We use many-body perturbation theory to examine the interaction of pos
itrons with atoms. Our calculations predict positron s-type bound stat
es with binding energies 0.87, 0.23, 0.35, and 0.045 eV for Mg, Zn, Cd
, and Hg atoms, respectively. This binding is due to the positron-atom
polarization potential and virtual positronium formation. A simple cr
iterion is used to find other atoms that are likely to form bound stat
es with positrons. Among the most probable candidates are Ti, V, Cr, M
n, Zr, Nb, and Mo.