Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2

Abstract

We present self-consistent calculations of the spin-averaged pair distribution function $g(r)$ for a homogeneous electron gas in the paramagnetic state in both three and two dimensions, based on an extension of a model that was originally proposed by A. W. Overhauser [Can. J. Phys. {\bf 73}, 683 (1995)] and further evaluated by P. Gori-Giorgi and J. P. Perdew [Phys. Rev. B {\bf 64}, 155102 (2001)]. The model involves the solution of a two-electron scattering problem via an effective Coulombic potential, that we determine within a self-consistent Hartree approximation. We find numerical results for $g(r)$ that are in excellent agreement with Quantum Monte Carlo data at low and intermediate coupling strength $r_s$, extending up to $r_s\approx 10$ in dimensionality D=3. However, the Hartree approximation does not properly account for the emergence of a first-neighbor peak at stronger coupling, such as at $r_s=5$ in D=2, and has limited accuracy in regard to the spin-resolved components $g_{\uparrow \uparrow }(r)$ and $g_{\uparrow \downarrow }(r)$. We also report calculations of the electron-electron s-wave scattering length, to test an analytical expression proposed by Overhauser in D=3 and to present new results in D=2 at moderate coupling strength. Finally, we indicate how this approach can be extended to evaluate the pair distribution functions in inhomogeneous electron systems and hence to obtain improved exchange-correlation energy functionals.

14 pages, 7 figuers, to apear in Physical Review B

References in corpus (3)

• Correlation energy and spin polarization in the 2D electron gas
• Short-range correlation in the uniform electron gas: Extended Overhauser model
• Interplay between disorder and intersubband collective excitations in the two-dimensional electron gas

Cited by in corpus (20)

• Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities
• Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence
• Momentum distribution of the uniform electron gas: improved parametrization and exact limits of the cumulant expansion
• Simple model for the spherically- and system-averaged pair density: Results for two-electron atoms
• System-adapted correlation energy density functionals from effective pair interactions
• Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization
• Simple Physical Picture of the Overhauser Screened Electron-Electron Interaction
• Intracule densities in the strong-interaction limit of density functional theory
• Ground-state densities and pair correlation functions in parabolic quantum dots
• Conditional probability density functional theory
• The on-top pair-correlation density in the homogeneous electron liquid
• New sum rules relating the 1-body momentum distribution of the homogeneous electron gas to the Overhauser 2-body wave functions of its pair density
• Pair densities at contact in the quantum electron gas
• Low rank perturbations and the spectral statistics of pseudointegrable billiards
• Kohn-Sham calculations combined with an average pair-density functional theory
• 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
• Exchange and correlation as a functional of the local density of states
• Pair distribution function in a two-dimensional electron gas
• Self-consistent Overhauser model for the pair distribution function of an electron gas at finite temperature