One- and two-electron excitations of helium in the s-wave model

The energies of the bound states and energies and widths of autoionizing resonant states of helium are calculated within the s-wave model, where the individual orbital angular momenta of both electrons are zero. The energies of the bound 1sns states differ from the corresponding energies in real helium only via a small n-independent shift in the quantum defects, which amounts to =0.011 for singlet states and =0.004 for triplet states. The quantum defects of more than 50 bound and resonant states with singlet or triplet symmetry are reproduced by an empirical four-parameter formula to within an rms deviation of less than 0.016. The normalized widths of the autoionizing Nsns resonant states increase with the smaller quantum number N, and the widths of the singlet states tend to become larger than the separation of successive resonances in the Rydberg series for N8. Effects of interference of Rydberg series can be described in the framework of multichannel quantum-defect theory. In the 7sns singlet series of resonances, interference due to the 8s8s perturber inhibits autoionization by more than three powers of 10. Semiclassical quantization based on unstable periodic orbits reproduces the energies of states with equal or similar quantum numbers rather well in a standard application of the cycle-expansion technique and very well in an application using only three nonretracing periodic orbits.