10 for the up-spin channel, while the intensities are con- centrated near the threshold with no satellite peak for the down-spin channel. The origin of such behavior has been explained in relation to the 3 d band modified by the core-hole potential and the overlap integral between the final states and the ground state. Bound or quasi-bound states are formed by the core-hole potential, and the e-h excitations from such quasi-bound states to the unoccu- pied levels would usually give rise to satellite intensities. However, the presence of the quasi-bound state is not a sufficient condition to the presence of satellite; the d - band should be partially occupied in the ground state, and thereby the one-electron wave functions constituting the final states include the amplitudes of the unoccupied one-electron states in the ground state. If the d -band is fully occupied, the satellite intensity would not come out even in the presence of the bound state. Note that the satellite peak position has no direct relation to the 3 s level exchange splitting; the LDA calculation gives such splittings as 0 . 7 , 1 . 9 , and 2 . 5 eV for Ni, Co, and Fe, re- spectively. These results indicate that the presence of satellite is not directly related to the ferromagnetic ground state. We have clarified this point by calculating the spectra in nonmagnetic metals Cu, V, and Ru. For V and Ru, we have obtained shoulder structures in the XPS spectra, although the structure is rather small for Ru. The origin of these behaviors is the same as in the ferromagnetic metals. For Cu, only a symmetric peak is found with no structure, although the localized bound states are clearly formed below the bottom of the conduction band. This is because the 3 d band is completely occupied in the ground state. We have calculated the XPS spectra in Ni, Co, Fe, and Cu in good agreement with the experiment, while we could not find experimental XPS data for V and Ru. Acker et al. observed the satellite structures even in some Pauli paramagnetic Fe compounds, 8 The present results would provide an interpretation of their findings. Fi- nally, as regards the L -edge spectra, experimental data for XPS spectra and the x-ray absorption spectra are ac- cumulated, and ab initio approach has been tried. 26 The extension of the present method to the L -edge spectra is left in future study. Acknowledgments We used the FLAPW code developed by Noriaki Hamada. We thank him for allowing us to use his code and fruitful discussions. This work was partially sup- ported by a Grant-in-Aid for Scientific Research in Pri- ority Areas “Development of New Quantum Simulators and Quantum Design” (No.19019001) of The Ministry of Education, Culture, Sports, Science, and Technology, Japan. IV. CONCLUDING REMARKS Figure 12: 4 s XPS spectra in nonmagnetic ruthenium as a function of binding energy for the 4 s down-spin core-hole. We have developed an ab initio method to calculate the 3 s and 4 s core-level XPS spectra in ferromagnetic metals Ni, Co, and Fe, and in nonmagnetic metals Cu, V, and Ru. For the ferromagnetic metals, we have found that the spectral intensities are distributed in a wide range of binding energy with satellite or shoulder structures For Ru, | A$_{↓}$ | 2 is again close to unity by the same reason as in V. The A$_{↑}$ | 2 is smaller than unity, although it is larger than that in V. This indicates that one-electron wave functions constituting | f$_{0}$ 〉 are less modified by the core-hole potential in comparison with V. Final states | f$_{1}$ 〉 ’s containing one e-h pair with up-spin give rise to a shoulder structure with a little smaller intensity than in V. Figure 11: 3 s XPS spectra in nonmagnetic vanadium as a function of binding energy in the down-spin channel. -15 -10 -5 0 5 10 15 Binding Energy (eV) 0.0 0.1 0.2 Intensity (arb.units) total |f$_{0}$> up |f$_{1}$> dn |f$_{1}$> |f$_{2}$> Ru 4s XPS -15 -10 -5 0 5 10 15 Binding Energy (eV) 0.0 0.1 0.2 Intensity (arb.units) total |f$_{0}$> up |f$_{1}$> dn |f$_{1}$> |f$_{2}$> V 3s XPS shows the calculated spectra. We have a main peak com- ing from the final state | f$_{0}$ 〉 at the threshold and the noticeable shoulder coming from the final states | f$_{1}$ 〉 ’s.