Many Body Effects in the Electron Gas And Position Annihilation

Abstract

<p> A number of questions are examined concerning many body correlations in connection with electron gas at metallic densities (2 < = rs <= 5.7) and the annihilation of a positron in simple metals, by means of a technique involving the two particle correlation Green's function. Estimates are made of low temperature contributions to angular correlation data, which describe the momentum distribution of annihilating electron positron pairs, in the form of smearing at the sharp cutoff corresponding to the Fermi momentum from electron- and positron- photon interactions, and in the form of broad tails beyond the cutoff resulting from the high-momentum components introduced into the electron wave function by the presence of a periodic crystal lattice. </p> <p> Phonon effects are introduced into the perturbation expansion of the two particle Green's function describing an electron positron pair. A calculation of the lowest order phonon contribution seems to indicate that such effects do not explain the smearing at the Fermi momentum. </p> <p> A Green's function calculation of the first-order enhancement of the lattice tails, due to the positron-electron correlation, is made by introducing particle-lattice interactions explicitly in a model based on a simple metal such as sodium. It considers a weak potential and treats as zero the lattice components corresponding to other than nearest-neighbours points in reciprocal lattice space. The enhancement for rs =4, which is almost a constant, is very similar to that for the main part of angular correlation data. This indicates that, for simple metals at least, angular correlation data can be interpreted directly from a free-particle model. </p> <p> Short-range correlations among opposite-spin electrons are examined by field-theoretic techniques as a step to obtaining a fundamental understanding of the correlations among electrons at metallic densities. A calculation of the p.d.f. for opposite-spin electrons is positive over a wide range of metallic densities and seems to account for short-range correlations of the Coulomb hole through the multiple scattering of particle-particle ladders. </p>