8 values for the reasons discussed earlier. In summary we have used a modified one-component DFT code to calculate the relaxation energy, contact PCF, and annihilating-pair MD of a single positron in a HEG by working in the frame in which the positron is stationary. It is interesting to observe that the data required to parameterize a two-component exchange-correlation density functional can be obtained using one-component DFT calculations. Our results for the positron relaxation energies and annihilation rates are in broad agreement with earlier theoretical work based on many-body-theory results. The annihilating-pair MDs are particularly sensitive to the description of the electron-positron correlation. We have reported MDs for a wider range of densities than previous studies, and our calculations extend above the Fermi edge where we find an exponential decay of the MD with momentum. We acknowledge financial support from the Leverhulme Trust, Jesus College, Cambridge, and the UK Engineering and Physical Sciences Research Council (EPSRC). We thank P.J. Hasnip for assistance with the castep code. ∗ Current address: University College London, Gower Street, London WC1E 6BT, United Kingdom. [1] P. Hohenberg and W. Kohn, Phys. Rev. 136 , 864 (1964). [2] W. Kohn and L.J. Sham, Phys. Rev. 140 , 1133 (1965). [3] E.P. Gross, Nuovo Cimento 20 , 454 (1961). [4] L.P. Pitaevskii, Sov. Phys. JETP 13 , 451 (1961). [5] R. Krause-Rehberg and H.S. Leipner, Positron Annihilation in Semiconductors , Springer-Verlag (1999). [6] E. Boro´ nski and R.M. Nieminen, Phys. Rev. B 34 , 3820 (1986). [7] M.J. Puska and R.M. Nieminen, Rev. Mod. Phys. 66 , 841 (1994). [8] We use Hartree atomic units ( ℏ = | e | = m e = 4 πϵ 0 = 1) throughout. Electron densities are specified by the radius r s of the sphere that contains one electron on average in units of the Bohr radius. [9] C.H. Leung, M.J. Stott, and C.O. Almbladh, Phys. Lett. 57A , 26 (1976). [10] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.J. Probert, K. Refson, and M.C. Payne, Z. f¨ ur Krystallographie 220 , 567 (2005). [11] A.M. Frolov, Phys. Lett. A 342 , 430 (2005). [12] J. Arponen, J. Phys. C 11 , L739 (1978). [13] J. Arponen and E. Pajanne, Ann. Phys. 121 , 343 (1979). [14] L.J. Lantto, Phys. Rev. B 36 , 5160 (1987).