A relativistic method for the calculation of positron binding to atoms is p
resented. The method combines a configuration-interaction treatment of the
valence electron and the positron, with a many-body perturbation-theory des
cription of their interaction with the atomic core. We apply this method to
positron binding by the copper atom and obtain a 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 1.2
18 eV, in good agreement with the experimental value of 1.236 eV. The probl
em 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. [S1050-2947(99)08311-0].