are the possible final states. $\hat{P}=\sum\hat{h}_{i,\sigma}\hat{e}_{j,-\sigma}$ adds up all dipole allowed electron-hole recombinations [@Chithrani2005].

With the presented formalism, we estimate that the intensity of the radiative Auger transition from $s$- to the $d_0$-shell is about hundred times weaker than the resonance fluorescence. However, this intensity is tendentially overestimated compared to the experimentally obtained values. The issue could be that the exact diagonalization only converges when taking into account very high single-particle shells. In reality, not all of these states exist due to close-by continuum states.

Cross-Correlation: Theory {#sec:crosstheory}
=========================

![image](fig_s3){width="1.8\columnwidth"}

![\[fig:g2Model\]Model used for the simulation of the auto-correlation measurement of the resonance fluorescence together with the cross-correlation between the resonance fluorescence and the radiative Auger emission.](fig_s4b){width="0.9\columnwidth"}

The $g^{(2)}$-measurements are modeled with the level scheme shown in Fig. \[fig:g2Model\]. There are 4 different states which are taken into account for our simulation: the ground state, $\ket{g}$, with a single electron in the QD; the excited state, $\ket{e}$, a trion with two $s$-shell electrons; the state after a radiative Auger emission, $\ket{p}$, where a single electron occupies the $p$-shell of the QD; and the ionized QD-state, $\ket{b}$, where the electron has tunneled out of the QD. We simulate the system by assuming 