VLT/UVES constraints on the cosmological variability of the fine-structure constant

We propose a new methodology for probing the cosmological variability of a from pairs of Fe II lines (SIDAM, single ion differential a measurement) observed in individual exposures from a high resolution spectrograph. By this we avoid the influence of the spectral shifts due to (i) ionization inhomogeneities in the absorbers; and (ii) non-zero offsets between different exposures. Applied to the Fe II lines of the metal absorption line system at z(abs) = 1.839 in the spectrum of Q 1101-264 obtained by means of the UV-Visual Echelle Spectrograph (UVES) at the ESO Very Large Telescope (VLT), SIDAM provides Delta alpha/alpha = (2.4 +/- 3.8(stat)) x 10(-6). The Z(abs) = 1.15 Fe II system toward HE 0515-4414 has been re-analyzed by this method thus obtaining for the combined sample Delta alpha/alpha = (0.4 +/- 1.5(stat)) x 10(-6). These values are shifted with respect to the Keck/HIRES mean Delta alpha/alpha = (-5.7 +/- 1.1(stat)) x 10(-6) (Murphy et al. 2004) at very high confidence level (95%). The fundamental photon noise limitation in the Delta alpha/alpha measurement with the VLT/UVES is discussed to figure the prospects for future observations. It is suggested that with a spectrograph of similar to 10 times the UVES dispersion coupled to a 100 in class telescope the present Oklo level (Delta alpha/alpha >= 4.5 x 10(-8)) can be achieved along cosmological distances with differential measurements of Delta alpha/alpha.