in Fig. \[fig:dispersion\](a,b) for an InGaAs QD and in Fig. \[fig:dispersion\](c,d) for a GaAs QD. At high magnetic fields, the two red-shifted emission lines, which are the closest in photon energy to the resonance-fluorescence, have a dispersion of $\pm\frac{1}{2}\hbar\omega_c$ (cyclotron frequency: $\omega_c=\frac{eB}{m^*}$, electron effective mass $m^*$). This strong magnetic field dispersion shows that the emission is connected to an energy transfer to the $p$-shells.

![image](fig3c){width="1.8\columnwidth"}

In this measurement, the separation between resonance fluorescence and radiative Auger emission corresponds to the single-particle energies. The radiative Auger lines, therefore, allow the single-particle spectrum of a quantum dot to be determined with very high precision. At zero magnetic field ($B=0\ \text{T}$), there is a splitting between the two $p$-shell-related Auger lines, revealing an asymmetry of the QD. This asymmetry lifts the four-fold degeneracy of the $p$-shells into two doublets at zero magnetic field. For both types of QDs, we also observe radiative Auger emission involving $d$-shells (Fig. \[fig:dispersion\](e)). At high magnetic fields, the upper $p$-shell ($p_-$) shows an anti-crossing with the lowest $d$-shell ($d_+$). For the GaAs QD, we even observe radiative Auger emission lines involving all three $d$-shells. For the InGaAs QD, the $d_+$-shell is only visible in the radiative Auger emission 