Relativistic extension of the complex scaling method

We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction, additional vector, scalar, and pseudo-scalar coupling to short-range potentials could also be included in the same representation. Using that, we are able to obtain highly accurate values for the relativistic bound states and resonance energies. A simple program code is developed to perform the calculation for a given charge, angular momentum and potential configuration. The resonance structure in the complex relativistic energy plane is also shown graphically. Illustrative examples are given and we verify that in the nonrelativistic limit one obtains known results. As an additional advantage of this tridiagonal representation, we use it to obtain a highly accurate evaluation of the relativistic bound states energies for the Woods-Saxon potential (as a model of nuclear interaction) with the nucleus treated as solid sphere of uniform charge distribution.