  The spectral problem of the Dirac equation in an external quadratic vector
potential is considered using the methods of the perturbation theory. The
problem is singular and the perturbation series is asymptotic, so that the
methods for dealing with divergent series must be used. Among these, the
Distributional Borel Sum appears to be the most well suited tool to give
answers and to describe the spectral properties of the system. A detailed
investigation is made in one and in three space dimensions with a central
potential. We present numerical results for the Dirac equation in one space
dimension: these are obtained by determining the perturbation expansion and
using the Pad\'e approximants for calculating the distributional Borel
transform. A complete agreement is found with previous non-perturbative results
obtained by the numerical solution of the singular boundary value problem and
the determination of the density of the states from the continuous spectrum.
