  The high frequency (instantaneous) shear modulus of three-dimensional Yukawa
systems is evaluated in a wide parameter range, from the very weakly coupled
gaseous state to the strongly coupled fluid at the crystallization point (Yukwa
melt). This allows us to quantify how shear rigidity develops with increasing
coupling and inter-particle correlations. The radial distribution functions
(RDFs) needed to calculate the excess shear modulus have been obtained from
extensive molecular dynamics (MD) simulations. MD results demonstrate that
fluid RDFs appear quasi-universal on the curves parallel to the melting line of
a Yukawa solid, in accordance with the isomorph theory of Roskilde-simple
systems. This quasi-universality, allows to simplify considerably calculations
of quantities involving integrals of the RDF (elastic moduli represent just one
relevant example). The calculated reduced shear modulus grows linearly with the
coupling parameter at weak coupling and approaches a quasi-constant asymptote
at strong coupling. The asymptotic value at strong coupling is in reasonably
good agreement with the existing theoretical approximation.
