Ro-vibrational collective interpretation of supermultiplet classifications of intrashell levels of two-electron atoms

We investigate whether the intrashell portion of the double-excitation spectrum of the helium atom may be interpreted in terms of collective rotational and bending vibrational motion, analogous to the ro-vibrational motion of molecules. Earlier work by us had identified a few levels in each atomic shell as having a rotorlike spectrum cutoff at higher energies, analogous to the cutoff rotorlike spectra of some nuclei. In this paper we use the $I$ and $d$ supermultiplets of the preceding paper of this journal, to interpret the entire intrashell manifold for each principal quantum number $N$, as resembling cutoff rotational and bending vibrational levels of a highly nonrigid linear symmetric $\mathrm{XYX}$ "molecular" structure. We obtain a good qualitative fit of each intrashell spectrum using leadingorder ro-vibrational energy formulas from molecular spectroscopy including anharmonicity, centrifugal distortion, and rotation-vibration coupling. We interpret these effects for low-lying intrashell states of two-electron atoms, and find them to be consistent with an average equilibrium configuration ${\theta }_{12}=180\mathrm{}°$ for the interelectronic angle. Analysis of the time scales of the proposed rotational, bending, and other degrees of freedom suggests approximate separability. We also identify parts of the spectrum analogous to molecular $l$ doubling, and indicate a possible link between the related Coriolis force and a recently proposed mechanism for decay by autoionization. Certain aspects of our collective interpretation of the atomic supermultiplets are discussed which have close parallels in nuclear physics, including the Elliott model and the SU(6) interacting boson model for nuclear collective motion.