Equation of state of a hard core fluid with a Yukawa tail

It appears that for the hard-core potential with Yukawa tail, -epsilon exp[-z(x-1)]/x, thermodynamic properties calculated through the variational theory are obtainable in almost fully analytic form with the use of hard-core fluid as the reference system. For one negative Yukawa tail minimization of the right-hand side of the variational inequality for the Helmholtz free energy gives diameters of hard-cores of both systems equal, independently of the temperature and the density. Therefore, the whole scheme of calculations is equivalent to adopting the first order Zwanzig 1/T expansion. Comparison with recent calculations of properties of Yukawa system with z=1.8 presented by Henderson et al. shows that our results for free energy are very good, mainly due to the smallness of the A2 term for this system. The promising features of the variational method for other Yukawa type potentials are outlined. (author)