Autoionizing states of two-electron atoms

A modified Complex Quantum Defect Theory is implemented within Z-dependent perturbation theory to approximate the resonance position and width of autoionizing states of two-electron atoms below the N=2 threshold. This approach relies on the fact that in some instances screening of the nuclear charge is not complete, and an effective screening parameter, different from unity, is needed in order to better describe these states. For states where the screening is complete, the usual quantum defect method is employed. The quantum defect, μ, or effective screening, σ, are expressed in terms of the level of excitation, n, and of the first-order energy. In addition, use of a complex quantum defect theory makes it possible to relate the second- and third-order widths to each other. Therefore, an estimate of the width is obtained from knowledge of lowest-order contribution to the width. Two methods are developed for obtaining the lowest-order contribution to the width. In the first method, the second-order widths are calculated in closed form using the expression for the width in the Feshbach-projection method. In the second method, a combined complex rotation and Feshbach projection method is implemented within Z-dependent perturbation theory to obtain the lowest-order contribution to the shift and width. In the present paper, estimates of the resonance position and width for the lowest lying singlet and triplet autoionizing S- and P-states below the N=2 threshold are given. Comparisons to total values for the isoelectronic series are made, indicating that even for relatively low values of Z, these low-order results can yield useful estimates of the total resonance position and width. This approach is particularly useful for states with extremely narrow widths, as these are difficult to calculate accurately with other methods. Hence, the lowest-order estimates obtained here give useful information for such states, even for small values of Z