The spectra exhibit a peak splitting as a consequence of the coupling between the excitonic shell and the plasmonic core. Larger oscillator strengths result in higher coupling strengths and consequently in a larger peak splitting between the upper and lower polariton peak. In addition to the polariton resonances, a third peak emerges roughly at the uncoupled resonance position. This peak arises not only in the dipolar approximation discussed here, but also in the full Mie solution as well as in numerical Maxwell simulations and is an intrinsic feature of the classical material model, i.e. the Lorentzian permittivity. To underline how the additional resonance grows larger with respect to the polariton peaks, Figure ) presents the extinction cross sections for f = 0.03, f = 0.08 and f = 0.13 (blue, orange and red line). For f = 0.03, only the two polariton peaks are visible, for f = 0.08, the additional peak is clearly visible and for f = 0.13, it is already of comparable magnitude. The nature of this additional peak has been comprehensively discussed by Antosiewicz et al. It has been attributed to a so-called shell mode that resonates over the whole particle and that absorbs the electric energy predominantly in the shell. Despite the fact that the third peak is predicted by such a well-established and frequently used model, it has not been observed in experiments. Furthermore, other models for strong coupling do not predict another (polariton) mode. In the following we show that this discrepancy can be lifted by taking the quantum character of the system into account.