Analysis of correlation effects in autoionizing doubly excited states of barium using Coulomb Green’s function

Abstract

Though one would expect that large-angular momentum doubly excited states exhibit weak electronic correlations, it is shown in this paper that a first-order perturbation theory ignoring such correlations may completely fail in predicting correct autoionization probabilities: quadrupolar transitions are poorly described by lowest-order perturbation theory, except for very large angular momenta. Inclusion of second-order dipole-dipole term considerably improves the accuracy of the method. This effect is computed using Coulomb Green's function in its analytical form, probably applied here for the first time to autoionization processes. Examples are given in barium for 5d j 5g [k] states (j = 3/2, 5/2) and for 5d 5/2 nl [k] states with l > 4.

The Coulomb Green's function and multiphoton calculations

“…Although extremely compact, this expression suffers from the drawback that the variables r and r are not separated, which can make the actual computation of matrix elements involving G l difficult. It has nevertheless been used by a number of authors, see Laplanche and Rachman (1975) and Laplanche et al (1976); a recent reference is Poirier (1997). Note also that formally similar expressions can be derived for the Green's function associated with more general potentials with an asymptotic Coulomb tail (Vetchinkin and Bachrach 1972).…”