Nonlinear Static Screening of Positive Charges in an Electron Gas: Contact Hartree Energy

2026/06/22 by M. Sherafati, G. Rodway-Gant, A. X. Chen · 1 voice
Physics and Astronomy · #cond-mat.other

paper · pdf

arxiv published 2026/06/22 · arxiv updated 2026/07/05

Abstract

Electron screening of positive charges in metals is most strongly nonlinear in the static near-field regime. We revisit the static screening of a proton embedded in a homogeneous electron gas, focusing on the induced electron density and the contact Hartree energy U_{\rm H}(0). Although evaluated at the impurity site, U_{\rm H}(0) is a nonlocal radial moment of the induced density in a formulation applicable to both linear-response and nonlinear density-functional descriptions. We compare Thomas--Fermi, random-phase-approximation, and local-field-corrected dielectric screening with nonlinear density-functional-theory benchmarks. The Estreicher--Meier local-density-approximation parametrization closely reproduces the contact Hartree energies from our direct LDA calculations and from Almbladh et al. [\hrefhttps://doi.org/10.1103/PhysRevB.14.2250Phys. Rev. B 14, 2250 (1976)], separating hydrogenic core and Friedel-oscillation contributions. The contact energy and on-top density are nearly insensitive to the choice between modern quantum-Monte-Carlo-consistent local-field factors. We then analyze Yukawa, hydrogenic, and Hulthén screened Coulomb potentials using a variable-phase formulation constrained by the Friedel sum rule. These model potentials provide a useful phase-shift representation of static screening, but a single Friedel constraint does not determine the nonlinear contact Hartree energy quantitatively. The results establish a one-center nonlinear screening benchmark for protons in jellium and a baseline for future two-center screening calculations in metallic environments.

Citations

• Generalized density functional theory framework for the non-linear density response of quantum many-body systems
• Solar fusion III: New data and theory for hydrogen-burning stars
• The IAEA electronic stopping power database: modernization, review, and analysis of the existing experimental data
• Trajectory sampling and finite-size effects in first-principles stopping power calculations
• On-Top Density in the Nonlinear Metallic Screening and its Implication on the Exchange-Correlation Energy Functional
• Low and intermediate energy stopping power of protons and antiprotons in canonical targets
• The uniform electron gas
• Emergence of a Kondo singlet state with the Kondo temperature well beyond 1,000K in the proton-embedded electron gas: Possible route to high-Tc superconductivity
• Nonlinear electromagnetic response of a uniform electron gas
• Power
• Second-order Born approximation for the scattering phase shifts: Application to the Friedel sum rule
• Second‐order response of a uniform three‐dimensional electron gas to a longitudinal electric field
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• Variational QMC study of a Hydrogen atom in jellium with comparison to LSDA and LSDA-SIC solutions
• A simple classical mapping of the spin-polarized quantum electron gas: distribution functions and local field corrections
• Classical Electrodynamics, 3rd ed.
• Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_xc(r) of the homogeneous electron gas
• Generalized Gradient Approximation Made Simple
• Path integrals in the theory of condensed helium
• Self-interaction correction to density-functional approximations for many-electron systems
• Explicit local exchange-correlation potentials
• Self-Consistent Equations Including Exchange and Correlation Effects
• Bound Eigenstates of the Static Screened Coulomb Potential
• Penetration of Protons, Alpha Particles, and Mesons

Discussions

• M. Sherafati, G. Rodway-Gant, A. X. Chen: Nonlinear Static Screening of Positive Charges in an Electron Gas: Contact Hartree Energy https://arxiv.org/abs/2606.23065 https://arxiv.org/pdf/2606.23065 ht [bsky, 0 points, 0 comments]

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