The Dispersion and Absorption of Helium

An investigation is made of the relative importance of singly-excited, doubly-excited, and continuous states in the dispersion and absorption spectrum of helium. The $f$-values of the lines due to singly-excited and doubly-excited states are calculated by using wave functions of a screening-constant type, the most important of them having been obtained by variational methods. The $f$-sum of the continuous spectrum is then obtained by difference, from the Kuhn-Reiche sum rule. It is shown that the role of the singly-excited states is moderate, of the doubly-excited states small, and of the continuous spectrum very large. A table is given of relative intensities in the principal series absorption spectrum. Incidentally, a variational calculation of a wave function for the doubly-excited state $\mathrm{}\left(2s\right)\mathrm{}\left(2p\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P$ places this level 302,000 ${\mathrm{cm}}^{-1\mathrm{}}$ above the limit of single ionization. The corresponding absorption line comes out about one-thirtieth as strong as the first absorption line of the principal series or about as strong as the fifth line of this series.