The pair correlations down to r = 0 in a fully ionized dilute and homogeneous hydrogen plasma in equilibrium

The pair correlations in a fully ionized dilute and homogeneous hydrogen plasma in equilibrium are calculated down to r = 0 on the basis of the equilibrium hierarchy of statistical mechanics and the linear superposition approximation. Thereby the Coulomb potential between electron and proton is modified by a damped potential with finite value at r = 0 which is due to quantum corrections given by Hagenow and Koppe. The solution of the hierarchy equations is quite simple: For $\text{r > γ}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{l}{}_{\mathrm{D}}\text{(γ = 5 × plasma parameter, l}{}_{\mathrm{D}}\text{= Debye-length)}$ one obtains the well-known result by Debye and Hückel, for $\text{r < γ}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{l}{}_{\mathrm{D}}$ the pair distribution functions are simply given by the corresponding Boltzmann factors. The calculation of the energy of the system leads to the result that the nonideal part is coming from the Debye-Hückel part of the pair correlations only.