The bound-state spectra of the positronium hydrides ${}_{}{}^{\mathrm{\infty }}{}_{}{}^{}\mathrm{HPs}$, TPs, DPs, ${}_{}{}^1{}_{}{}^{}\mathrm{HPs}$, and MuPs are considered. The properties of the bound ground S states (L=0) in these systems and the ${\mathrm{Ps}}_2$ molecule have been determined by extensive variational calculations. The hyperfine structure of these states is also investigated. The positron annihilation rates have been evaluated for the positronium hydrides, the ${\mathrm{Ps}}_2$ molecule, and the ${\mathrm{Ps}}^{\mathrm{-}}$ ion and compared. The positron annihilation rates ${\mathrm{\Gamma }}_{\mathrm{n}\gamma }$ (where n⩾2) in the positronium hydrides are significantly closer to those in the ${\mathrm{Ps}}^{\mathrm{-}}$ ion (the three-body system) than in the ${\mathrm{Ps}}_2$ molecule.

DOI:https://doi.org/10.1103/PhysRevA.55.2662