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We present the first spectroscopic studies of the $C \ ^1\Sigma^+$ electronicstate and the $A \ ^1\Sigma^+$ - $b \ ^3\Pi_{0^+}$ complex in $^7$Li -$^{85}$Rb. Using resonantly-enhanced, two-photon ionization, we observed $v =7$, 9, 12, 13 and $26-44$ of the $C \ ^1\Sigma^+$ state. We augment the REMPIdata with a form of depletion spectra in regions of dense spectral lines. The$A \ ^1\Sigma^+$ - $b \ ^3\Pi_{0^+}$ complex was observed with depletionspectroscopy, depleting to vibrational levels $v=0 \rightarrow 29$ of the $A \^1\Sigma^+$ state and $v=8 \rightarrow 18$ of the $b \ ^3\Pi_{0^+}$ state. Forall three series, we determine the term energy and vibrational constants.Finally, we outline several possible future projects based on the datapresented here.

The $C \: ^1 \Sigma ^+$, $A \: ^1 \Sigma ^+$, and $b \: ^3 \Pi_{0^+}$ states of LiRb