  The aim of this work is to investigate to what extent the structural
properties of a short-range square-well (SW) fluid of range $\lambda$ at a
given packing fraction and reduced temperature can be represented by those of a
sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective
stickiness parameter $\tau$. Such an equivalence cannot hold for the radial
distribution function since this function has a delta singularity at contact in
the SHS case, while it has a jump discontinuity at $r=\lambda$ in the SW case.
Therefore, the equivalence is explored with the cavity function $y(r)$.
Optimization of the agreement between $y_{\sw}$ and $y_{\shs}$ to first order
in density suggests the choice for $\tau$. We have performed Monte Carlo (MC)
simulations of the SW fluid for $\lambda=1.05$, 1.02, and 1.01 at several
densities and temperatures $T^*$ such that $\tau=0.13$, 0.2, and 0.5. The
resulting cavity functions have been compared with MC data of SHS fluids
obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)].
Although, at given values of $\eta$ and $\tau$, some local discrepancies
between $y_{\sw}$ and $y_{\shs}$ exist (especially for $\lambda=1.05$), the SW
data converge smoothly toward the SHS values as $\lambda-1$ decreases. The
approximate mapping $y_{\sw}\to y_{\shs}$ is exploited to estimate the internal
energy and structure factor of the SW fluid from those of the SHS fluid. Taking
for $y_{\shs}$ the solution of the Percus--Yevick equation as well as the
rational-function approximation, the radial distribution function $g(r)$ of the
SW fluid is theoretically estimated and a good agreement with our MC
simulations is found. Finally, a similar study is carried out for short-range
SW fluid mixtures.
