Abstract
Abstract An efficient formulation for the problem of a charged light impurity in a homogeneous electron gas is presented. The approach is based on a parametric dielectric function obtained from the linearized Thomas-Fermi-von Weizsacker treatment of screening in an extended system. A nonperturbative constraint, provided by the cusp condition, is used to determine the value of the parameter. Analytic expressions for the static effective potential and screening electron density are given. The calculated annihilation rates are in impressive agreement with experiments.
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