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We investigate the basic quantum mechanical processes behind non-proportionalresponse of scintillators to incident radiation responsible for reducedresolution. For this purpose, we conduct a comparative first principles studyof quasiparticle spectra on the basis of the $G_0W_0$ approximation as well asabsorption spectra and excitonic properties by solving the Bethe-Salpeterequation for two important systems, NaI and SrI$_2$. The former is a standardscintillator material with well-documented non-proportionality while the latterhas recently been found to exhibit a very proportional response. We predictband gaps for NaI and SrI$_2$ of 5.5 and 5.2 eV, respectively, in goodagreement with experiment. Furthermore, we obtain binding energies for thegroundstate excitons of 216 meV for NaI and 195$\pm$25 meV for SrI$_2$. Weanalyze the degree of exciton anisotropy and spatial extent by means of acoarse-grained electron-hole pair-correlation function. Thereby, it is shownthat the excitons in NaI differ strongly from those in SrI$_2$ in terms ofstructure and symmetry, even if their binding energies are similar.Furthermore, we show that quite unexpectedly the spatial extents of the highlyanisotropic low-energy excitons in SrI$_2$ in fact exceed those in NaI by afactor of two to three in terms of the full width at half maxima of theelectron-hole pair-correlation function.

Quasi-particle spectra, absorption spectra, and excitonic properties of sodium iodide and strontium iodide from many-body perturbation theory