The nodal structure of doubly-excited resonant states of helium

We examine the nodal structure of accurate helium wavefunctions calculated by direct diagonalization of the full six-dimensional problem. It is shown that for fixed interelectronic distance R (or hyperspherical radius R) the symmetric doubly-excited resonant states have well-defined λ, μ structure indicating a near separability in prolate spheroidal coordinates. For fixed λ, however, a clear mixing of R, μ nodes is demonstrated. This corresponds to a breakdown of the adiabatic approximation and can be understood in terms of the classical two-electron motion. (Author)