Eur. Phys. J. D 18, 277-293 (2002)
https://doi.org/10.1140/epjd/e20020032

Properties of doubly excited states of H^- and He associated with the manifolds from N = 6 up to N = 25

¹ Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou Ave., Athens 11635, Greece
² Physics Department, National Technical University, Athens, Greece

Corresponding authors: ^a stheme@eie.gr - ^b ykomn@eie.gr - ^c can@eie.gr

Received: 10 September 2001
Revised: 12 November 2001
Published online: 15 March 2002

Abstract

This paper discusses theory and results on ¹P⁰ doubly excited states (DES) in He and in H^- of very high excitation, up to the N=25 manifold. Our calculations employed full configuration interaction (CI) with large hydrogenic basis sets and produced correlated wavefunctions for the four lowest roots at each hydrogenic manifold by excluding open channels and the small contribution of series belonging to lower thresholds. The suitability of the hydrogenic basis sets for such calculations is justified, apart from their practicality, by the fact that, by computing from them natural orbitals, the results were shown to be the same with those of earlier multiconfigurational Hartree-Fock (MCHF) calculations on low-lying DES. In total, 160 states were computed, most of them for the first time. Their energy spectrum should be of use to possible future photoabsorption experiments. For certain low-lying DES up to N=13, for which previous reliable results are available, comparison of the calculated energies shows good agreement. The correlated wavefunctions contain systematically chosen single and double excitations from each hydrogenic manifold of interest. From their analysis, we determined the “goodness" of different quantum numbers and the geometry (average angles and radii) as a function of excitation. For the Sinanolu-Herrick (K, T) classification scheme, whose basis is a restricted CI with hydrogenic functions and which has thus far been tested only on low-lying DES, we established that, whereas T remains a good index as energy increases, K does not. Consequently, a more flexible than K quantum number is needed in order to account for most of the additional correlation. This number, represented by , where N and K are not good numbers anymore, produces consistently a much higher degree of purity than the (K, T) scheme does, especially as N increases and as the relative significance of various virtual excitations due to electron correlation increases. Among the four states of each manifold, in all cases in H^- and in most cases in He, the three are of the intrashell type and one is of the intershell type with (F, T)=(0,0). The lowest intrashell states and the lowest intershell states exhibit a wide angle geometry tending to 180 as .