energy spectrum from near UV up to 40 eV, either below and above the QP direct gap. The first structure is a $\Gamma$ exciton, while the second and the third peaks are excitons which may originate from *X*, *L*, or *W* transitions between valence and conduction bands. Since we calculated the spectra directly by the method of Schmidt, we have no access to excitonic eigenvalues or eigenfunctions and can just speculate on the basis of single-QP eigenvalues.

However, on the basis of the experimental spectra of Bourdillon[@bourdillon] as shown in Fig. \[fig:3\], the value of $\varepsilon_{\infty}$ is seemingly about 1.8, which is in large discrepancy to our value of 2.5. However, one should mention that the data of Bourdillon have been extracted indirectly from reflection spectra and that there exist other values for $\varepsilon_{\infty}$ from more direct methods. Most probably, the best directly measured value is about 2.4,[@bosomworth] and it is also indirectly confirmed by Krukowska[@krukowska] from measurements of the refraction index at visible optical frequencies, obtaining a value slightly larger than 2.4, i.e., about 2.462.5. Furthermore, by using the Lyddane-Sachs-Teller (LST) relation[@fox] the consistency of our result could also be indirectly confirmed from measurements of $\epsilon_0$ (which yield values 