  We present spectroscopic measurements of seven vibrational levels $v=29-35$
of the $A(1^1\Sigma_u^+)$ excited state of Li$_2$ molecules by the
photoassociation of a degenerate Fermi gas of $^6$Li atoms. The absolute
uncertainty of our measurements is $\pm 0.00002$ cm$^{-1}$ ($\pm 600$ kHz) and
we use these new data to further refine an analytic potential for this state.
This work provides high accuracy photo-association resonance locations
essential for the eventual high resolution mapping of the $X(1^1\Sigma_g^+)$
state enabling further improvements to the s-wave scattering length
determination of Li and enabling the eventual creation of ultra-cold ground
state $^6$Li$_2$ molecules.
