Abstract
The limits of validity of the correlation-energy calculations in the regions of high density, low density, and actual metallic electron densities are discussed. Simple physical arguments are given which show that the high-density calculation of Gell-Mann and Brueckner is valid for while the low-density calculation of Wigner is valid for . For actual metallic densities it is shown that the contribution to the correlation energy from long-wavelength momentum transfers () may be accurately calculated in the random phase approximation. This contribution is calculated using the Bohm-Pines extended Hamiltonian, and is shown to be An identical result is obtained by a suitable expansion of the result of Gell-Mann and Brueckner; the validity of the Bohm-Pines neglect of subsidiary conditions in the calculation of the ground-state energy is thereby explicitly established. The contribution to the correlation energy from sufficiently high momentum transfers () will arise only from the interaction between electrons of antiparallel spin, and may be estimated using second-order perturbation theory. The contribution arising from intermediate momentum transfers () cannot be calculated analytically; the interpolation procedures for this domain proposed by Pines and Hubbard are shown to be nearly identical, and their accuracy is estimated as ∼15%. The result for the over-all correlation energy using the interpolation procedure of Pines is
- Received 24 February 1958
DOI:https://doi.org/10.1103/PhysRev.111.442
©1958 American Physical Society