Solid helium ground-state energy, pressure, compressibility and phase transition at high densities

Abstract

The ground-state energy, the pressure and the compressibility of solid helium is calculated by means of a modified Brueckner theory. A Bethe-Goldstone-type equation is solved to give a reaction matrix or an effective interaction in coordinate space, and the ground-state energy of fcc 3He and 4He is calculated. Also, the pressure and the compressibility are estimated from the dependence of the ground-state energy on density or molar volume. The calculations are done for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. The possibility of a phase transition into a metallic state at very high densities is also considered. The ground-state energy and pressure for metallic helium are calculated, and a phase transition is found to occur at a pressure of approximately 2 × 10 7 atm.