Abstract
The authors describe a non-local positron-electron density functional theory and show how it can be used to find the correlation potential for a positron in inhomogeneous systems where non-local effects are important. The theory is applied to the image potential induced surface state at a metal surface. Here the image potential arises from interactions between the positron and its screening cloud, which become increasingly long ranged and non-local as the positron leaves the surface. They have tested the theory with calculations of the binding energy and lifetime of a positron at an aluminium surface which agree well with experimental values.