Lowest-order contribution to the width and shift of autoionizing states of two-electron 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 width and shift of autoionizing states of two-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. Use of the complex rotation method here simultaneously yields the lowest-order contributions to both the width and shift. It also simplifies the calculation by making this wave function square-integrable while simultaneously rotating the interacting continuum away from the real energy axis, thereby eliminating the degeneracy in zeroth order between the doubly excited states and the adjacent continuum. In the present paper, the lowest-order contributions to the width and shift for the 50 lowest singlet and triplet autoionizing P states below the n=2 threshold are calculated. These results represent the limiting values of the width and shift for high Z in the nonrelativistic approximation. The dependence of these results on the level of excitation N is studied. Comparisons to total values for the isoelectronic series are made, indicating that even for relatively low values of Z, these lowest-order results can yield useful estimates of the total widths and shifts. 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.