Positron binding to silver and gold atoms was studied using a fully ab init
io relativistic method, which combines the configuration-interaction method
with many-body perturbation theory. It was found that the silver atom form
s a bound state with a positron with binding energy 123 (+/-30%) meV, while
the gold atom cannot bind a positron. Our calculations reveal the importan
ce of the relativistic effects for positron binding to heavy atoms. The rol
e of these effects was studied by varying the value of the fine-structure c
onstant alpha. In the nonrelativistic limit, alpha=0, both systems e(+)Ag a
nd e(+)Au are bound with binding energies of about 200 meV for e(+)Ag and 2
20 meV for e(+)Au. Relativistic corrections for a negative ion are essentia
lly different from that for a positron interacting with an atom. Therefore
the calculation of electron affinities cannot serve as a test of the method
used for positron binding in the nonrelativistic case. However, it is stil
l a good test of the relativistic calculations. Our calculated electron aff
inities for silver (1.327 eV) and gold (2.307 eV) atoms are in very good ag
reement with corresponding experimental values (1.303 and 2.309 eV, respect
ively).