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We develop the complex scaling method within the framework of the relativistic mean-field (RMF) model. With the self-consistent nuclear potentials from the RMF model, the complex scaling method is used to study single-particle resonant states in spherical nuclei. As examples, the energies and widths of low-lying neutron resonant states in 120 Sn are obtained. The results are compared with those from the real stabilization method, the scattering phase-shift method, and the analytic continuation in the coupling constant approach and satisfactory agreements are found.

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The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthén potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching conditions on the wavefunctions and the condition for the existence of transmission resonances are investigated. It is shown how the zero-reflection condition depends on the shape of the potential.

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