screenedCoulomb

ScreenedCoulomb refers to the modification of the bare Coulomb interaction between charges by the dielectric response of the surrounding medium or other charges. In many contexts, this screening weakens the long-range 1/r behavior and introduces a characteristic length scale over which the interaction is significant.

A common mathematical form is the Yukawa or Debye-screened potential: V(r) = (1/(4π ε0)) (q1 q2 / r) e^{−κ r}, where κ is the inverse screening length. In plasmas, κ is related to temperature and density (static Debye screening). In solids, κ encodes electronic screening and can be derived from the dielectric function or from carrier statistics. In reciprocal space, the screened interaction is often written as W(q, ω) = ε^{-1}(q, ω) v(q), with v(q) = e^2/(ε0 q^2) and ε the dielectric function. In the static, long-wavelength limit, W reduces to W(q) = ε^{-1}(q) v(q). The random phase approximation (RPA) is a common theoretical framework to compute ε.

Applications span plasma physics, electrolytes, and condensed matter. Screening determines how charges interact in ionic solutions, influences charge transport, and plays a key role in electronic structure calculations, such as the GW approximation, where the screened Coulomb interaction governs quasiparticle energies. It also affects exciton binding and band gaps in semiconductors and insulators.

Variants and limitations include nonlocal and dynamic screening, frequency dependence, and anisotropy. The simple isotropic Yukawa form is an approximation; real materials may require full dielectric functions and local-field corrections to capture screening accurately. See also dielectric function, Debye screening, Yukawa potential, Thomas-Fermi screening, and W in many-body theory.