The Effective Electron-Positron Potential in Jellium

One of the methods of determining theoretical annihilation characteristics in real metals is the approximation called Bloch modified ladder approach. In this approach a Bethe-Goldstone type equation is solved with an effective electron-positron potential obtained previously for jellium of the corresponding electron density. If one wishes to include the dependence on the local electron density of the e$\text{}^{+}$-e$\text{}^{-}$ effective potential in this formalism, it is necessary to know this potential for jellium, for metallic and above metallic densities. A review of different proposed e$\text{}^{+}$-e$\text{}^{-}$ potentials is presented and their correctness is evaluated from the point of view of their application in a Bethe-Goldstone type formalism which is the jellium analogue of Bloch modified ladder approach.