Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization

Abstract

We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma {\sigma }^{\prime }}(r)$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational principle and the von Weizsäcker-Herring ideal kinetic energy functional to derive a zero-energy scattering Schrödinger equation for $\sqrt{g_{\sigma {\sigma }^{\prime }}(r)}$. The solution of this equation is implemented within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock limit and is shown to satisfy an important set of sum rules. We present numerical results for the ground-state energy at selected values of the spin polarization and for $g_{\sigma {\sigma }^{\prime }}(r)$ in both a paramagnetic and a fully spin-polarized electron gas, in comparison with the available data from Quantum Monte Carlo studies over a wide range of electron density.

13 pages, 8 figures, submitted to Phys. Rev. B

References in corpus (2)

• Self-consistent scattering theory of the pair distribution function in charged Bose fluids
• Spin-density functional approach to thermodynamic and structural consistence in the charge and spin response of an electron gas

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