Spectroscopic investigation of the $A$ and 3 $^{1}\Sigma ^{+}$ states of $^{39}$K$^{85}$Rb

We have explored the absorption spectra of ultracold $^{39}$K$^{85}$Rb molecules in the region 11,000-12,000 cm$^{-1}$ above the ground state dissociation limit, formed by radiative decay following photoassociation(PA) to either the 3(0$^{+})$ or the 3(0$^{-})$ state. Recently we have reported that molecules formed by using the 3(0$^{-})$ PA level are not excited to the $A$ and 3 $^{1}\Sigma ^{+}$ states, but rather the 1 $^{1}\Pi $, 2 $^{3}\Sigma ^{+}$, and $b \quad ^{3}\Pi $ states. However, we have observed high vibrational levels of these $^{1}\Sigma ^{+ }$states by using the 3(0$^{+})$ level for PA. The absence of the $^{1}\Sigma ^{+}$ states in the spectra from levels formed by the 3(0$^{-})$ PA level has been explained by considering Hund's case (c) selection rules and the transition dipole moment calculations by Kotochigova \textit{et al}.[1] between the upper excited $A$ $^{1}\Sigma ^{+}$(2(0$^{+}))$ state and the three $\Omega $ components at the ground state dissociation limit. Unexpectedly, many high vibrational levels(v$\prime $=26-52) of the 3 $^{1}\Sigma ^{+}$ state, with a small transition dipole moment from the 1(0$^{+})$ state[1], have also been observed. The observed energies of the v$\prime $=26-44 levels match well with those observed from molecular beam experiments. Thus we have fully analyzed the $^{39}$K$^{85}$Rb electronic states in the entire region 11,000-12,000 cm$^{-1}$ above the ground state dissociation limit. \\[4pt] [1]. S. Kotochigova, E. Tiesinga, and P. S. Julienne, Phys. Rev. A \textbf{68}, 022501 (2003). This work is supported by NSF and AFOSR.