On the relation between the compressibility and the static structure factor of a fluid with a state-dependent pair-potential

The compressibility equation of a fluid with an effective, state-dependent, pair-potential is derived. It is shown that the thermodynamic states for which the infinite wavelength limit of the static structure factor diverges are not consistent with the thermodynamic states for which the compressibility diverges whenever the effective potential is density-dependent. This result is in agreement with some recent numerical simulations. (C) 2003 American Institute of Physics.