Existence of Dirac resonances in the semi-classical limit

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials $V$ decaying like $\langle x \rangle ^{-\d}$ at infinity for some $\d >0$. By studying analytic singularities of a certain distribution related to $V$ and by combining two trace formulas, we prove that the perturbed Dirac operators possess resonances near $\sup V + 1$ and $\inf V -1$. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter.