Analytic continuation of single-particle resonance energy and wave function in relativistic mean field theory

Abstract

Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant state $\ensuremath{\nu}1{g}_{9∕2}$ in $^{60}\mathrm{Ca}$ as an example, we examine the analyticity of the eigenvalue and eigenfunction for the Dirac equation with respect to the coupling constant by means of a Pad\'e approximant of the second kind. The RMF-ACCC approach is then applied to $^{122}\mathrm{Zr}$ and, for the first time, this approach is employed to investigate both the energies, widths, and wave functions for $l\ensuremath{\ne}0$ resonant states close to the continuum threshold. Predictions are also compared with corresponding results obtained from the scattering phase shift method.