Electron-correlation effects in the positions and widths of two-electron autoionizing resonances

Abstract

Some recent numerical results for complex resonance eigenvalues of the helium isoelectronic sequence are analyzed in terms of $\frac{1}{Z}$ perturbation theory in order to study the physical factors governing resonance lifetimes. It is pointed out that principal trends in the asymptotic behavior of resonance positions and widths can be rationalized in terms of Hund's rules and familiar principles of bound-state electron-correlation theory, particularly in terms of the radial correlations and their third-order coupling to angular correlations. Such analysis shows, for example, why resonance lifetimes may often shorten with increasing $Z$, even though the $Z=\infty$ (hydrogenic) limit seems to imply an infinite lifetime. The analysis also suggests the possibility of highly correlated, two-electron "bound states" embedded in the continuum for certain critical noninteger values of nuclear charge $Z$.