The density-fluctuation spectra S/sub i/j(k,..omega..) (i,j = 3,4) are evaluated with a matrix dispersion-relation representation in terms of characteristic frequencies and complex self-energies by the incorporation of damping via decay into /sup 3/He quasiparticle-quasihole excitations and by the use of renormalized fluctuation frequencies. The hybridization of /sup 4/He rotons with /sup 3/He quasiparticle excitations is too small to induce a peak splitting in S/sub 44/(k,..omega..) at the level crossing while the effective phonon-roton exchange potential between /sup 3/He quasiparticles splits the spectrum S/sub 33/(k,..omega..) into two peaks. The energy shift of the main neutron scattering intensity with respect to pure /sup 4/He agrees semiquantitatively with experiments. It is caused by partly competing effects listed in the order of their importance: frequency changes induced by the altered structure of /sup 4/He in the mixture, coupling between /sup 4/He and /sup 3/He restoring forces, hybridization with /sup 3/He quasiparticle-quasihole excitations, and the contribution of S/sub 34/(k,..omega..). Decay into two-mode density excitations is investigated within a mode-coupling approximation.
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