Percus-Yevick and hypernetted-chain approximations

Abstract

Percus-Yevick and hypernetted-chain models connecting the structure factor $S\left(k\right)\mathrm{}$ with effective pair potential $\phi \mathrm{}\left(r\right)\mathrm{}$ have been studied in detail. Recent neutron-scattering data of Yarnell et al., for liquid argon at 85°K, have been employed to generate these potentials. Using 0.01 uncertainty in the experimental data, the uncertainty in the pair potentials has been computed. Having developed a general method of error propagation analysis, the effect of experimental errors in $S\left(k\right)\mathrm{}$ on Percus-Yevick and hypernetted-chain potentials is investigated and the resulting potentials are compared with Lennard-Jones and Barker, Fisher, and Watts potentials.