Rubidium dimers residing on the surface of He nanodroplets are doubly ionized by an intense femtosecond laser pulse leading to fragmentation into a pair of Rb^{+} ions. We show that the kinetic energy of the Rb^{+} fragment ions can be used to identify dimers formed in either the X ^{1}Σ_{g}^{+} ground state or in the lowest-lying triplet state, a ^{3}Σ_{u}^{+}. From the experiment, we estimate the abundance ratio of dimers in the a and X states as a function of the mean droplet size and find values between 4∶1 and 5∶1.
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