Hypernetted-chain indications of phase transitions in theHe4and charged-Bose systems

Optimal hypernetted-chain (HNC) methods provide a useful approach to the study of the liquid state of many-body systems. They give reasonable numerical results and yet many analytical manipulations may be made with them. Previously, the behavior of the energy functional in an infinitesimal region of the optimal liquid correlation function was studied. This eigenvalue analysis reliably characterized the droplet formation of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at the spinodal point and indicated the possibility of a solid phase at higher density. In this paper we examine ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and the charged-Bose gas for both infinitesimal and noninfinitesimal deviations from the liquid wave function. We find that considerable information on the location and nature of the liquid-solid phase transition may be obtained with very little effort from calculations on the liquid alone. Constrained HNC calculations of a solid phase using nonspherically symmetric correlation function confirm the association between the behavior of the energy surface near the liquid phase and the structure of the solid phase. The method is recommended for other systems; ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and the Coulomb gas are quite different, but it gives transitions in these systems.