2 defects such as vacancies, where the nuclear repulsion is weak. The positron lifetime is measured as the time interval between the detection of a photon emitted in the β + radioactive decay that produces the positron and the detection of the two 0.511 MeV photons emitted when the positron annihilates an opposite-spin electron [5]. The lifetime is characteristic of the defect at which the positron settles, and positron annihilation spectroscopy is an important, non- destructive technique for characterizing open-volume defects. Measuring the Doppler broadening of the annihilation radiation or the angular correlation between the two 0.511 MeV photons yields information about the momentum density of the electrons in the presence of the positron. Modeling is then required to extract information about the unperturbed system from the experimental data. The most widely used method for modeling positrons in real materials is two-component DFT [6], in which the interaction between the electrons and the positron is described by a functional of the densities of the electron and positron components. Within the local density approximation (LDA), this functional is obtained directly from the relaxation energy ΔΩ of a positron in a HEG, which is the difference between the energy of a HEG with and without a positron immersed in it. Equivalently, ΔΩ is the electron-positron correlation energy. Two-component DFT can lead to accurate electron and positron densities, but the DFT orbitals yield very poor annihilating-pair momentum densities (MDs) ρ ( p ) and electron-positron pair-correlation functions (PCFs) g ( r ) be- cause they do not include the full effects of the strong electron-positron correlation [6, 7]. The results can, however, be substantially improved by correcting the calculated PCFs and MDs using accurate data for a positron in a HEG [6, 7]. The effective electron density felt by the positron, and hence the annihilation rate, is proportional to the contact PCF between the positron and the electrons, g (0). The annihilation rate for a positron immersed in a paramagnetic HEG is [8] λ = 3 g (0) / (4 c $^{3}$r3 $_{s}$), where r$_{s}$ is the electron density parameter, and c is the speed of light in vacuo. If the electron and positron motions were uncorrelated then g (0) would be unity, but the strong Coulomb attraction leads to much larger values, particularly at low densities, where a bound state may be formed. Together, our results for ΔΩ, g (0), and ρ ( p ) permit the construction of a two-component DFT within the LDA for a positron in a HEG, which in turn will enable the calculation of the annihilation rates and MDs used to interpret the results of positron annihilation experiments. We follow the suggestion of Leung et al. [9] that it is useful to describe a positron in a HEG using the set of electron positions relative to the position of the positron, { x i } . Neglecting the center-of-mass motion, which is zero in the