Short-range correlation in the uniform electron gas: Extended Overhauser model

Abstract

We use the two-electron wavefunctions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function g(r) for a uniform electron gas, finding the exact g(0) for this model and extending the results from g(0) to g(r). We find that the short-range (r < rs) part of this g(r) is in excellent agreement with Quantum Monte Carlo simulations for a wide range of electron densities. We are thus able to estimate the value of the second-order (r 2 ) coefficient of the small interelectronic-distance expansion of the pair-distribution function. The coefficients of the small-r expansion of the spin-resolved g σσ ′ (r) have density or rs dependences which we parametrize in a way that makes it easy to find their coupling-constant averages. Their spin-polarization or ζ dependences are estimated from a proposed spin scaling relation.

Calculation of pair correlations in a high-density electron gas: Constraints for effective interparticle potentials

“…The system is described by a single Slater determinant of momentum eigenstates, i.e., plane waves. In this noninteracting case one has, 5 in a partial-wave representation for the gemi-nals, the following expression for the so-called ideal ͓g 0 ͑r͔͒ pair distribution function:…”

“…The embedded-pair approximation [4][5][6][7][8][9][10][11][12] rests, basically, on the scattering aspects of correlated motions. Therefore, similarities and differences in comparison with well-known results obtained for the screening problem of a chargedimpurity are conceptually important.…”

“…3 The idea of pair-approximation to realize the important short-range correlation in the model system directly by using effective ͑screened͒ interactions in a two-body Schrödinger equation for the spatial part of two-electron wave functions ͑geminals͒ has attracted a considerable interest. [4][5][6][7][8][9][10][11][12] Based on the effective potential concept, and focusing on the important pair-correlation function g͑r͒, the description of the standard many-body system can be simplified by transferring a part of complexities from the total wave function to a model Hamiltonian. This intuitive treatment of complexities via effective potentials for particle-interaction is quite similar to the one used in nuclear physics.…”

Electron-electron interaction in a two-dimensional electron gas: Bound states at low densities

“…13,14 Moreover, this kind of channel could explain the recent finding of a bosonic contribution to the thermal conductivity of underdoped YBa 2 Cu 3 O x . 15 Recent success using the geminal representation for a correlated-pair state and different effective pair potentials [16][17][18][19][20] to calculate associated pair-correlation functions has motivated a further study on the possibility of pairing in 2D. As the onset of superconductivity is related to some form of increased order in the motion of the electrons, it is necessary, therefore, to take into account ways in which electrons interact with each other.…”

“…As the onset of superconductivity is related to some form of increased order in the motion of the electrons, it is necessary, therefore, to take into account ways in which electrons interact with each other. 21 Briefly, the motivating attempts [16][17][18][19][20] are based on properly weighted positive-energy scattering states ͑below the Fermi energy͒ needed to construct pair correlation functions. The success achieved suggests a similar attempt in the negativeenergy, bound-state region of the pair interaction.…”