Stark and Zeeman Effects on Neutral-Helium Lines

The effect of a static electromagnetic field on the $2P-\mathrm{nS}$ and $2S-\mathrm{nP}$ He I isolated lines is systematically investigated. Exact expressions are given for the shift of the allowed component, and the behavior of the corresponding transition probability under static perturbation is considered in detail. The usual hydrogenic approximations for the Stark constants are discussed with reference to the most recent values for the oscillator strengths available. They are found to be consistent, expecially for the $2{}_{}{}^1{}_{}{}^{}P-n{}_{}{}^1{}_{}{}^{}S$ and $2{}_{}{}^1{}_{}{}^{}S-n{}_{}{}^1{}_{}{}^{}P$ lines with $n\ge 3$, when accurate data are used for the unperturbed excitation energies. The shifts determined with either nondegenerate or degenerate perturbation theory are critically compared, and the greatest difference is found for the magnetic sublevels in the presence of crossed fields. The fourth-order Stark effect is also considered. Calculated shifts are compared with the existing experimental data, and attention is also given to the methods used in plasma spectroscopy for the evaluation of the static Stark effect.