  The decay of Rydberg-atom-ion molecules (RAIMs) due to non-adiabatic
couplings between electronic potential energy surfaces is investigated. We
employ the Born-Huang representation and perform numerical simulations using a
Crank-Nicolson algorithm. The non-adiabatic lifetimes of rubidium RAIMs for the
lowest ten vibrational states, $\nu$, are computed for selected Rydberg
principal quantum numbers, $n$. The non-adiabatic lifetimes are found to
generally exceed the radiative Rydberg-atom lifetimes. We observe and explain a
trend of the lifetimes as a function of $\nu$ and $n$, and attribute
irregularities to quantum interference arising from a shallow potential well in
an inner potential surface. Our results will be useful for future spectroscopic
studies of RAIMs.
