Electron-Positron Interaction in Jellium: Optimization of the Perturbed Hypernetted-Chain Approach

H. Stachowiak and E. Boroński W. Trzebiatowski Institute for Low Temperature and Structure Research, Polish Academy of Sciences, P.O.Box 1410, 50-950 Wrocław 2, Poland

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Received: 5 06 2006;

The perturbed hypernetted-chain approach to electron-positron interaction in jellium consists in assuming the wave function of the system in the form of a Slater determinant built of single-electron functions presented as ψk(s)=w(s)φk(s). s is the distance between the electron and the positron. The function w(s) is obtained by solving the equation of Gondzik and Stachowiak. The function φk(s) is computed by applying a self-consistent Born approximation. The idea of the paper is to modify the function w(s) in such a way as to obtain from the Born approximation as precise results as possible. It is shown that the influence of such modifications on physical predictions is small. This shows how good is the perturbed hypernetted-chain approach. The annihilation rates obtained in such a way decrease somewhat, becoming closer to experimental expectations.

DOI: 10.12693/APhysPolA.110.709 PACS numbers: 71.60.+z, 78.70.Bj, 71.10.Ca