Observation of spin-dependent relativistic effects in ultra-long-range Cs$_{\mathrm{2}}$ Rydberg molecules*

Recent research reveals spin-dependent relativistic effects play a significant role in the structure of ultra-long-range Rydberg molecules formed by the scattering of an electron from a ground state atom. Spin-dependent relativistic effects lead to striking features in the spectra of these molecules, like mixing between singlet and triplet states. To give a more precise prediction of the spectra, spin-orbit coupling and hyperfine interactions have to be considered. These effects are particularly important for Cs because several prominent, low energy p-wave resonances exist in the electron-ground state atom scattering and cause avoided crossings to occur. We use a Hamiltonian that includes spin-dependent interactions between the Rydberg electron and ground state atoms, to reproduce experimentally measured Cs ultra-long-range Rydberg molecule spectra correlating to the 31D$+$6S, 32D$+$6S, 38D$+$6S and 39D$+$6S asymptotes. Good agreement is found between theory and experiment. New, interesting features in the spectra can be related to the corresponding spin-dependent relativistic effects.