The Complex Absorbing Potential (CAP) method is widely used to computeresonances in Quantum Chemistry, both for nonrelativistic and relativisticHamiltonians. In the semiclassical limit $\hbar \to 0$ we consider resonancesnear the real axis and we establish the CAP method rigorously for the perturbedDirac operator by proving that individual resonances are perturbed eigenvaluesof the nonselfadjoint CAP Hamiltonian, and vice versa. The proofs are based onpseudodifferential operator theory and microlocal analysis.
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