Abstract
Verification of theoretical predictions of an oscillating behavior of the fine-structure constant, alpha, with cosmic time requires high precision measurements at individual redshifts, while in earlier studies the mean Delta alpha/alpha values averaged over wide redshift intervals were usually reported. This requirement can be met via the Single Ion Differential alpha Measurement (SIDAM) procedure. We apply SIDAM to the FeII lines associated with the damped Ly-alpha system observed at z=1.15 in the spectrum of HE0515-4414. The weighted mean calculated on base of carefully selected 34 FeII pairs is =(-0.07+/-0.84)10^{-6}. The precision of this estimate represents the absolute improvement with respect to what has been done in the measurements of Delta alpha/alpha.
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