Metastable doubly-charged Rydberg molecules

H₃^2+ is a one-electron system with three positive nuclei and is known to be unstable in its electronic ground-state. We examine an analogous one-electron system composed of a ^87Rb Rydberg atom interacting with a pair of cations and predict the existence of metastable vibrationally-bound states of ^87Rb₃^2+. These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favourable scaling of the Rydberg atom's quadrupole moment with the principal quantum number n. Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of ^87Rb₃^2+ arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to n. We do not expect these states to exist below n=24 and for n 35, their lifetime is limited by tunnelling of the Rydberg electron. In contrast, at very large n the lifetime will be limited by tunnelling of the vibrational wavepacket. In between these limits, we expect a range of bound states at intermediate n for which both tunnelling rates are smaller than the radiative decay rate of the Rydberg state.