Electron liquid in collective description. III. Positron annihilation

Abstract We give a new, computationally effective, formulation for the problem of a charged impurity in an interacting electron gas. Our approach is based on the previously introduced formalism in which the collective excitations of the electron system are represented by interacting bosons. This enables one to include in a logical way the most important terms of the electron-electron interaction beyond the random-phase approximation (RPA). The numerical application to positron annihilation shows that the added non-RPA terms remove from the annihilation rate λ and the correlation energy E the divergences, which have troubled the earlier theories. The rate λ and the energy E are both continuous functions of the electron density and approach their correct limiting values for low densities. The numerical values of λ at physical densities correspond closely to the measured positron lifetimes in metals. A very noteworthy characteristic of the present theory is that the sum rule for the displaced charge is fulfilled typically to the accuracy of 1%. Numerical results are also given for the positron kinetic energy, the various components of the positron correlation energy, the pair-correlation function, and the electrostatic potential at various electron densities.