  An experimental study of the long range behavior of the ground state
X^1\Sigma^+_g of Sr_2 is performed by high resolution spectroscopy of
asymptotic vibrational levels and the use of available photoassociation data.
Ground state levels as high as v"=60 (outer turning point at 23 \AA and 0.1
cm^-1 below the asymptote) could be observed by Fourier-transform spectroscopy
of fluorescence progressions induced by single frequency laser excitation of
the v'=4, J'=9 rovibrational level of the state 2^1\Sigma^+_u. A precise value
of the scattering length for the isotopologue ^88Sr_2 is derived and
transferred to all other isotopic combinations by mass scaling with the given
potential. The derived potential together with already published information
about the state 2^1\Sigma^+_u directs to promising optical paths for producing
cold molecules in the electronic ground state from an ultracold ensemble of Sr
atoms.
