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

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.Comment: 14 pages, 7 figuers, to apear in Physical Review

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

We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma\sigma'}(r)$ 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 Weizs\"{a}cker-Herring ideal kinetic energy functional to derive a zero-energy scattering Schr\"{o}dinger equation for $\sqrt{g_{\sigma\sigma'}(r)}$. 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 $g_{\sigma\sigma'}(r)$ 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.Comment: 13 pages, 8 figures, submitted to Phys. Rev.

Many-body aspects of positron annihilation in the electron gas

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003

SPATIAL CORRELATIONS IN SPIN-POLARIZED 3He LIQUID

On présente des calculs utilisant la méthode variationnelle FHNC appliqués à 3He orienté à basse température. La fonction d'essai est optimisée en résolvant une équation d'Euler-Lagrange dans l'approximation FHNC. On compare les résultats obtenus pour la fonction de structure du liquide et la distribution d'impulsion à une particule avec les mêmes quantités pour le liquide sans orientation de spin.Variational Fermi HNC calculations are performed for spin-polarized 3He liquid at zero temperature. The trial wave function is optimized by solving an Euler-Lagrange equation in the Fermi HNC approximation. Results for liquid structure function and one-particle momentum distribution are compared with the corresponding quantities of the spin-saturated liquid

CALCULATED PROPERTIES OF TWO-DIMENSIONAL SPIN-POLARIZED ATOMIC HYDROGEN

Des calculs variationnels HNC-Jastrow ont été effectués pour l'hydrogène polarisé à deux dimensions. Il en résulte des valeurs précises pour l'énergie du niveau fondamental, la fonction de distribution radiale, l'énergie d'échange moyenne et la distribution d'impulsions à faibles densités atomiquesOptimal HNC-Jastrow calculations have been carried out for gaseous spin-polarized hydrogen in two space dimensions. Accurate values for the ground state energy, radial distribution function, average exchange energy and momentum distribution are obtained at low atomic densities

GROUND STATE AND ELEMENTARY EXCITATIONS OF SPIN-ALIGNED ATOMIC HYDROGEN

Nous avons obtenus des solutions Jastrow-HNC optimales sans paramètres pour l'hydrogène atomique 1 spin polarisé. Nous avons calculé l'énergie fondamentale, la fonction de diffusion inélastique, la fonction de structure ainsi que la fraction condensée de Bose Einstein. Les excitations élémentaires et la stabilité du système ont été étudiées par des méthodes empruntées à la théorie de l'4He liquide.Non parametrized, optimal Jastrow-HNC solutions have been obtained for condensed spinaligned atomic hydrogen. Accurate values have been calculated for the energy, the pair correlation and the structure function as well as for the Bose condensate fraction. The elementary excitations and the stability of the system have been studied using methods adapted from the theory of liquid 4He