  A simple 1-D relativistic model for a diatomic molecule with a double point
interaction potential is solved exactly in a constant electric field. The
Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density
function, allowing the correct normalization of continuum states. The boundary
conditions at the potential wells are evaluated using Colombeau's generalized
function theory along with charge conjugation invariance and general properties
of self-adjoint extensions for point-like interactions. The resulting spectral
density function exhibits resonances for quasibound states which move in the
complex energy plane as the model parameters are varied. It is observed that
for a monotonically increasing interatomic distance, the ground state resonance
can either go deeper into the negative continuum or can give rise to a sequence
of avoided crossings, depending on the strength of the potential wells. For
sufficiently low electric field strength or small interatomic distance, the
behavior of resonances is qualitatively similar to non-relativistic results.
