**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

This paper discusses theory and results on ^{1}P^{0} 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 .

PACS: 31.25.Jf – Electron correlation calculations for atoms and ions: excited states / 31.50.Df – Potential energy surfaces for excited electronic states / 31.15.Ar – Ab initio calculations / 32.80.Dz – Autoionization

*© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002*