  Three core-softened families of potentials are checked for the presence of
density and diffusion anomalies. These potentials exhibit a repulsive core with
a softening region and at larger distances an attractive well. We found that
the region in the pressure-temperature phase diagram in which the anomalies are
present increases if the slope between the core-softened scale and the
attractive part of the potential decreases. The anomalous region also increases
if the range of the core-softened or of the attractive part of the potential
decreases. We also show that the presence of the density anomaly is consistent
with the non monotonic changes of the radial distribution function at each one
of the two scales when temperature and density are varied. Then, using this
anomalous behavior of the structure we show that the pressures and the
temperatures in which the radial distribution functions of the two length
scales are equal are identified with the Widom line.
