First-Principles $\mathit{T}$-Matrix Theory with Application to the 6 eV Satellite in Ni

In photoemission spectra of strongly correlated systems one usually observes a satellite structure below the main peak. Description of such satellite structures in the commonly used $\mathrm{GW}$ approximation has been found to be insufficient. To account for these satellite structures that originate from short-range correlations, we have developed a $T$-matrix formalism for performing ab initio calculations on real systems. The method is applied to Ni and we obtain a satellite structure below the Fermi level as well as a reduced exchange splitting. We also found a new interesting satellite structure above the Fermi level, which can be ascribed to particle-particle scattering.