Theory of electron-positron interaction in simple metals: Application to lithium

In spite of many efforts devoted to this phenomenon, the electron-positron interaction in metals remains an unsolved problem. The development of the partial density amplitude approach to the electronic structure of simple metals offers the possibility to perform direct many-body calculations of the electron-positron interaction in these materials. A theory of this interaction based on the hypemetted-chain approach of Gondzik and Stachowiak is proposed and applied to lithium. It leads to a nonlinear three-dimensional integro-differential equation for the enhancement amplitude. This equation is solved for two cases in which it reduces to one dimension and also for a model. The relation between the results obtained in this way for the annihilation rate and the predictions of the local density approximation and other approaches is studied. The role of core electrons in the interaction is commented.