Non-adiabatic interaction effects in the spectra of ultralong-range Rydberg molecules

Ultralong-range Rydberg molecules (ULRM) are highly imbalanced bound systems formed via the low-energy scattering of a Rydberg electron with a ground-state atom. We investigate for $^{23}$Na the $d$-state and the energetically close-by trilobite state, exhibiting avoided crossings that lead to the breakdown of the adiabatic Born-Oppenheimer (BO) approximation. We develop a coupled-channel approach to explore the non-adiabatic interaction effects between these electronic states. The resulting spectrum exhibits stark differences in comparison to the BO spectra, such as the existence of above-threshold resonant states without any adiabatic counterparts, and a significant rearrangement of the spectral structure as well as the localization of the eigenstates. Our study motivates the use of $^{23}$Na ULRM, as a probe to explore vibronic interaction effects on exaggerated time and length scales.