The low-lying excited states in a system of coupled layers of electron
s in a gallium arsenide heterostructure are strongly affected by many-
body correlations between the electrons for densities as high as r(s)
= 5. For a layer spacing of less than 100 nm the function Im(chi)(q, o
mega) near q = 1.9k(F) has a large peak at small omega which is appare
ntly a soft-mode precursor to a charge density wave instability. This
new peak should be observable with present experimental techniques in
realistic samples. The linear gradient of the ''acoustic'' plasmon is
depressed so much by many-body effects that for r(s) = 5 it can become
degenerate with the single-particle excitation spectrum for all q.