Most precise single redshift bound to Δα/α

Aims. Verification the theoretical prediction of oscillation of the fine-structure constant alpha (= e(2)/hc) over cosmic time requires high precision Delta alpha/alpha measurements at individual redshifts. In earlier studies the mean Delta alpha/alpha values averaged over wide redshift intervals were usually reported. This requirement can be met using the single ion differential a measurement (SIDAM) procedure. We apply SIDAM to the Fe II lines associated with the damped Ly alpha system observed at z(abs) = 1.15 in the spectrum of HE 0515 - 4414. Methods. The spectrum was obtained by means of the UV-Visual Echelle Spectrograph (UVES) at the ESO Very Large Telescope (VLT). Results. The weighted mean [Delta alpha/alpha] calculated using carefully selected 34 Fe II pairs {lambda 1608, X} (X = 2344, 2374, and 2586 angstrom) is [Delta a/alpha] = (- 0.07 +/- 0.84) x 10(-6) (1 sigma C. L.). The precision of this estimate improves by a factor of 2 the previous one reported for the same system. The obtained result represents an absolute improvement with respect to what has been done in the measurements of Delta alpha/alpha.