  Pipelines of state-of-the-art spectrographs dedicated to planet detection
provide, for each exposure, series of Cross-Correlation Functions (CCFs) built
with a Binary Mask (BM), and the absolute radial velocity (RV) derived from
Gaussian fit of a weighted average CCF$_{tot}$ of the CCFs. Here we tested the
benefits of the application of the shift finding algorithm developed by Pierre
Connes directly to the total CCF$_{tot}$, comparing the resulting RV shifts
(DRVs) with the results of the Gaussian fits. In a second step, we investigated
how the individual DRV profiles along the velocity grid can be used as an easy
tool for detection of stellar line shape variations. We tested this new
algorithm on 1151 archived spectra of the K2.5 V star HD 40307 obtained with
ESO/ESPRESSO during a one-week campaign in 2018. Tests were performed based on
the comparison of DRVs with RVs from Gaussian fits. DRV profiles along the
velocity grid (DRV(i)) were scrutinized and compared with direct CCF$_{tot}$
ratios. The dispersion of residuals from a linear fit to RVs from 406 spectra
recorded within one night, was found to be $\sigma$=1.03 and 0.83 ms$^{-1}$ for
the Gaussian fit and the new algorithm respectively, a significant 20\%
improvement in accuracy. The two full one-week series obtained during the
campaign were also fitted with a 3-planet system Keplerian model. The residual
divergence between data and best-fit model is significantly smaller for the new
algorithm than for the Gaussian fit. This new algorithm is an easy tool
allowing to obtain additional diagnostics on the RV measurements in series of
exposures. It increases the accuracy of velocity variation determinations.
Also, departures from constancy of the DRVi profiles, as well as varying
differences between RVs from this new method and RVs from a Gaussian fit
provide diagnostics of line shape variations due to stellar activity.
