Extensions of the complex-coordinate method to the study of resonances in many-electron systems

Abstract

Difficulties in the straightfoward application of the complex-coordinate method to the calculation of resonance states in many-electron systems are examined. For the case of shape resonances, it is shown that many of these difficulties can be avoided by using complex coordinates only after reduction of the system to an effective one-electron problem. Further simplifications are achieved by the use of an inner-projection technique to facilitate the computation of the complex Hamiltonian matrix elements. The method is first illustrated by application to a model-potential problem. Its suitability for studying many-electron problems is demonstrated by calculation of the position and width of a low-energy $^{2}P^{o}$ shape resonance in ${\mathrm{Be}}^{\ensuremath{-}}$. We discuss the modifications necessary to study core-excited (Feshbach) resonances.