although the observed spectra show small satellite intensity around ω$_{q}$ − ϵ = 97 . 5 eV, the present calculation gives no inten- sity there. It is unclear on the mechanism giving the intensity to our knowledge. Figure 6(a) shows the calculated spectra for Fe. The calculated spectra consist of a peak around ω$_{q}$ − ϵ = 92 eV and a satellite peak around 95 eV. The satellite peak is larger than the peak around the threshold. The final states | f$_{1}$ 〉 ’s containing one down-spin e-h pair give rise to the satellite intensity. The final states | f$_{2}$ 〉 ’s containing two e-h pairs give rise to a shoulder to the satellite around ω$_{q}$ = ϵ = 97 ∼ 100 eV, as shown in the figure. The excitations of three e-h pairs gives rise to finite but small intensities in the wide energy range around 98 eV. Figure 6: 3 s XPS spectra in ferromagnetic iron as a function of binding energy. (a) and (b) are for the up-spin and down- spin channels, respectively. The experimental data are taken from Ref. [11]. B. Nonmagnetic metals 2. Down-spin channel In ferromagnetic metals Fe, Co, and Ni, the XPS spec- tral shapes remarkably depend on the spin channel, ow- ing to the exchange interaction between the core hole and the conduction electrons. Although the spectral shape is found closely related to the filling of band states, the pres- ence of the satellite in the XPS spectra seems to have no direct relation to ferromagnetic states. In this subsection, taking up typical nonmagnetic metals Cu, V and Ru, we clarify this issue. Since the spectra are independent of the spin channel in nonmagnetic metals, we consider the down-spin channel in the following. We assume the fcc structure for Cu and Ru, and the bcc structure for V. Figure 7 show the d -DOS for Cu. The DOS calcu- lated with no core-hole are essentially the same as those reported by Moruzzi, Janak and Williams. 25 The d -DOS at the core-hole site is shifted downward to the deeper en- ergy region. The localize bound-states are clearly created When a down-spin 3 s electron is removed in a unit cell, the screening behavior is quite different from the situation where a up-spin 3 s electron is removed. As shown in Figs. 2(c) and 3(c), and the bottom panel in Fig. 3 in Ref. 19, the d -DOS’s at the core-hole site for Ni, Co, and Fe are strongly modified by the core-hole potential. Different from the up-spin channel, the effect is larger for up-spin conduction states than for down-spin conduction states; large weights are transferred to the bottom of the conduction band in the up-spin d -DOS’s, while the weights are slightly shifted downward to the lower energy region in the down-spin d -DOS’s. The screening electron numbers are rather smaller in the up-spin state than in the down-spin state, as listed in Table I. This difference arises from the fact that up-spin 3 d states are almost occupied in the ground state. The 75 80 85 90 95 100 105 0.0 0.1 0.2 Intensity (arb.units) expt. total |f$_{0}$> dn |f$_{1}$> |f$_{2}$> |f$_{3}$> 75 80 85 90 95 100 105 Binding Energy (eV) 0.0 0.2 0.4 Intensity (arb.units) expt. total |f$_{0}$> dn |f$_{1}$> a) up spin channel b) dn spin channel Fe 3s XPS