Spectroscopic ellipsometry (SE) has been utilized during the past decades for the measurement of the dielectric function of semiconductors. By using SE, interband critical point parameters such as energy gaps and broadenings are routinely determined. In the direct-space analysis approach, these parameters are known by taking the numerical energy derivatives of the dielectric function and fitting the spectra by using a Lorenzian line shape. However, in many cases the noise of the spectra does not allow the determination of such parameters as precisely as they are needed. Additionally, the determination of the character of the transitions, which is uncorrelated (one electron) or correlated (discrete excitons), is necessary for the analysis of the dielectric function. For instance, different values for the broadening parameter are obtained by using uncorrelated or correlated line shapes. We use a reciprocal-space analysis instead of the most commonly used direct-space analysis for determining without any uncertainty the character and, consequently, a precise value of the broadening parameter of the $E_1$ transitions of GaP, GaAs, Si, CdTe, GaSb, HgTe, and an alloy semiconductor: ${\mathrm{Cd}}_{0.18}{\mathrm{Hg}}_{0.82}\mathrm{Te}$ .