Positron-electron annihilation rates in an electron gas studied by variational Monte Carlo simulation

The studies of the electron-positron (e-p) interaction in condensed matter using the quantum Monte Carlo (QMC) simulations brought only fragmentary or incorrect results and have been suspended for a longer time. In the present work using the variational quantum Monte Carlo (VQMC) method correct and reasonable annihilation rates for a positron in an electron gas (EG) in a wide range of electron densities have been obtained. This has been achieved owing to an appropriate construction of the trial function which takes into account the 3-particle correlations (i.e. the dependence of the e-e interaction on the distance from the positron) and Friedel oscillations of the e-p correlation function. The annihilation rates have been found by “direct determination" of e-p contact densities on the basis of the variational trial function. We also have found the scheme for calculating of the momentum-dependent enhancement factors (MDEF), quantities not achievable within the MC method until now