  We collected over 6000 high-resolution spectra of four dozen field RR Lyrae
(RRL) variables pulsating either in the fundamental (39 RRab) or in the first
overtone (9 RRc) mode. We measured radial velocities (RVs) of four strong
metallic and four Balmer lines along the entire pulsational cycle and derived
RV amplitudes with accuracies better than 1$-$2~\kmsec. The new amplitudes were
combined with literature data for 23~RRab and 3~RRc stars (total sample 74
RRLs) which allowed us to investigate the variation of the Bailey diagram
(photometric amplitude versus period) when moving from optical to mid-infrared
bands and to re-cast the Bailey diagram in terms of RV amplitudes. We found
that RV amplitudes for RRab are minimally affected by nonlinear phenomena
(shocks) and multi-periodicity (Blazhko effect). The RV slope ($\log
P$--A(V$_r$)) when compared with the visual slope ($\log P$--A($V$)) is
shallower and the dispersion, at fixed period, decreases by a factor of two. We
constructed homogeneous sets of Horizontal Branch evolutionary models and
nonlinear, convective pulsation models of RRLs to constrain the impact of
evolutionary effects on their pulsation properties. Evolution causes, on the
Bailey diagram based on RV amplitudes, a modest variation in pulsation period
and a large dispersion in amplitude. The broad dispersion in period of the
Bailey diagram is mainly caused by variation in RRL intrinsic parameters
(stellar mass, chemical composition). Empirical evidence indicates that RV
amplitudes are an optimal diagnostic for tracing the mean effective temperature
across the RRab instability strip.
