  We investigate the basic quantum mechanical processes behind non-proportional
response of scintillators to incident radiation responsible for reduced
resolution. For this purpose, we conduct a comparative first principles study
of quasiparticle spectra on the basis of the $G_0W_0$ approximation as well as
absorption spectra and excitonic properties by solving the Bethe-Salpeter
equation for two important systems, NaI and SrI$_2$. The former is a standard
scintillator material with well-documented non-proportionality while the latter
has recently been found to exhibit a very proportional response. We predict
band gaps for NaI and SrI$_2$ of 5.5 and 5.2 eV, respectively, in good
agreement with experiment. Furthermore, we obtain binding energies for the
groundstate excitons of 216 meV for NaI and 195$\pm$25 meV for SrI$_2$. We
analyze the degree of exciton anisotropy and spatial extent by means of a
coarse-grained electron-hole pair-correlation function. Thereby, it is shown
that the excitons in NaI differ strongly from those in SrI$_2$ in terms of
structure and symmetry, even if their binding energies are similar.
Furthermore, we show that quite unexpectedly the spatial extents of the highly
anisotropic low-energy excitons in SrI$_2$ in fact exceed those in NaI by a
factor of two to three in terms of the full width at half maxima of the
electron-hole pair-correlation function.
