  We re-visit the competition between attractive and repulsive interparticle
forces in simple fluids and how this governs and connects the macroscopic phase
behavior and structural properties as manifest in pair correlation functions.
We focus on the asymptotic decay of the total correlation function $h(r)$ which
is, in turn, controlled by the form of the pair direct correlation function
$c(r)$. The decay of $r h(r)$ to zero can be either exponential (monotonic) if
attraction dominates repulsion and exponentially damped oscillatory otherwise.
The Fisher-Widom (FW) line separates the phase diagram into two regions
characterized by the two different types of asymptotic decay. We show that
there is a new and physically intuitive thermodynamic criterion which
approximates well the actual FW line. This new criterion defines a line where
the isothermal compressibility takes its ideal gas value
$\chi_T=\chi_T^\text{id}$. We test our hypothesis by considering four commonly
used models for simple fluids. In all cases the new criterion yields a line in
the phase diagram that is close to the actual FW line for the thermodynamic
state points that are most relevant. We also investigate (Widom) lines of
maximal correlation length, emphasizing the importance of distinguishing
between the true and Ornstein-Zernike correlation lengths
