Semiclassical formulation of term energies and electrostatic intervals in He I

A semiclassical core-polarization-penetration model has been used to parametrize energy-level and energy-interval data for He I. Various contributions to the energy of the form $〈\gamma r^{-s}〉$ with $s\le 10$ were tested in attempts to account for different types of polarizabilities, dynamical correlations, and relativistic and retardation effects, which are all exactly calculable for the hydrogenlike core. Penetration effects were simulated by replacing expectation values by time averages over classical Kepler orbits that penetrate a parametrized hollow shell of core charge. It was found that the best fits were obtained if only dipole, quadrupole, lowest-order dynamical correlations, and relativistic mass corrections to the gross energy were included, and that higher-order polarizabilities and retardation effects worsened the fit. The approach generally reproduces observed $J=L$ singlet-triplet averages to within experimental uncertainties for $n\ge 5$ and $l\ge 2$. Three free parameters each are necessary to describe the $D$ and $F$ Rydberg series, whereas the $l\ge 4$ series can be described with no free parameters. The model can be very precisely tested with the use of available microwave-optical resonance data for the $\Delta n=0\mathrm{} F-G-H-I$ intervals, for which the relativistic and polarization energies have been observed directly.