Hypernetted-chain approximation and quasiparticle energies in the (1/3 fractional quantized Hall effect

We review some details of the hypernetted-chain (HNC) approximation and its application to the Laughlin quasihole and quasielectron trial wave functions. We then develop a generalized HNC approximation for calculating the three-body correlation function g₁₁₂ of a classical plasma with two particle species. We apply this approximation to the Laughlin trial wave functions for the case {ν}=(1/3 and we estimate their energies. Our quasihole energy is in good agreement with past calculations, but our quasielectron energy is considerably higher than the accepted result. However, the approximation has the correct property that near a quasielectron, the electron pair correlation function vanishes as {}r₁{{{-}}r}₂² for {}r₁{{{-}}r}₂→0, where{r}₁$ and ${r}₂$ are electron positions. We show that an approximation analogous to Laughlin's pseudopotential approximation does not have this property.