arXiv:1002.4748v1 [cond-mat.mes-hall] 25 Feb 2010 First-Principles Study of a Positron Immersed in an Electron Gas (Dated: July 24, 2018) N. D. Drummond, P. L´ opez R´ıos, C. J. Pickard, ∗ and R. J. Needs TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom PACS numbers: 78.70.Bj, 71.60.+z, 71.10.Ca, 71.15.Mb Calculations of the relaxation energy, contact pair-correlation function, and annihilating-pair momentum density for a single positron immersed in a homogeneous electron gas are presented. We achieve an accurate description of the electron-positron correlation effects by working in the reference frame in which the positron is stationary and using a mean-field approach based on single- component density functional theory. Our positron relaxation energies and annihilation rates are similar to those from the best existing many-body calculations. Our annihilating-pair momentum densities are significantly different from previous data, and include a “tail” beyond the Fermi edge. Quantum impurity problems are of widespread interest in condensed matter physics. Here we study a positron in a homogeneous electron gas (HEG) as an example of an impurity problem in which a particle of one species is immersed in a fluid of another species, and where quantum effects are important for both the host and impurity. Examples of other problems of this type are the Mahan exciton in semiconductor physics, in which a hole in the valence band interacts with an electron gas in the conduction band (or an electron interacts with a hole gas), and an impurity atom in a Bose-Einstein condensate. Our approach requires knowledge of the explicit interaction between the host and impurity particles and the availability of a reasonably accurate mean-field description of the host, such as the Kohn-Sham density functional theory (DFT) [1, 2] of electrons or the Gross-Pitaevskii equation [3, 4] for Bose- Einstein condensates. An important characteristic of our approach is the inclusion of nonadiabatic impurity-host effects. We have chosen to present results for the positron problem, firstly, because they can be compared with data in the literature to gauge their accuracy and, secondly, because nonadiabatic effects are expected to be important as the electron and positron are of equal mass. Applications of our method to other problems such as those mentioned above require only straightforward modifications. On entering condensed matter, a low-energy positron thermalizes rapidly and may be trapped by open-volume