Complex absorbing potential method for Dirac operators. Clusters of resonances

For both nonrelativistic and relativistic Hamiltonians, the complex absorbing potential (CAP) method has been applied extensively to calculate resonances in physics and chemistry. We study clusters of resonances for the perturbed Dirac operator near the real axis and, in the semiclassical limit, we establish the CAP method rigorously by showing that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa.