  From a physical/dynamical system perspective, the potential well represents
the proportional mass of points that escape the neighbourhood of a given point.
In the last 20 years, several works have shown the importance of this quantity
to obtain precise approximations for several recurrence time distributions in
mixing stochastic processes and dynamical systems. Besides providing a review
of the different scaling factors used in the literature in recurrence times,
the present work contributes with two new results: (1) for $\phi$-mixing and
$\psi$-mixing processes, we give a new exponential approximation for hitting
and return times using the potential well as scaling parameter. The error terms
are explicit and sharp. (2) We analyse the uniform positivity of the potential
well.
