Level structure of deeply bound levels of the $c^3Σ_g^+$ state of $^{87}\text{Rb}_2$
We spectroscopically investigate the hyperfine, rotational and Zeeman structure of the vibrational levels $\text{v}'=0$, $7$, $13$ within the electronically excited $c^3Σ_g^+$ state of $^{87}\text{Rb}_2$ for magnetic fields of up to $1000\,\text{G}$. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a^3Σ_u^+$ potential. As a byproduct, we present optical two-photon transfer of weakly bound Feshbach molecules into $a^3Σ_u^+$, $\text{v}=0$ levels featuring different nuclear spin quantum numbers. A simple model reproduces well the molecular level structures of the $c^3Σ_g^+$ vibrational states and provides a consistent assignment of the measured resonance lines. Furthermore, the model can be used to predict the relative transition strengths of the lines. From fits to the data we extract for each vibrational level the rotational constant, the effective spin-spin interaction constant, as well as the Fermi contact parameter and (for the first time) the anisotropic hyperfine constant. In an alternative approach, we perform coupled-channel calculations where we fit the relevant potential energy curves, spin-orbit interactions and hyperfine functions. The calculations reproduce the measured hyperfine level term frequencies with an average uncertainty of $\pm9\:$MHz, similar as for the simple model. From these fits we obtain a section of the potential energy curve for the $c^3Σ_g^+$ state which can be used for predicting the level structure for the vibrational manifold $\text{v}'=0$ to $13$ of this electronic state.