  A many-body theory approach developed by the authors [Phys. Rev. A 70, 032720
(2004)] is applied to positron bound states and annihilation rates in atomic
systems. Within the formalism, full account of virtual positronium (Ps)
formation is made by summing the electron-positron ladder diagram series, thus
enabling the theory to include all important many-body correlation effects in
the positron problem. Numerical calculations have been performed for positron
bound states with the hydrogen and halogen negative ions, also known as Ps
hydride and Ps halides. The Ps binding energies of 1.118, 2.718, 2.245, 1.873
and 1.393 eV and annihilation rates of 2.544, 2.482, 1.984, 1.913 and 1.809
ns$^{-1}$, have been obtained for PsH, PsF, PsCl, PsBr and PsI, respectively.
