Intra-shell states of doubly excited atoms: diagonalization within a basis of symmetrically excited electrons

We calculate ¹S^e intra-shell wavefunctions of highly doubly excited two-electron atoms by diagonalizing the corresponding Hamiltonian in a Sturmian-type basis set representing symmetrically excited electrons. We take into account couplings between different intra-shell manifolds. The Z-dependence of the energies of all intra-shell states up to principal quantum numbers N=n=12 is examined. We investigate the nodal structure of the wavefunctions in the manifold N=8 for nuclear charges Z=2 and Z=10 to examine the validity of the Herrick classification scheme. It turns out that this scheme appropriately describes the structure of the lower states in the multiplets but it breaks down for the higher lying states. A comparison with wavefunctions from large-scale calculations reveals that the intra-shell diagonalization overestimates the radial independent-electron character of the wavefunctions. A semiclassical interpretation of the wavefunctions is given in terms of fundamental modes of the electron-pair motion.