Padé Approximants for Radial Distribution Functions of the Gaussian Model

Radial distribution functions $\mathrm{(g)}$ are computed for the Gaussian model of a fluid by approximating the density expansion with a Padé approximant $\mathrm{g(m,\; n)}$ . Several choices of $m$ and $n$ are studied by comparing these calculated $\mathrm{g\text{'}}\mathrm{s}$ with those previously obtained using the Percus–Yevick and hypernetted chain integral equations, a Monte Carlo method, and simple truncation of the density expansion. It is found that, if a few terms in the density expansion are known, the range of densities for which this information is useful may be extended by the proper choice of $m$ and $n$ in the Padé approximant. A form of $\mathrm{g(m,\; n)}$ is presented which approximates $g$ quite well for a large range of densities.