The long wavelength limit of the liquid structure factor-a theory for the compressibility of liquid rare gases and metals

A theory for the isothermal compressibility of monatomic liquids at temperatures close to their triple points is presented. Assuming that the atoms interact through pairwise potentials, an exact relation for the direct correlation function of the fluid in terms of that of a reference fluid is derived. This is used to construct approximations for the long wavelength behaviour of the liquid structure factor a(q). By dividing the pairwise potential into a reference part, representing the short range repulsive forces, and a perturbation part, representing the long range 'attraction', the compressibility can be expressed in a mean field fashion in terms of an effective hard sphere contribution modified by the perturbation potential. The theory has been used to calculate the long wavelength limit a(q=0) in liquid Ne, Ar, Kr and CH ₄ and in a wide range of liquid metals.