From bound states to resonances: analytic continuation of the wave function

Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the Schroedinger equation with respect to the coupling strength is exploited to analytically continue the bound-state solutions into the positive-energy region by means of Pade’ approximants of the second kind. The method is here applied to single-particle wave functions of the ${}^{154}Sm$ and ${}^{131}Eu$ nuclei. A comparison of the results with the direct solution of the Schroedinger equation shows that the method can be confidently applied also in coupled-channel situations requiring high numerical accuracy.