Self-consistent solution of the Kahana equation for a positron in an electron gas

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Abstract
A self-consistent development of the Kahana formalism is presented. The merits of this approach in comparison with the traditional one consist of including the effect of electron-electron correlations and achieving full self-consistency between the potential used in the Bethe-Goldstone equation and the screening charge distribution around the positron, obtained from its solutions. In this way the well-known low-density divergence of the annihilation rate λ is removed. At low electron densities the latter approaches the averaged free-positronium value. The annihilation parameters obtained in this work are in reasonable agreement with experimental results.