The theory of two-electron atoms: between ground state and complete fragmentation

Since the first attempts to calculate the helium ground state in the early days of Bohr-Sommerfeld quantization, two-electron atoms have posed a serie s of unexpected challenges to theoretical physics. Despite the seemingly si mple problem of three charged particles with known interactions, it took mo re than half a century after quantum mechanics was established to describe the spectra of two-electron atoms satisfactorily. The evolution of the unde rstanding of correlated two-electron dynamics and its importance for doubly excited resonance states is presented here, with an emphasis on the concep ts introduced. The authors begin by reviewing the historical development an d summarizing the progress in measuring the spectra of two-electron atoms a nd in calculating them by solving the corresponding Schrodinger equation nu merically. They devote the second part of the review to approximate quantum methods, in particular adiabatic and group-theoretical approaches. These m ethods explain and predict the striking regularities of two-electron resona nce spectra, including propensity rules for decay and dipole transitions of resonant states. This progress was made possible through the identificatio n of approximate dynamical symmetries leading to corresponding collective q uantum numbers for correlated electron-pair dynamics. The quantum numbers a re very different from the independent particle classification, suitable fo r low-lying states in atomic systems. The third section of the review descr ibes modern semiclassical concepts and their application to two-electron at oms. Simple interpretations of the approximate quantum numbers and propensi ty rules can be given in terms of a few key periodic orbits of the classica l three-body problem. This includes the puzzling existence of Rydberg serie s for electron-pair motion. Qualitative and quantitative semiclassical esti mates for doubly excited states are obtained for both regular and chaotic c lassical two-electron dynamics using modern semiclassical techniques. These techniques set the stage for a theoretical investigation of the regime of extreme excitation towards the three-body breakup threshold. Together with periodic orbit spectroscopy, they supply new tools for the analysis of comp lex experimental spectra.