Upper bounds for the ground-state energies of liquid and solid phases of metallic hydrogen and metallic deuterium have been calculated with variational methods and Monte Carlo techniques. At four densities ($r_s=0.8,1.2,1.36,\mathrm{and} 1.488$) crystalline phases are clearly preferred in the sense that the energy difference, when compared to the liquid, is in excess of the errors inherent in the numerical procedures. At a fifth density $r_s=1.6\mathrm{}$, the energy differences between solid and liquid phases are smaller than these errors.

• Received 18 May 1979

DOI:https://doi.org/10.1103/PhysRevB.21.2641