We have analysed a sample of 18 RR Lyrae stars ( 17 fundamental-mode — RRab — and one first overtone — RRc ) and three Population II Cepheids ( two BL Her stars and one W Vir star ) , for which high-resolution ( R \geq 30 000 ) , high signal-to-noise ( S/N \geq 30 ) spectra were obtained with either SARG at the Telescopio Nazionale Galileo ( La Palma , Spain ) or UVES at the ESO Very Large Telescope ( Paranal , Chile ) .
Archival data were also analyzed for a few stars , sampling \gtrsim 3 phases for each star .
We obtained atmospheric parameters ( T _ { eff } , log g , v _ { t } , and [ M/H ] ) and abundances of several iron-peak and \alpha -elements ( Fe , Cr , Ni , Mg , Ca , Si , and Ti ) for different pulsational phases , obtaining \langle [ \alpha /Fe ] \rangle =+0.31 \pm 0.19 dex over the entire sample covering –2.2 < [ Fe/H ] < –1.1 dex .
We find that silicon is indeed extremely sensitive to the phase , as reported by previous authors , and can not be reliably determined .
Apart from this , metallicities and abundance ratios are consistently determined , regardless of the phase , within 0.10–0.15 dex , although caution should be used in the range 0 \la \phi \la 0.15 .
Our results agree with literature determinations for both variable and non-variable field stars , obtained with very different methods , including low and high-resolution spectroscopy .
W Vir and BL Her stars , at least in the sampled phases , appear indistinguishable from RRab from the spectroscopic analysis point of view .
Our large sample , covering all pulsation phases , confirms that chemical abundances can be obtained for RR Lyrae with the classical EW-based technique and static model atmospheres , even rather close to the shock phases .