Observation of many-body effects in positron annihilation in alkali metals

The momentum distribution of photon pairs from positrons annihilating in lithium, sodium, potassium, and rubidium has been measured over a wide temperature range. The results were analyzed to yield the momentum dependence of the enhancement factor, positron effective mass, and positron minimum energy in these metals. The annihilation rate at the Fermi momentum was found to be considerably higher than that at zero momentum. The magnitude of this momentum dependence of enhancement factor as well as its variation with the electron density are in good quantitative agreement with the many-body theoretical calculations. Assuming free-particle behavior, the positron effective mass has been determined to be approximately $1.8m$ in lithium and sodium, $2.1m$ in potassium, and $2.3m$ in rubidium. Using a more realistic momentum distribution for the positron, which includes the positron-phonon interaction, the effective mass observed for sodium would be about 1.4-1.6 in fair agreement with a calculation yielding 1.2. The thermalization of positrons was observed to be complete before annihilation down to—for example in $\frac{\mathrm{Na}-160m}{m^{*}}$ °K. Below this temperature positrons seem to annihilate with certain minimum effective temperatures or minimum energies. These results are compared with theoretical calculations of the thermalization time of positrons in metals.