Many-electron effects in Co $3 s$ X-ray photoelectron spectra of diamagnetic ScCoO$_3$ and paramagnetic BiCoO$_3$ cobaltites

A new method based on the solution of the Dyson equation in the basis of atomic wavefunctions has been developed to quantitatively describe the influence of the dynamic effect on the structure of X-ray photoelectron spectra of $3s$ electrons of $3d$ elements. The method has been tested for BiCoO$_3$ and ScCoO$_3$ cobaltites containing Со$^{3+}$ cations in high-spin ($S = 2$) and low-spin ($S = 0$) states, respectively. The calculations are in quantitative agreement with the structure of observed spectra of $3s$ electrons. For the diamagnetic cation Co$^{3+}$, a significant influence of the dynamic effect on the energy of the unsplit $3s$ line of ScCoO$_3$ has been demonstrated for the first time both experimentally and theoretically and its energy position has been calculated. For the paramagnetic cation Co$^{3+}$, the results obtained have been generalized to the case of transition $3d$ metals with an arbitrary number of unpaired electrons. It also has been shown that, if the $3d$ shell is filled by half or more, the dynamic effect affects only the energy position of the low-spin component, which reduces splitting by a factor of about $3$ (from $13.4$ to $4.7$ eV in the case of BiCoO$_3$).