Ground state of the strongly coupled, charged Bose gas

Using a Jastrow trial wave function and the hypernetted-chain integral equation, as well as Monte Carlo computations, to calculate energy expectation values, we have obtained a variational upper bound to the ground-state energy of the charged Bose gas over an extensive range of densities. In the high-density region our data are in good agreement with previous weak-coupling results. In the low-density (strong-coupling) limit, comparison of our fluid energies with the self-consistent phonon calculations of Glyde and Keech in the solid allow us to locate the Wigner transition for charged bosons at $r_s=139\mathrm{}$, where $r_s$ is the usual density parameter. We propose a simple and accurate equation of state based on our numerical data. Furthermore, we find that the Bose condensate fraction drops from a value of about 80% at $r_s=2\mathrm{}$, to a small but finite value (∼1%) at crystallization. Finally we use our results for the charged Bose gas to derive a heuristic equation of state of the electron gas in the strong-coupling limit ($r_s\gg 1$).