  The square-well fluid with hard-sphere diameters is studied within the
framework of Thermodynamic Geometry (TG). Coexistence and spinodal curves, as
well as the Widom line for ranges $\lambda^{*} = 1.25, 1.5, 2.0, 3.0$ for this
fluid are carefully studied using geometric methods. We are able to show that,
unlike coexistence curves, an exact result can be given along all the
thermodynamic space and for all potential ranges for spinodal curves.
Additionally, $R$-Widom line which is defined as the locus of extrema of the
curvature scalar is calculated as a function of the potential range, satisfying
near the critical point a kind of Clausius-Clapeyron equation. It is argued
that this relation could be a signature of certain type of characteristic phase
transition when crossing the boundary of the Widom line.
