  In many-body systems the convolution approximation states that the 3-point
static structure function, $S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, can
approximately be "factorized" in terms of the 2-point counterpart,
$S^{(2)}(\textbf{k}_{1})$. We investigate the validity of this approximation in
3-dimensional strongly-coupled Yukawa liquids: the factorization is tested for
specific arrangements of the wave vectors $\textbf{k}_{1}$ and
$\textbf{k}_{2}$, with molecular dynamics simulations. With the increase of the
coupling parameter we find a breakdown of factorization, of which a notable
example is the appearance of negative values of
$S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, whereas the approximate factorized
form is restricted to positive values. These negative values -- based on the
quadratic Fluctuation-Dissipation Theorem -- imply that the quadratic part of
the density response of the system changes sign with wave number. Our
simulations that incorporate an external potential energy perturbation clearly
confirm this behavior.
