  We present a radial velocity analysis of 20 solar neighborhood RR Lyrae and 3
Population II Cepheids variables. We obtained high-resolution, moderate-to-high
signal-to-noise ratio spectra for most stars and obtained spectra were covering
different pulsation phases for each star. To estimate the gamma
(center-of-mass) velocities of the program stars, we use two independent
methods. The first, `classic' method is based on RR Lyrae radial velocity curve
templates. The second method is based on the analysis of absorption line
profile asymmetry to determine both the pulsational and the gamma velocities.
This second method is based on the Least Squares Deconvolution (LSD) technique
applied to analyze the line asymmetry that occurs in the spectra. We obtain
measurements of the pulsation component of the radial velocity with an accuracy
of $\pm$ 3.5 km s$^{-1}$. The gamma velocity was determined with an accuracy
$\pm$ 10 km s$^{-1}$, even for those stars having a small number of spectra.
The main advantage of this method is the possibility to get the estimation of
gamma velocity even from one spectroscopic observation with uncertain pulsation
phase. A detailed investigation of the LSD profile asymmetry shows that the
projection factor $p$ varies as a function of the pulsation phase -- this is a
key parameter which converts observed spectral line radial velocity variations
into photospheric pulsation velocities. As a byproduct of our study, we present
41 densely-spaced synthetic grids of LSD profile bisectors that are based on
atmospheric models of RR Lyr covering all pulsation phases.
