Stability of three-unit-charge systems

We discuss the binding of three unit charges ${\mathit{q}}_{\mathit{i}}$=±1,∓1,∓1, with various constituent masses ${\mathit{m}}_{\mathit{i}}$. It is found that the most convenient variables are the normalized inverse masses defined by ${\mathrm{\alpha }}_{\mathit{i}}$=${\mathit{m}}_{\mathit{i}}^{\mathrm{-}1}$/(${\mathit{m}}_1^{\mathrm{-}1}$+${\mathit{m}}_2^{\mathrm{-}1}$+${\mathit{m}}_3^{\mathrm{-}1}$). The region where this three-body system is stable against dissociation into a neutral atom and an isolated charge is restricted to a narrow band that is characterized by small values of ‖${\mathrm{\alpha }}_2$-${\mathrm{\alpha }}_3$‖ and includes the well-known cases ${\mathrm{H}}_2^{+}$, ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ ${\mathit{e}}^{\mathrm{-}}$, and ${\mathrm{H}}^{\mathrm{-}}$. Some properties of this region of stability are presented. A method of proof of instability of ${\mathit{e}}^{\mathrm{-}}$ ${\mathit{pe}}^{+}$ is proposed.