Convergence of the Two-Component Plasma Correlation Function

It has been suggested that the divergence of the two-component plasma correlation function at small interparticle distances may be removed by taking quantum corrections to the classical result in a certain manner. It is shown here that this approach is not possible in general. A completely quantum-mechanical treatment is given instead, and an explicit convergent expression for the radial distribution function at small $\mathcal{r}$ is obtained. Also discussed is the fact that there does not seem to exist any simple interpolation formula that bridges the classical and the quantum-mechanical results for $\mathcal{r}$ in the region of thermal de Broglie wavelengths.