Context :

Aims : We present a detailed analysis of a very high resolution ( R \approx 112 , 000 ) spectrum of the quasar HE 0515 - 4414 obtained using the High Accuracy Radial velocity Planet Searcher ( HARPS ) mounted on the ESO 3.6 m telescope at the La Silla observatory .
The main aim is to use HARPS spectrum of very high wavelength calibration accuracy ( better than 1 mÅ ) , to constrain the variation of \alpha = e ^ { 2 } / \hbar c and investigate any possible systematic inaccuracies in the wavelength calibration of the UV Echelle Spectrograph ( UVES ) mounted on the ESO Very Large Telescope ( VLT ) .

Methods : A cross-correlation analysis between the Th-Ar lamp spectra obtained with HARPS and UVES is carried out to detect any possible shift between the two spectra .
Absolute wavelength calibration accuracies , and how that translate to the uncertainties in \Delta \alpha / \alpha are computed using Gaussian fits for both lamp spectra .
The value of \Delta \alpha / \alpha at z _ { abs } = 1.1508 is obtained using Many Multiplet method , and simultaneous Voigt profile fits of HARPS and UVES spectra .

Results : We find the shift between the HARPS and UVES spectra has mean around zero with a dispersion of \sigma \simeq 1 mÅ .
This is shown to be well within the wavelength calibration accuracy of UVES ( i.e \sigma \simeq 4 mÅ ) .
We show that the uncertainties in the wavelength calibration induce an error of about , \Delta \alpha / \alpha ~ { } \leq 10 ^ { -6 } , in the determination of the variation of the fine-structure constant .
Thus , the results of non-evolving \Delta \alpha / \alpha reported in the literature based on UVES/VLT data should not be heavily influenced by problems related to wavelength calibration uncertainties .
Our higher resolution spectrum of the z _ { abs } = 1.1508 Damped Lyman- \alpha system toward HE 0515 - 4414 reveals more components compared to the UVES spectrum .
Using only Fe ii lines of z _ { abs } = 1.1508 system , we obtain \Delta \alpha / \alpha = { ( 0.05 \pm 0.24 ) \times 10 ^ { -5 } } .
This result is consistent with the earlier measurement for this system using the UVES spectrum alone .

Conclusions :