with experimental XPS results. [@re:Ni-expt-XPS1; @re:Ni-expt-spinXPS] Moreover, this satellite structure is strongly spin-dependent, much enhanced in the spectrum of the majority spin. These effects mainly come from the multiplet scattering of ${\mbox{d}}^8 {\rightarrow}{\mbox{d}}^7$, which is assigned by spin-dependent peak of LFT spectrum of ${\mbox{d}}^8 {\rightarrow}{\mbox{d}}^7$ at around $-5~{\mbox{eV}}$ in Fig. \[fig:dos-Fe-Ni\]-(2c). The satellite is due to hole-hole scattering process, [@re:Ni-satellite] and can appear only when one treats whole on-site dynamical correlation effects. It should be noted that $6~{\mbox{eV}}$ satellite is not observed in GW approximation (GWA) [@re:yamasaki-GW-TM] since GWA includes the dynamical correlation only within RPA (electron-hole excitations) and thus not the electron-electron and hole-hole scattering processes.

Let us focus on the atomic spectrum obtained by LFT in Fig. \[fig:dos-Fe-Ni\]. The atomic spectra are separately shown in Figs. \[fig:dos-Fe-Ni\]-(1c) (2c) for ionization spectra and Figs. \[fig:dos-Fe-Ni\]-(1d) (2d) for affinity spectra. The initial state is a mixture of ${\mbox{d}}^6$, ${\mbox{d}}^7$ in Fe and ${\mbox{d}}^8$, ${\mbox{d}}^9$ in Ni, since the total occupation numbers are non-integers, $n^{{\scriptsize{\mbox{Fe}}}}_{\rm tot}=6.829$ and $n^{{\scriptsize{\mbox{Ni}}}}_{\rm tot}=8.799$ from the results of bulk systems. The excited state is then a mixture of ${\mbox{d}}^5$, ${\mbox{d}}^6$, ${\mbox{d}}^7$, ${\mbox{d}}^8$ in Fe and ${\mbox{d}}^7$, ${\mbox{d}}^8$, ${\mbox{d}}^9$, ${\mbox{d}}^{10}$ in Ni. Small components appear in ionization 