Positron thermalization and non-thermal trapping in metals

We have made a detailed study of the thermalization of positrons implanted into metals, using aluminium as an example. This is done by solving the Boltzmann equation for the positron momentum distribution in a homogeneous medium, allowing the positrons to scatter off electrons and phonons. We obtain both the time-dependent and steady-state solutions. The former gives the time evolution of the positron momentum distribution and the average energy and energy loss rate as functions of time after implantation. The full statistical description of the slowing-down process and the inclusion of both electron and phonon scattering mean that our energy loss rates are more accurate than earlier results, which are considerably lower than ours. The steady-state solution gives the momentum distribution from which positrons annihilate. Our formulation allows us to evaluate the influence of non-thermal trapping into defects, such as vacancies, on measurable parameters in positron experiments. The results show that, even if resonances are present in the momentum-dependent trapping rates, the differences between the results from the full calculation and for trapping from a thermal momentum distribution are exceedingly small. Thus we conclude that non-thermal trapping is not important for positron studies of vacancies in metals. (author)