Collective excitations in simple metal systems can be successfully des
cribed in terms of a local one-body excitation operator Q, due to the
long-range nature of the Coulomb interaction. For the plasmon modes of
a simple metal slab, momentum expansions of Q are calculated using a
variational procedure equivalent to a restricted RPA calculation. The
dispersion relation and the density fluctuation for each mode are foun
d in the sudden approximation using the proper Q operator and the RPA
sum rule formalism. The contributions of the exchange and correlation
energy are estimated using a local density functional. The positive ba
ckground is described within a jellium model, while the ground-state e
lectronic density is approximated by a double step profile. The densit
y fluctuation of the plasmon modes above the plasma frequency form sta
nding waves across the slab. The spectra below the plasma frequency ar
e qualitatively different to those of local optics calculations due to
the appearance of two multipole plasmon modes which shift the origin
of the omega(+) plasmon down. The dependence of the results on the wid
th of the slab, the density of the simple metal and the surface diffus
eness is discussed. The response of the slab to a q-dependent external
excitation operator is analyzed. Throughout, the difference with to R
PA and TDLDA calculations is stressed. (C) 1997 Elsevier Science B.V.