  A new relativistic method for calculation of positron binding to atoms is
presented. The method combines a configuration interaction treatment of the
valence electron and the positron with a many-body perturbation theory
description of their interaction with the atomic core. We apply this method to
positron binding by the copper atom and obtain the binding energy of 170 meV (+
- 10%). To check the accuracy of the method we use a similar approach to
calculate the negative copper ion. The calculated electron affinity is 1.218
eV, in good agreement with the experimental value of 1.236 eV. The problem of
convergence of positron-atom bound state calculations is investigated, and
means to improve it are discussed. The relativistic character of the method and
its satisfactory convergence make it a suitable tool for heavier atoms.
