The collinear helium atom: adiabatic potential curves and quasi-separable approximation in hyperspherical coordinates

Abstract

The collinear models of the helium atom, where the electrons reside on the opposite sides of the nucleus (eZe configuration) and on the same side (Zee configuration), are studied using the adiabatic approach in hyperspherical coordinates. Adiabatic potential curves are evaluated for both configurations and related to hyperspherical channels. The eigenenergies are calculated by applying the quasi-separable (single-channel) approximation and found to be in good agreement with those obtained using other methods. It is demonstrated that the widths of autoionizing states can be estimated by taking into account the coupling between different channels. The adiabatic potential curves and energy levels for the collinear atom are compared to those for the full three-dimensional (3D) model. It is shown that the S states of the 3D model with minimal and maximal angular excitations, as well as the corresponding adiabatic potential curves at large values of the hyperradius, can be related to the eZe and Zee collinear configurations, respectively. It is demonstrated that a set of curves of the 3D atom converging to the same ionization threshold is then confined in the area delimited by the pair of eZe/Zee curves also converging to this threshold. A class of anticrossings of the adiabatic potential curves in the 3D model, located along the eZe adiabatic curves at small values of the hyperradius, is observed and related to the unstable character of the classical configuration corresponding to the eZe collinear model in this domain.