be very sound for short-range potentials (for one-component SHS fluids this was confirmed by recent numerical simulations [@Miller03]), one has to conclude that, in the multi-component (polydisperse) case, the PY solution has a very limited practical usefulness, since its solution scheme cannot be fully accomplished. This is the reason why other possible routes have been attempted, as we discuss next.

Simplified closures: the class of $C_{n}$ approximations
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A ‘closure’ is a relationship, added to the OZ equation, between the direct correlation function $c_{ij}(r)$ and $h_{ij}(r)=g_{ij}(r)-1$ or $\gamma
_{ij}(r)=h_{ij}(r)-c_{ij}(r)$ ($g_{ij}(r)$ being the radial distribution function) [@Barrat03].

Let us go back to Baxter’s SW model given by Eq. (\[eq0\]) (i.e. *before* the ‘sticky limit’), and consider the following general class of ‘closures’ [@Gazzillo04] $$c_{ij}(r)=\left\{ 
\begin{array}{cc}
-1-\gamma _{ij}\left( r\right)  & 0<r<\sigma _{ij} \\ 
c_{ij}^{\mathrm{shrink}}(r) & \text{ \ \ \ \ }\sigma _{ij}\leq r\leq
R_{ij}\qquad  \\ 
0 & \text{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }r>R_{ij}\text{ .}\qquad 
\end{array}%
\right.   \label{eq6}$$The expression $c_{ij}(r)=-1-\gamma _{ij}\left( r\right) $ inside the core ($%
r<\sigma _{ij}$) is exact and dictated by the HS potential. The form outside the well ($r>R_{ij}$) may then be identified with the PY approximation, $$c_{ij}^{\mathrm{PY}}(r)=f_{ij}(r)\left[ 1+\gamma 