  We study the Dirac equation in confining potentials with pure vector
coupling, proving the existence of metastable states with longer and longer
lifetimes as the non-relativistic limit is approached and eventually merging
with continuity into the Schr\"odinger bound states. We believe that the
existence of these states could be relevant in high energy model construction
and in understanding possible resonant scattering effects in systems like
Graphene. We present numerical results for the linear and the harmonic cases
and we show that the the density of the states of the continuous spectrum is
well described by a sum of Breit-Wigner lines. The width of the line with
lowest positive energy, as expected, reproduces very well the Schwinger pair
production rate for a linear potential: we thus suggest a different way of
obtaining informations on the pair production in unbounded, non uniform
electric fields, where very little is known.
