  We consider for a monatomic liquid the density and current autocorrelation
functions from the point of view of the Vibration-Transit (V-T) theory of
liquid dynamics. We also consider their Fourier transforms, one of which is
measured by X-ray and neutron scattering. In this description, the motion of
atoms in the liquid is divided into vibrations in a single characteristic
potential valley, called a random valley, and nearly-instantaneous transitions
called transits between valleys. The theory proposes a Hamiltonian for the
vibrational motion, to be corrected to take transits into account; this
Hamiltonian is used to calculate the autocorrelation functions, giving what we
call their vibrational contributions. We discuss the multimode expansions of
the autocorrelation functions, which provide a physically helpful picture of
the decay of fluctuations in terms of n-mode scattering processes; we also note
that the calculation and Fourier transform of the multimode series are
numerically problematic, as successive terms require larger sums and carry
higher powers of the temperature, which is a concern for the liquid whose
temperature is bounded from below by melt. We suggest that these problems are
avoided by directly computing the autocorrelation functions, for which we
provide straightforward formulas, and Fourier transforming them numerically.
