Analytic Continuation in the Coupling Constant Method for the Dirac Equation

On the basis of the Dirac equation, the analytic continuation in the coupling constant method is employed to investigate the energies and widths of single-particle resonant in square-well, harmonic-oscillator, and Woods-Saxon potentials. The influences of the coupling constant interval and the Padé approximant order are analysed. It is shown that, by properly choosing the coupling constant interval and the Padé approximant order, stable and convergent energies and widths of single-particle resonant states can be obtained, which makes the application of the analytic continuation in the coupling constant for the relativistic mean field theory possible.