Singlet-Triplet Mixing in Excited Helium Atoms

Abstract

Experiments in collisional transfer of excitation, as well as theoretical considerations, have shown that singlet-triplet mixing occurs for $\mathrm{nF}$ states of helium. In this work the helium fine structure has been calculated using polarized orbitals to determine the amount of mixing and its dependence on the state ($\mathrm{nl}$) of the excited electron, and on the polarization of the orbital of the inner electron. Results are presented for $n=3\mathrm{}-10$ and $l=2\mathrm{}(n-1\mathrm{})\mathrm{}$. All $P$ states gave poor results because of a large exchange effect involving the polarization term in the wave function. However, the $3{}_{}{}^3{}_{}{}^{}D$ and $4{}_{}{}^3{}_{}{}^{}D$ levels showed improved agreement with experiment for the fine structure. The singlet-triplet mixing is essentially zero for $l=2\mathrm{}$, is significant for $l=3\mathrm{}$, and is virtually complete for $l\ge 4$. It is also found that the mixing decreases slightly with increasing $n$.