Spectroscopic data, spin-orbit functions, and revised analysis of strong perturbative interactions for theA 1Σ+andb 3Πstates of RbCs

The current interest in producing ultracold RbCs molecules by optical excitation from weakly bound Feshbach resonances and stimulated decay to the absolute ground state requires detailed analyses of the intermediate excited states. In this study, we present two sets of experimental Fourier-transform spectroscopic data of the $A{ }^{1}{\ensuremath{\Sigma}}^{+}$-$b{ }^{3}\ensuremath{\Pi}$ complex. The $A$-$b$ mixed vibrational levels are the most likely candidates to be intermediates in the molecular formation. The more recent and more accurate data set is from mixed $A$-$b\ensuremath{\rightarrow}X$ transitions, while the second is derived in large part from $(4){ }^{1}{\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}A$-$b$ emission and extends to higher $A$-$b$ energy levels. From a detailed analysis of the spectroscopic data we obtain term values which allow one to construct potentials and spin-orbit functions. Vibrational numbering of the $A$ state has been raised by one quantum over a previous report [T. Bergeman et al., Phys. Rev. A 67, 050501 (2003)] while the numbering of the $b$ state is established with a considerable degree of certainty with help of data on the $^{85}\mathrm{Rb}$$^{133}\mathrm{Cs}$ and $^{87}\mathrm{Rb}$$^{133}\mathrm{Cs}$ isotopomers. In addition, we have performed calculations of spin-orbit functions by two distinct methods. The fitted spin-orbit coupling matrix element between the two ${\ensuremath{\Omega}}^{p}={0}^{+}$ states, $A{ }^{1}{\ensuremath{\Sigma}}^{+}$ and $b{ }^{3}{\ensuremath{\Pi}}_{0+}$, happens to agree rather well with the results from both of these methods, while for the diagonal $b{ }^{3}\ensuremath{\Pi}$ state spin-orbit function, the fitted function agrees fairly well with that obtained by the other method.