Z-Dependent Perturbation Theory and Complex Rotation Method in Autoionizing States of Atoms

Abstract

A combined Complex Rotation and Feshbach Projection method is implemented within Z-dependent perturbation theory to obtain the lowest-order contribution to the widths of autoionizing states of two- and three-electron atoms. This approach relies on the fact that in the complex rotation method, it is the open-channel part of the wave function that produces the imaginary component of the energy. Calculation of this part of the wave function involves the solution of a simple one-electron differential equation which, in lowest-order, can be obtained to any desired level of accuracy. These results represent the limiting values of the width for high Z values in the non-relativistic approximation, and are particularly useful for states with extremely narrow widths, as these are difficult to calculate accurately with other methods.