Zero-Point Energy of an Electron Lattice

At very low densities an electron gas in a compensating uniform background of positive charge crystallizes into a bcc lattice for which the correlation energy per electron is (−1.792/rs) ry. At higher densities the first correction to this result arises from the zero-point energy of the electrons, which can be expanded in terms of the even moments of the frequency spectrum. We have computed the first five nonvanishing moments and have estimated the contribution to the zero-point energy from the remaining moments using their known asymptotic behavior. This procedure leads to the value (2.638/rs32) ry for the zero-point energy per electron. The low temperature specific heat per electron is found to be 56.21krs9/2· (kT)3 ry. The range of rs values for which these results should be valid is discussed on the basis of Lindemann's melting formula.