  The Complex Absorbing Potential (CAP) method is widely used to compute
resonances in Quantum Chemistry, both for nonrelativistic and relativistic
Hamiltonians. In the semiclassical limit $\hbar \to 0$ we consider resonances
near the real axis and we establish the CAP method rigorously for the perturbed
Dirac operator by proving that individual resonances are perturbed eigenvalues
of the nonselfadjoint CAP Hamiltonian, and vice versa. The proofs are based on
pseudodifferential operator theory and microlocal analysis.
