Correlation Function in a Plasma at Zero Particle Separation

We derive the radial distribution functions at zero particle separation for like and unlike particles in a plasma. No account is taken of many-body (screening) effects, but the sum over Coulomb wave functions in the two-particle density matrix is evaluated exactly to give a convergent power series in the dimensionless parameter ${\gamma }^{\frac{1}{2}}$, where $\gamma =\frac{2\mu e^4}{{\hslash }^2\mathrm{kT}}$, and $\mu$ is the reduced mass of the two-particle system.