Positron Annihilation in an Interacting Electron Gas

The effects of self-energy, as well as hole-particle interaction processes, on the angular correlation of gamma rays from positrons annihilating in an electron gas are studied. The two regions corresponding to emission of momentum smaller and greater than the Fermi momentum $p_F$ are discussed separately. In the first instance, it is found that self-energy effects, at least in the high-density limit, can be accounted for adequately simply by using the static approximation to the dynamic potential in the first-order ladder graph and ignoring altogether first-order self-energy corrections, provided, of course, a plasmon correction is made. In the second case it is shown that owing to dynamic polarization effects the tails occurring beyond $p_F$ are not at all comparable to those expected on a simple model where the positron force is ignored but correlations within the electron gas are treated properly. Hole-particle interaction graphs are not important since they occur in pairs which cancel each other.