0 0.5 1 1.5 2 2.5 p / k$_{F}$ 0.2 0.4 0.6 0.8 1 1.2 ( p ) r$_{s}$  = 1 r$_{s}$  = 2 r$_{s}$  = 3 r$_{s}$  = 4 r$_{s}$  = 6 r$_{s}$  = 8 r$_{s}$  = 8 ; No extra r$_{s}$  = 2 ; Kahana r$_{s}$  = 3 ; Kahana r$_{s}$  = 4 ; Kahana r$_{s}$  = 2 ; Stach. r$_{s}$  = 4 ; Stach. r$_{s}$  = 6 ; Stach. Noninteracting 6 FIG. 2: (Color online) Annihilating-pair MDs ρ ( p ) for different densities. k F is the Fermi wave vector. The solid lines show the MDs calculated with the extra interaction included; the dotted line shows the MD calculated at r s = 8 without the extra interaction. Model functions have been fitted to the results obtained with N = 406 electrons at r s = 1, N = 246 electrons for 2 ≤ r s ≤ 7, and N = 162 electrons at r s = 8. MD data calculated by Kahana [18] and Stachowiak [19] using other approaches are also shown. for the decrease in the enhancement that we find at the Fermi edge. We find the exponent s to be of the order of r$_{s}$ over the range of densities we have studied. It is essential to include the extra interaction when calculating the MD: omitting it results in a dramatic increase in the enhancement at the Fermi edge and substantial transfer of weight beyond the Fermi edge, as shown in Fig. 2. The Kohn-Sham orbitals do not describe the electron-electron correlation. Such correlation effects (i) tend to oppose the enhancement at the Fermi edge, particularly at low densities, and (ii) introduce an algebraically decaying tail in the MD. The electron-positron PCF g ( r ) is proportional to the charge density in the frame in which the positron is stationary. However, the fact that we used a plane-wave basis set for our orbitals results in a significant finite-basis error near r = 0, because the Kimball cusp condition [20] is not satisfied. We therefore extrapolated the contact PCF to basis-set