  We investigate the homogeneous linewidth of localized type-I excitons in
type-II GaAs/AlAs superlattices. These localizing centers represent the
intermediate case between quasi-two-dimensional (Q2D) and
quasi-zero-dimensional localizations. The temperature dependence of the
homogeneous linewidth is obtained with high precision from
micro-photoluminescence spectra. We confirm the reduced interaction of the
excitons with their environment with decreasing dimensionality except for the
coupling to LO-phonons. The low-temperature limit for the linewidth of these
localized excitons is five times smaller than that of Q2D excitons. The
coefficient of exciton-acoustic-phonon interaction is 5 ~ 6 times smaller than
that of Q2D excitons. An enhancement of the average exciton-LO-phonon
interaction by localization is found in our sample. But this interaction is
very sensitive to the detailed structure of the localizing centers.
