Inelastic neutron measurements on some selected polycrystalline alkali halides (namely LiBr, LiI, NaBr, NaI), where the mass difference between anions and cations is large, are proposed in the temperature interval ranging from room temperature up to T=660 K. From the measured scattering law the generalized density of phonon states will be extracted making use of well-known Bredov's method. The purpose of the experiment is to observe and study intrinsic vibrational modes (i.e. breathers), localized in three dimensions, occurring at single frequency values near the end of the gap between acoustic and optical phonon bands. A recent low-resolution inelastic neutron measurement (Manley et al., 2009) has provided some clues about the existence of such a mode in NaI at T>555 K around the frequency value of 11 meV. However, a wider and more accurare study on this interesting subject is needed.