Relation between occupation in the first coordination shells and Widom line in core-softened potentials

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 pressure and the temperature at which the radial distribution function of one of the two length scales equals the radial distribution function of the other length scales identify the Widom line.