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Effect of alpha variation on the vibrational spectrum of Sr_2

We consider the effect of $α$ variation on the vibrational spectrum of Sr$_2$ in the context of a planned experiment to test the stability of $μ\equiv m_e/m_p$ using optically trapped Sr$_2$ molecules [Zelevinsky et al., Phys. Rev. Lett. {\bf 100}, 043201; Kotochigova et al., Phys. Rev. A {\bf 79}, 012504]. We find the prospective experiment to be 3 to 4 times less sensitive to fractional variation in $α$ as it is to fractional variation in $μ$. Depending on the precision ultimately achieved by the experiment, this result may give justification for the neglect of $α$ variation or, alternatively, may call for its explicit consideration in the interpretation of experimental results.