First measurement of Mg isotope abundances at high redshifts and
  accurate estimate of Delta alpha/alpha
  (Abridged) We use a high-resolution spectrum of the quasar HE0001-2340
observed with the UVES/VLT to measure Mg isotope abundances in the intervening
absorption-line systems at high redshifts. Line profiles are prepared
accounting for possible shifts between the individual exposures. Due to unique
composition of the selected systems - the presence of several transitions of
the same ion - we can test the local accuracy of the wavelength scale
calibration which is the main source of errors in the sub-pixel line position
measurements. In the system at zabs = 0.45 which is probably a fragment of the
outflow caused by SN Ia explosion of high-metallicity white dwarf(s) we
measured velocity shifts of MgII and MgI lines relative to other lines (FeI,
FeII, CaI, CaII): Delta V(MgII) = -0.44 +/- 0.05 km/s and Delta V(MgI) = -0.17
+/- 0.17$ km/s. This translates into the isotopic ratio 24Mg:25Mg:26Mg = (19
+/- 11):(22 +/- 13):(59 +/- 6) with a strong relative overabundance of heavy Mg
isotopes, (25Mg+26Mg)/24Mg = 4, as compared to the solar ratio 24Mg:25Mg:26Mg =
79:10:11, and (25Mg+26Mg)/24Mg = 0.3. At zabs = 1.58, we put a strong
constraint on a putative variation of alpha: Delta alpha/alpha = (-1.5 +/-
2.6)x10^{-6} which is one of the most stringent limits obtained from optical
spectra of QSOs. We reveal that the wavelength calibration in the range above
7500 A is subject to systematic wavelength-dependent drifts.
