Direct correlation function of the hard-sphere fluid
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Two analytic approximations for the direct correlation function of
a hard-sphere fluid are considered. The first one M. S. Ripoll
and C. F. Tejero, Mol. Phys. 85, 423 (1995) follows from
a generalization of the Percus-Yevick result in $d$ dimensions,
whereas the second one arises in the rational function
approximation method S. B. Yuste and A. Santos, Phys. Rev. A
43, 5418 (1991); M. Lopez de Haro, A. Santos, and S. B. Yuste,
J. Chem. Phys. 124, 236102 (2006). Both approximations require the
equation of state of the hard-sphere fluid as input. The results
derived after use of the Carnahan-Starling equation of state and
of the Pade 4,3 of van Rensburg and Sanchez in both approaches
are compared to the simulation data of R. D. Groot, J. P. van der
Eerden, and N. M. Faber, J. Chem. Phys. 87, 2263
(1987). The comparison shows that that the Ripoll-Tejero results
are rather accurate in the region inside the core, but inherit the
limitation of the Percus-Yevick theory for distances beyond the
hard-sphere diameter. On the other hand, the results of the
rational function approximation method are also accurate inside
the core and capture well the initial part of the tail beyond the
hard-sphere diameter, but fail to account for the subsequent
oscillations observed in the simulations. Other merits and limitations
of the two approaches will be pointed out.