when it is coupled to the $p_-$-shell. For both types of QDs, the dispersion of the emission lines is quite well described by the Fock-Darwin spectrum. This shows that the confinement potential is close to harmonic.

For a rotationally symmetric confinement potential, angular momentum is a good quantum number such that promotion of the Auger electron to the $d_0$ shell is possible, but promotion to the other $p$- and $d$ shells is forbidden. In practice, we find that the radiative Auger involving the $p$-shells is relatively strong and that the intensity of these processes is not strongly dependent on the magnetic field. This shows that angular momentum is not a good quantum number in practice. However, in the experiment all the processes are spin-conserving: we do not observe for instance Zeeman splittings in the radiative Auger lines. This shows that spin is a good quantum number; equivalently, that spin-orbit interactions of the electron states are weak.

There are several additional red-shifted emission lines that are not related to electron shells or continuum states (see Fig. \[fig:dispersion\](a,b)): An emission red-shifted by $\sim36\ \text{meV}$ corresponds to an optical recombination along with the creation of an LO-phonon (Fig. \[fig:dispersion\](f)). The magnetic field dispersion 