Degrees of validity ofmodels for the description of doubly excited states of H-and He

Abstract

There are models for the description of doubly excited states(DES) of H- and He whose degrees of validity can be testedby comparing their results to those from theory based on thesolution of the Schrödinger equation with the fullHamiltonian. Such comparisons are meaningful and definitivewhen a reasonably wide range of data are available. We presentresults for the energies and the nature of the wavefunctions of the four lowest 1Po DES of H- and of He foreach hydrogenic manifold from N = 6 up to 25. These are usedto establish the degree and range of validity of thequantum number n2 introduced by Herrick and Kellman (Herrick D Rand Kellman M E 1980 Phys. Rev. A 21 418) in their triatomicmodel for qualitative description of the spectra of DES, aswell as of two classification schemes, as a function of levelof excitation and of type of state. According to the model, thenumber n2 is equal to the number of nodes of the density ρ(θ12) of the corresponding DES. We presentresults of calculations of ρ(θ12) usingcorrelated wavefunctions for the four lowest states in theN = 10 and 25 manifolds. These show for the first time forsuch highly excited states how the angle opens as excitationincreases. Furthermore, they indicate that n2 provides a valid picture even up to N = 25. The first of the twoclassification schemes examined here is the (K,T) scheme, introducedby Herrick and Sinanoglu (Herrick D R and Sinanoglu O1975 Phys. Rev. A 11 97). It is shown quantitatively that itdeteriorates as N increases and Z decreases. The secondscheme is the (F,T) scheme, introduced by Komninos et al (Komninos Y,Themelis S, Chrysos M and Nicolaides C A 1993 Int. J. Quantum Chem. Suppl. 27 399), where F = N-K-1 and N,K arenot good numbers anymore. It is shown that it constitutes aconsistently better representation, especially as the relative significance of electron correlation increases, as inthe high-lying DES of H-. For the lowest intrashell andintershell states of each N-manifold, for which thecalculation incorporates the effects of electron correlation tovery high accuracy, the (F,T) `purity' coefficient is very high, close to one.